Play and pedagogy essay

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All rights reserved. Resume Rabbit is caltech essay, a trademark of eDirect Publishing, Inc. Contents are protected by and pedagogy essay international copyright laws. Unauthorized copying or duplication in caltech books any form is strictly prohibited without prior written consent. 50StateJobs ActiveHire America's Job Exchange Beyond.com Career Exposure CareerBoard CareerBuilder CareerCast CareerLink CareerMatrix CareersInGovernment ChiliJobs FindJobz GovtJobs HotResumes JKLjobs Job.com Jobalized JobBank JobBoardNetwork Jobing JobServe JobsExcite JobsWeb Jobucopia Jobvertise LocalJobBoard NationalJobBank Resume Library Thingamajob US.jobs USAJobRepository USJobNetwork ZillionResumes ZipRecruiter. AccountantCareers AccountingClassifieds AccountingJobsToday iHireAccounting. AllDiversity Diversity Employers DiversityClassifieds DiversityInc DiversityWorking EmployDiversity IMDiversity WorkplaceDiversity. eKornFerry HeadHunter Heidrick Struggles MRInetwork. Bankjobs CareerBank FinancialJobsWeb FinancialPositions iHireFinance MoneyJobs.

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Resume Rabbit is and pedagogy essay, a trademark of management, eDirect Publishing, Inc. Contents are protected by essay international copyright laws. Unauthorized copying or duplication in masters any form is strictly prohibited without prior written consent. Who is Resume Rabbit and why should I use your service? Resume Rabbit provides a unique service that multiplies your chances of finding a great job. We post your Resume information on up to 85 different career sites. How do I know Resume Rabbit is a credible company?

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Copyright 2017 eDirectPublishing, Inc. All rights reserved. Play And Pedagogy? Resume Rabbit is help, a trademark of eDirect Publishing, Inc. Play? Contents are protected by indian banks international copyright laws. And Pedagogy? Unauthorized copying or duplication in any form is strictly prohibited without prior written consent. I signed up with Resume Rabbit two months ago, and today I accepted a position with a company that is located less than 2 miles from my home. My resume got into my new employers hands as a direct result of reasoning essay writing, one the play and pedagogy essay career site postings performed by your great service. I just joined 10 minutes ago and best and worst essays, my resume has been posted to numerous job sites - most of which I had no idea existed! Thank you very much! What is your 'time' worth?

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That was fast and easy. There are so many job sites out dissertation help usa, there it would have taken weeks. Sr. Sales Representative. Resume Rabbit is a fabulous user friendly site. with real people behind the scenes who send real responses to inquires. Development Resource Coordinator. Copyright 2017 eDirectPublishing, Inc. All rights reserved. Resume Rabbit is a trademark of play and pedagogy, eDirect Publishing, Inc. Contents are protected by international copyright laws. Unauthorized copying or duplication in doctoral any form is strictly prohibited without prior written consent.

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Use of play and pedagogy essay, any device, software or routine to interfere or attempt to interfere with the reasoning writing proper working of the play Site or services of Resume Rabbit, or taking any action which imposes an reasoning writing, unreasonable or disproportionately large load on the Site's infrastructure or the infrastructure of Resume Rabbit is expressly prohibited. Violations of these Security Rules may result in civil or criminal liability. And Pedagogy Essay? Resume Rabbit will investigate occurrences that may involve such violations and and worst, may involve, and cooperate with, law enforcement authorities in prosecuting users who are involved in such violations. You are responsible for maintaining the confidentiality of your information, username and password. You shall be responsible for play all uses of masters, your registration, whether or not authorized by play you. You agree to dissertation usa, immediately notify Resume Rabbit of any unauthorized use of your registration, information, username or password. By using the Site and Service you acknowledge that you have pro-actively hired Resume Rabbit to act on your behalf, as your Agent (hereafter Agency Relationship), to create accounts and and pedagogy essay, post your Personal Information on the Career Sites and caltech, web portals, subject to play essay, the terms, conditions, rules and regulations governing the management services provided by each of these sites. You hereby further convey to Resume Rabbit power of attorney to sign on your behalf (whether on paper or digitally) specifically indicating to each of these Career Sites that you have read, understood and agree to abide by their terms, conditions, rules and play essay, regulations. Click here to review the current list of Career Sites Resume Rabbit posts to, and to access links where their terms of service may be found.

You additionally acknowledge your understanding that Resume Rabbit has standardized its web based information gathering forms (hereafter Forms) in order to correct masters thesis, make easy the re-posting of and pedagogy, your Personal Information on the various web forms and in the various formats required by the various Career Sites. Dissertation? With this understanding you further authorize Resume Rabbit to make its best efforts to interpret some of your answers to questions provided on play, the Forms in order to re-post whatever information Resume Rabbit believes, in its sole discretion, are substantially similar answers amongst the available choices on the various Career Sites. By entering into best and worst essays this Agreement you're accepting full and total responsibility for the actions Resume Rabbit performs on your behalf and at essay your request, as if you had performed those actions yourself. Your further acknowledge and agree that you will take full responsibility and dissertation usa, are personally liable for any consequences arising from the use of the Site and Services and from this Agreement. Once your resume has been posted, Resume Rabbit will provide you access to a Resume Posting Service Center where you can access your Real-Time Posting Report and your web-based Job Mail. This access is available for one year from the date you sign up with the play and pedagogy service. Once the year has expired you will no longer be able to view your Real-Time Posting Report or your Job Mail.

If you select Keep My Identity Confidential during an best, Online Order Interaction with Resume Rabbit, Resume Rabbit will select the confidentiality option on the Career Sites offering that feature. For sites that do not offer a confidentiality feature, Resume Rabbit will replace your personally identifiable information as follows: First Name Last Name are replaced with Confidential User Street Address is replaced with Address Withheld Phone Number is replaced with A/C-555-1212 Most Recent Company is replaced with Confidential. Additionally, it is recommended you remove all unwanted personal information from the and pedagogy cut and paste version of thesis indian banks, your resume and play, cover letter, as these will be posted exactly as you provide them via the Forms. Job Agents are automated search engines at Career Sites that search for job openings matching criteria given them and then email leads of personal essay prompts, matching jobs to the email address provided to the Career Site. For Non-Paid Customers. Resume Rabbit may set up Job Agents, also known as Job Alerts, as a courtesy to customers who create accounts on Resume Rabbit but do not pay for Resume Posting Services. These Job Agents can be edited, modified or deleted at any time. For Paid Customers. Resume Rabbit has selected some Career Sites with Job Agent services and has set up Job Agents to automatically be part of the Resume Posting Service.

Resume Rabbit does not setup Job Agents at play every Career Site that has Job Agents or related services. Resume Rabbit uses its best efforts to match the information given us via its Forms to make sure that the Job Agents setup match the type of position(s) desired. Resume Rabbit makes no guarantees that the Job Agents setup will match job leads you desire. Once you are posted to essay, the Career Sites, you may receive email from the Career Sites when Job Agent matches are found. It is play essay, your responsibility to refine the job search criteria used by reasoning writing the Job Agents, if you desire to do so. After being posted to and pedagogy essay, the Career Sites, your Real-Time Resume Posting Report clearly shows which sites have Job Agents setup. Management Thesis? The Real-Time Resume Posting Report provides links for play essay you to login to the Career Sites where you can customize these Job Agents. For more information on this feature please review our Privacy Policy. For your privacy, security and and worst, protection, we create a unique job search email address for you on essay, our westpost.net email servers (your Managed Email Address).

This new email will be used as part of books essay, your contact information whenever an email address is required in the promotion of your resume. By using this Service you understand and consent to the replacement of play essay, any email address provided by you with your Managed Email Address for the purposes of promoting your resume, whether provided in the body of your resume or otherwise. Spam Filtering Job Mail Web-Based Email Service. As part of reasoning essay writing, your Service, you receive a web-based email account where you will receive any communications sent to your Managed Email Address. These communications to your Managed Email Address (Job Mail) are made available to you through the Job Mail section of our Service Center.

This is where you'll go to pick up job opportunities and other Managed Email. Play Essay? The Job Mail email service helps keep your job related email in one place and separate from best and worst, your personal email box. The Job Mail web interface allows you to read, write, reply and organize your job related email messages online. It has an online calendar for scheduling interviews and a simple address book to store job opportunity contacts. To access Job Mail, simply log into the Service Center and click on the Job Mail link. Emails sent to your Managed Email Address will automatically go through our Spam Filtering servers before being delivered to your Job Mail Inbox. Play Essay? While no Spam filtering technique is 100% foolproof, our service should eliminate most non job-search related email.

This keeps the email address you provide during registration private, secure and caltech books, eliminates Spam that would have otherwise been sent to you. Privacy of Your Communications. Resume Rabbit considers email transmitted via the Managed Email Services to be the private correspondence of the sender and recipient. Play? Resume Rabbit generally will not monitor, review or disclose the contents of your Managed Email correspondence, except: (a) as required by law; (b) if necessary to management indian, enforce this Agreement; (c) to respond to claims that such contents violate the essay rights of third parties; (d) as necessary for the maintenance, monitoring and quality assurance of the doctoral dissertation usa operations of the Site or Services; or (e) to protect the rights, or property of Resume Rabbit, its third party service providers, or others. Limitations on Use of Email Services. Managed Email and related Services are made available to you for play and pedagogy your personal use only and correct spelling thesis, solely for and pedagogy the purpose of personal prompts, facilitating job search related correspondence resulting from the use of the Resume Rabbit Resume Promotion Services. You hereby agree not to use Managed Email and and pedagogy essay, related Services for any other communications or emailing activities other than as outlined herein. You agree: (a) not to use the best and worst Services for illegal purposes; (b) not to play and pedagogy, interfere with or disrupt the Services or servers or networks connected to the Services; (c) to banks, comply with all requirements, procedures, policies, and regulations of play, networks connected to essay, the Services; and and pedagogy, (e) to comply with all applicable laws regarding the transmission of banks, technical data exported from the essay United States. You further agree not to upload, post, email, or otherwise transmit through the Services: (a) any unlawful, harassing, libelous, privacy invading, abusive, threatening, harmful, vulgar, obscene, indecent, tortuous, or otherwise objectionable material of books essay, any kind; (b) any material that violates the rights of another, including, but not limited to, the intellectual property rights of another; (c) any material that violates any applicable local, state, national, or international law or regulation; or (d) unsolicited or unauthorized advertisements, promotional materials, junk mail, spam, chain letters, or other forms of and pedagogy essay, solicitation. (e) any material that contains software viruses or any other computer code, files or programs designed to college application essay prompts, interrupt, destroy or limit the functionality of any computer software or hardware or telecommunications equipment; General Email Services Provisions.

Please be advised that there is a risk involved whenever downloading email and/or associated attachments to your computer. Resume Rabbit Email Services may not be able to detect or repair viruses, or control or foresee any potential damages of using this Service. Resume Rabbit assumes no responsibility for the deletion or failure to store, deliver or deliver in a timely manner email messages. Additionally, Resume Rabbit, in its sole discretion, and without prior notice may place limits on the amount of email a user may send, receive and/or store on or through its servers within in any period of time for any reason whatsoever. Any notice provided by Resume Rabbit to you in connection with such limit(s) shall not create any obligation to provide future notification regarding any change(s) to such limit(s). Resume Rabbit additionally retains the play and pedagogy essay right to personal prompts, deactivate any Managed Email Address account or related service, with or without prior notice, for and pedagogy essay any reason without any liability whatsoever and you hereby release Resume Rabbit from any such liability. You acknowledge that Resume Rabbit makes no guarantees or warrantees of any kind related to doctoral dissertation usa, Resume Rabbit Email Services, and that your election to utilize this Service is and pedagogy, completely at your own risk. Resume Rabbit shall not accept any responsibility whatsoever or be held liable for any damages caused by your decision to use these services. You further acknowledge and agree that you are solely responsible for all acts or omissions that occur under your Resume Rabbit account or password, including the content of your transmissions through Job Mail and thesis, related Services, and that Resume Rabbit may recover damages from you if you violate any of the terms of this Agreement. By using the Services you agree to defend, indemnify and hold harmless Resume Rabbit from and against any claims, actions or demands, including without limitation reasonable legal and play and pedagogy essay, accounting fees, alleging or resulting from this Agreement, your breach of this Agreement, your use of the Site and Services, the provision by management thesis indian you of any Content to the Site or other Career Sites, or the Agency Relationship. Resume Rabbit shall provide notice to you promptly of any such claim, suit, or proceeding and shall assist you at your expense in their defense.

You further agree to play and pedagogy essay, release Resume Rabbit from any claims, demands and damages (actual, consequential, direct and indirect) of thesis, every kind and nature, known and unknown, suspected and play, unsuspected, disclosed and undisclosed, arising out of or in any way connected with this Agreement or the Agency Relationship. If you are a California resident, under this Agreement you are additionally waiving your rights under California Civil Code 1542 which says, A general release does not extend to claims which the creditor does not know or suspect to exist in his favor at the time of executing the release, which if known by him must have materially affected his settlement with the debtor. IN NO EVENT SHALL RESUME RABBIT BE LIABLE FOR ANY DAMAGES WHATSOEVER (INCLUDING, WITHOUT LIMITATION, INCIDENTAL AND CONSEQUENTIAL DAMAGES, LOST PROFITS, INCOME, OR DAMAGES RESULTING FROM LOST DATA, LOST EMPLOYMENT OPPORTUNITIES, OR BUSINESS INTERRUPTION) RESULTING FROM THE USE OR ACCESS TO, OR THE INABILITY TO USE OR ACCESS, SITE AND THE CONTENT AND/OR ANY DOCUMENT, WHETHER BASED ON WARRANTY, CONTRACT, TORT, OR ANY OTHER LEGAL THEORY, AND WHETHER OR NOT RESUME RABBIT IS ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. BECAUSE SOME STATES OR JURISDICTIONS DO NOT ALLOW THE EXCLUSION OR LIMITATION OF LIABILITY FOR CONSEQUENTIAL OR INCIDENTAL DAMAGES, THE ABOVE LIMITATION MAY NOT APPLY TO YOU. IF THIS EXCLUSION OR LIMITATION OF LIABILITY IS HELD INAPPLICABLE OR UNENFORCEABLE FOR ANY REASON, THEN RESUME RABBIT'S MAXIMUM LIABILITY FOR ANY TYPE OF DAMAGES SHALL NOT EXCEED THE AMOUNT PAID BY YOU FOR THE SERVICES PROVIDED HEREUNDER. By entering into this Agreement you acknowledge that Resume Rabbit is simply acting as a conduit or messenger and that it makes no warranties of any kind relating to the Career Sites that Resume Rabbit posts you to. Resume Rabbit will simply pass through information provided by you and will not verify the best and worst accuracy of that information nor accept any responsibility for your activities or conduct.

Resume Rabbit is and pedagogy, not an employment agency or recruiting firm. Resume Rabbit makes no warrantees or guarantees about caltech, any customer's ability to play and pedagogy, procure employment. Resume Rabbit does not control any of the deductive essay Career Sites it posts to, nor does it control any portion of the hiring process related to its customer. Resume Rabbit therefore makes no representations or guarantees regarding the play effectiveness or timeliness of its Site, Services, Content, or its effectiveness in indian meeting the employment or any other objectives of its customers. Furthermore nothing on the Site shall be considered an play essay, endorsement, representation, assumption of responsibility or warranty with respect to any third party, whether in regards to their web site, products, technologies, services, business practices or otherwise. Additionally, Resume Rabbit makes no warranties of any kind related to its standardization and interpretation of the doctoral dissertation usa information gathered in its Forms in order to provide information to Career Sites. Play And Pedagogy Essay? You acknowledge and agree that accuracy of your Personal Information on Career Sites is college application essay prompts, your sole responsibility, and play and pedagogy essay, that Resume Rabbit is not responsible for correcting, changing or modifying any information provided to 3rd parties on your behalf. RESUME RABBIT DOES NOT WARRANT THAT ITS SITE OR SERVICES WILL OPERATE ERROR-FREE OR THAT THE SITE OR ITS SERVERS ARE FREE OF COMPUTER VIRUSES OR OTHER HARMFUL MECHANISMS. IF YOUR USE OF THE SITE OR THE CONTENT RESULTS IN THE NEED FOR SERVICING OR REPLACING EQUIPMENT OR DATA, RESUME RABBIT IS NOT RESPONSIBLE FOR THOSE COSTS. YOU ASSUME FULL RESPONSIBILITY AND RISK FOR USE OF THIS SITE AND THE INTERNET IN GENERAL.

THE SITE AND CONTENT ARE PROVIDED ON AN AS IS BASIS WITHOUT ANY WARRANTIES OF ANY KIND. College Personal Prompts? RESUME RABBIT, TO THE FULLEST EXTENT PERMITTED BY LAW, DISCLAIMS ALL WARRANTIES, WHETHER EXPRESS OR IMPLIED, INCLUDING THE WARRANTY OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. RESUME RABBIT MAKES NO WARRANTIES ABOUT THE ACCURACY, RELIABILITY, COMPLETENESS, OR TIMELINESS OF THE CONTENT, SERVICES, SOFTWARE, TEXT, GRAPHICS AND LINKS. By submitting your Personal Information to the Site you automatically grant Resume Rabbit the play and pedagogy royalty-free, perpetual, irrevocable, non-exclusive, transferable right and license to use, reproduce, modify, adapt, publish, distribute, translate, create derivative works from, distribute, perform and personal essay, display such Personal Information (in whole or part) worldwide or to incorporate it in other works in any form, media, or technology now known or later developed, without restriction or compensation. And Pedagogy Essay? In addition, you warrant that all so-called moral rights in spelling masters the Personal Information have been waived. International Access : eDirect Publishing, Inc. is based in play San Diego County, California. eDirect Publishing, Inc. makes no claims that the Content of its Site is appropriate or legal to be viewed by certain persons or in certain countries. Correct Masters Thesis? If you access the essay Site or Services from outside of the United States, you do so at college application personal essay your own risk and are responsible for compliance with the laws of your jurisdiction. Partial Validity : If any provision of this Agreement is essay, found to be invalid by dissertation usa any court having competent jurisdiction, the essay invalidity of such provision shall not affect the validity of the usa remaining provisions of essay, this Agreement, which shall remain in spelling masters full force and effect.

No waiver of any term of this Agreement shall be deemed a further or continuing waiver of play and pedagogy, such term or any other term. Equitable Relief : You understand and doctoral help usa, agree that due to the nature of play and pedagogy, This Agreement, in addition to money damages, eDirect Publishing, Inc. will be entitled to college personal essay, equitable relief upon a breach of play essay, this Agreement by you. Governing Law : This Agreement is governed by the laws of the State of California without respect to spelling masters, its conflict of laws principles. Play And Pedagogy? Jurisdiction for any claims arising under this Agreement shall lie exclusively with the state or federal courts in San Diego County, California. Headings : Headings used in this Agreement are provided for essay convenience only and shall not be used to construe meaning or intent. Entire Agreement : Except as expressly provided in a particular Legal Notice, Software License or other notices or Content published on the Site, these terms represent the entire binding Agreement between us, and our respective successors and assigns, and supersede any and all prior understanding, statements or representations, whether electronic, oral or written, regarding Resume Rabbit, the Site, or Services. Digital Admissibility : You hereby agree that a printed version of this Agreement and of any other notice given in play electronic form by Resume Rabbit or in the Site, which is based upon or relating to this Agreement, shall be admissible in judicial or administrative proceedings and subject to the same conditions as other agreements, business documents or records originally generated, entered into, signed or maintained in printed form. Certain areas of this Web Site and additional services provided are subject to additional terms of college, use. By using such areas or any part thereof, you agree to be bound by the additional terms of use applicable to such areas. Questions concerning our Terms and Conditions should be addressed by contacting us here or by play postal mail at: c/o eDirect Publishing Inc. 3451 Via Montebello, Unit 192-104.

Carlsbad, California 92009. Updated April 27, 2009, 8:40 AM PST. Copyright 2017 eDirectPublishing, Inc. All rights reserved. Best? Resume Rabbit is a trademark of eDirect Publishing, Inc. Contents are protected by international copyright laws. Unauthorized copying or duplication in any form is strictly prohibited without prior written consent. Our Beliefs About Privacy. eDirect Publishing, Inc. and and pedagogy, Resume Rabbit are firmly committed to protecting your privacy. We created this Privacy Statement so you'll have the information you need to make a confident and and worst essays, informed online buying decision. We value your trust and pledge to do everything we can to handle your personal, private or sensitive information carefully, responsibly and play essay, securely.

Below are the information gathering, use and dissemination practices for Resume Rabbit. Caltech Essay? To communicate any questions or concerns you may have regarding our privacy practices, please click here. Resume Rabbit's One-Stop Resume Posting service allows customers to be automatically posted to multiple 3rd party career web sites using a single online form. Posting Your Resume Confidentially. If you select Keep My Identity Confidential during our registration process, we will select the play and pedagogy essay confidentiality option on the career websites offering that feature. For Career Websites that do not offer a confidentiality feature, we will replace your personally identifiable information as follows: First Last Name are replaced with Confidential User Street Address is replaced with Address Withheld Phone Number is replaced with A/C-555-1212 Most Recent Company is replaced with Confidential.

Additionally, we recommend you remove all unwanted personal information from the caltech cut and paste version of your resume and cover letter, as it will be posted exactly as you provide it to us. NOTE: These practices may conflict with the Terms of play and pedagogy, Service listed on some of the 3rd party career websites where we post your resume. If you choose to use this feature you must agree to and worst essays, do so at your own risk. To visit and review the terms of essay, service on books, these sites, click here. Spam Prevention Email Forwarding. Posting an and pedagogy essay, email address on the Internet can sometimes give rise to banks, unwanted email (Spam). To alleviate this problem, Resume Rabbit provides its Spam Prevention Email Forwarding Service, as defined in play and pedagogy essay this section. Resume Rabbit creates a new job search email address (Posted Email Address) for you and uses it as part of its Resume Posting Service. Caltech Books Essay? Emails sent to the Posted Email Address will automatically go through our Spam detection servers before being forwarded to the email you give via our Forms (Personal Email Address). This greatly reduces the amount of play essay, Spam you would receive at your Personal Email Address. By using the spelling Spam Prevention Email Forwarding service, you give Resume Rabbit the permission and power to choose which emails sent to your Posted Email Address should be filtered and which should be forwarded to play and pedagogy, your Personal Email Address.

You give Resume Rabbit the permission to reasoning essay, alter the content of essay, 3rd party emails for any reason. You also give Resume Rabbit the permission to store copies of the filtered and forwarded email on its servers. Resume Rabbit does not receive or accept any authority over your usage of doctoral help usa, your Personal Email Address, and will not be held liable for anything related to and pedagogy, your Personal Email Address. The Spam Prevention service and services of its type are not 100% effective and writing, from time to time our product may misclassify Spam as legitimate mail and play essay, legitimate mail as Spam. Resume Rabbit makes no guarantees that all Spam will be blocked from spelling, being forwarded to and pedagogy, your email account. Resume Rabbit also makes no guarantee that all legitimate email will be delivered to your email account. If you suspect that legitimate mail has been blocked as Spam, please contact Customer Service. Please be advised that the Spam Prevention service may not be able to detect or repair all viruses. There is a risk involved whenever downloading email attachments to your computer and Resume Rabbit is not responsible for any damages caused by your decision to do so.

Resume Rabbit may place limits on the amount of spelling masters, email a user may receive in a day in order to protect the health of the company's network. The customer may contact Customer Service for exemptions to this clause. Handling of Information Gathered from Customers. On our web site you provide contact information, your desired job requirements, your relevant experience and other personal information (collectively Personal Information). Your Personal Information will be electronically reformatted and play and pedagogy, submitted to usa, various 3rd party career web sites. Resume Rabbit will not rent or sell any information gathered from a customer's use of our web site. Your personal information will not be shared with any 3rd parties for any reason other than what's described in this Privacy Statement or lawfully requested by federal or state authorities. Payment Information collected from play essay, customers on application essay prompts, the Resume Rabbit web site is securely transmitted for and pedagogy essay payment processing in real-time utilizing PayPal/VeriSign's Online Payment Services. Upon real-time response, credit card or checking account numbers are immediately deleted from the Resume Rabbit system for both authorized and declined transactions. PayPal/VeriSign, using its own secure connections and encryption technology, then transmits your payment information for validation and processing to college application, an authorized and reputable payment-processing clearinghouse. The rest of the associated payment processing is then handled like any other credit card or bank debit transaction.

To the best of and pedagogy essay, our knowledge all of the companies and essay, banking institutions involved in our payment processing do not retain, share, store or use personally identifiable information for any purpose outside of processing our payments. In rare instances due to real-time data transmission failures outside of essay, our control, we'll inform customers that their Payment Information has been captured for later processing. Then we'll immediately encrypt the information and transfer it to a private server on our internal network using a secure connection. Only our Security Administrator has the encryption key to deductive reasoning essay writing, unlock Payment Information for play essay processing. Once processed the essay information is play and pedagogy essay, immediately deleted from our servers. When a customer logs in to our website with their user name and password a record of and worst essays, that log in may be captured, time stamped and stored in our database along with records of play essay, certain activities or functions performed by usa the customer during that session. The log in information will help us identify the customer associated with those activities and will be used for both statistical analysis as well as customer service. Log in information may also be used to trigger an email to play, communicate with a customer regarding a procedure they may have started but not finished or to correct spelling thesis, inform them that something they requested is now available online.

Only those Resume Rabbit employees that have a legitimate business purpose for accessing and handling personal information obtained by us are given authorization to do so. Play And Pedagogy Essay? The unauthorized access or use of indian banks, such information by essay any Resume Rabbit employee is dissertation help usa, prohibited and constitutes grounds for disciplinary action. Additionally, our information management systems are configured in essay such a way as to block or inhibit employees from accessing information that they have no authority to deductive reasoning essay, access. Information Generated By Our Web site. A cookie is a small data file that gets sent by a web site to your web browser and and pedagogy essay, may then be stored on your computer.

Most web browsers allow users to choose to: never to deductive essay, accept cookies, automatically accept cookies, be notified prior to essay, accepting receipt of correct spelling masters, a cookie from a web site. Essay? A received cookie is usually stored in a directory that can be deleted from your computer at doctoral dissertation any time. Resume Rabbit uses cookies solely for the following reasons: To track a customers movement through our web site and and pedagogy, provide meaningful related information from page to page. To help aggregate all the information a customer provides on management thesis indian banks, several web page forms into a single set of customer information for submission to 3rd party web sites and to PayPal/VeriSign for payment processing. Play? To avoid the deductive reasoning necessity of a customer having to continually enter his or her username and password after having logged on to our web site.

The information contained in a cookie created by play and pedagogy essay the Resume Rabbit web site includes a randomly generated session ID and doctoral usa, is combined with a portion of the customers IP address for essay added security. Caltech? A cookies usefulness along with all related records on our web server expire within hours of having been used. While not associated with any particular web site visitor's contact information, we retain standard log information gathered by play our web server software package for an indefinite period of time. Caltech Books? This information will be used solely for statistical analysis. Standard log information includes:

The web page requested. The host name or IP address of the user making the play essay request. The date and time of the request. The web page address visited prior to essay, the request. The users browser type.

The users operating system. Protection of Your Payment Information. To protect your Payment Information online we use SSL encryption technology and offer Credit Card Fraud Protection. Resume Rabbit holds a digital certificate from play and pedagogy essay, VeriSign, a trusted third-party Certification Authority. At Resume Rabbit we pride ourselves on our use of caltech books, secure e-commerce servers complete with digital certificates, secure server ID's, SSL encryption technology, and SSL authentication. And Pedagogy? These technologies help you verify the reasoning essay company you're dealing with and transmit Payment Information securely. In the case of and pedagogy, unauthorized use of best and worst, your credit card, with proper notification to play and pedagogy essay, your issuing bank the Fair Credit Billing Act provides that your maximum liability is limited to $50.00 US. Best And Worst? In the event you're held liable for unauthorized credit card charges resulting from a Resume Rabbit secure web site transaction, we'll happily reimburse you for your liability up to $50.00 US with the submission of supporting documents. Resume Rabbit services may be advertised using a variety of methods.

Examples can include print, radio, television, banner, public relations and essay, email marketing. In order to correct, determine the effectiveness of different advertising vehicles, Resume Rabbit may create different website addresses for advertising vehicles in order to play and pedagogy essay, track and college application prompts, understand which vehicles are most effective. Play? This would allow us to identify by virtue of the advertisement responded to, certain information about a customer that the customer didn't necessarily provide, such as their reading, viewing, listening or web surfing interests and habits. Resume Rabbit may use this information internally to determine what other products or services our customers may be interested in as well as for statistical analysis of what type of customers or advertising vehicles are most effective. Resume Rabbit may from time to time conduct surveys that ask you for feedback on our products and services. Doctoral Dissertation? We use that information for market research, to play, improve our product offerings, identify desirable new products, and perform site and correct spelling masters thesis, service enhancements. Play Essay? We do not release information from individual survey responses outside Resume Rabbit without prior permission. We may occasionally share aggregated data with selected business partners. Some surveys may be performed by outside professional firms on our behalf to minimize bias. Help? Those professionals are bound by these same restrictions.

Resume Rabbit may from time to time send its customers a promotional email messages to market a service or activity. Essay? However, we'll only best and worst, send promotional email when we reasonably believe our customers would be interested in and pedagogy the subject matter. Nonetheless in every case we will provide clear and simple instructions on personal essay prompts, how to play, be removed from our mailing list. Example topics for email messages to customers include: information about college application personal, a new product or service, offers to try one of our existing services, invitations to beta test a new service or requests to essay, participate in a survey. eDirect Publishing Inc's mission and objectives are to and worst essays, create innovative high quality products and services that: offer specific solutions to people with particular needs, save our customers time and money and play and pedagogy essay, offer exceptional value at writing reasonable prices. eDirect Publishing's Inc. is and pedagogy essay, not in support of untargeted, unsolicited mass email marketing to help usa, people who'd most likely have no interest in our products.

However we do believe in targeted email marketing where: the mail is responsibly delivered, the message is honestly and respectfully written, there's good reason to believe the recipient is and pedagogy, pre-disposed to be interested in the product, the recipient clearly understands why they'd receive such a message and personal essay, recipients can easily and play and pedagogy, effectively remove themselves from our mailing list. To that end, Resume Rabbit may from time to time obtain, create, or acquire email lists of prospective customers who are known to be seeking employment or who are otherwise likely to books essay, be interested in essay Resume Rabbit's services. We may directly email these prospective customers or may use a 3rd party email marketing company to send these prospective customers an invitation to visit our website. To better target and analyze our marketing efforts we may also keep database information and logs related to these prospective customers for internal use only. Deductive Reasoning Essay Writing? This information may include: a recipients first name, last name, email address, residential information, the source of the email list they're on, the date we acquired the list they're on, the date(s) we sent that prospective customer an email, the and pedagogy content of the email message we sent, and the date the prospective customer may have requested to be removed from our list. In the email itself we may include a special website address that would allow us to know which of the people we emailed actually visited our site. We would use this information for personal purposes such as: automatically removing web site visitors from our solicitation list, sending web site visitors a different email message than non visitors and to and pedagogy, perform internal statistical analysis to college essay prompts, fine tune our marketing methods. As you browse our site, advertising cookies will be placed on and pedagogy essay, your computer so that we can understand what portions of our site you have visited. Our display advertising partners then enable us to present you with retargeting advertising on other sites based on your previous interaction with us. The techniques our partners employ do not collect personal information such as your name, email address, postal address or telephone number. To Opt-Out or Unsubscribe from any future marketing related email send directly from Resume Rabbit, click the unsubscribe link that can be found at the bottom of the email you received.

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Algebraic Number Theory - Essay - Mathematics. Algebraic Number Theory. Version 3.03 May 29, 2011. An algebraic number field is a finite extension of Q; an algebraic number is an element of an algebraic number field. Algebraic number theory studies the arithmetic of algebraic number fields — the ring of essay, integers in the number field, the ideals and units in the ring of integers, the extent to which unique factorization holds, and so on. An abelian extension of a field is a Galois extension of the field with abelian Galois group. Class field theory describes the abelian extensions of a number field in terms of the arithmetic of the field. These notes are concerned with algebraic number theory, and the sequel with class field theory. v2.01 (August 14, 1996). First version on the web. v2.10 (August 31, 1998). Fixed many minor errors; added exercises and an index; 138 pages. v3.00 (February 11, 2008). Corrected; revisions and additions; 163 pages. v3.01 (September 28, 2008).

Fixed problem with hyperlinks; 163 pages. v3.02 (April 30, 2009). Fixed many minor errors; changed chapter and page styles; 164 pages. v3.03 (May 29, 2011). Best And Worst Essays. Minor fixes; 167 pages. Available at www.jmilne.org/math/ Please send comments and corrections to me at the address on and pedagogy essay, my web page. The photograph is of the Fork Hut, Huxley Valley, New Zealand. Copyright c 1996, 1998, 2008, 2009, 2011 J.S. Milne. Single paper copies for noncommercial personal use may be made without explicit permis- sion from the copyright holder. Deductive Writing. Notations. . . . . . Play. . . . Management Indian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Acknowledgements . . . . . . . . . . . . . . . . . Play And Pedagogy. . . . . . . . Essay. . Play Essay. . . . . . . . . 5 Introduction . . Thesis. . . . Play And Pedagogy Essay. . . . . . . . . . . . Correct Thesis. . . . And Pedagogy Essay. . . . . . . . . . . . . . . . Best And Worst Essays. . . . 1 Exercises . . . Play And Pedagogy. . . . . . . . . . . . . . . . . . . . . . . . . . Best And Worst Essays. . . . . . . . . . . 6. 1 Preliminaries from Commutative Algebra 7 Basic definitions . . . . . And Pedagogy. . . . . . . . . . . . . . . . . . . . . . . . . . Doctoral Dissertation Help. . . Play And Pedagogy. . . . 7 Ideals in products of masters thesis, rings . . . . . And Pedagogy. . . . . . . . . . . . . . . . . . . . . . . . . . 8 Noetherian rings . . . . Reasoning. . . . . . . . . . . . . . . . . . . . Play And Pedagogy Essay. . . . . Management Indian. . . Play And Pedagogy. . . . . . . 8 Noetherian modules . . . . . . . . . . Banks. . . . . . And Pedagogy. . . . . . . . . . . . Correct Spelling Masters Thesis. . . . . . . . 10 Local rings . . . . . Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Rings of fractions . . . . . . . . . . . . . . . . . . . . . . . Banks. . . . . . . And Pedagogy. . . . . . 11 The Chinese remainder theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Review of tensor products . . . . . . . . . . . . . . . . . . . . Management. . . . . . . . . . . 14 Exercise . . . . . . Play And Pedagogy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18. 2 Rings of Integers 19 First proof that the integral elements form a ring . . . . . . . . . . . . . . . . . . 19 Dedekind’s proof that the integral elements form a ring . . . Application Prompts. . . . . . . . And Pedagogy Essay. . . . . 20 Integral elements . And Worst. . . . . . . . . . . . . . . . . . . And Pedagogy. . . . . . . . . Deductive Reasoning Essay. . . . . . . . 22 Review of bases of A-modules . . . . . . . . . . . . . . . . . . . . . . . . Play. . . . 25 Review of norms and traces . . . . . . . . . . . Caltech. . . . . . . . . . . . . . . . . . . 25 Review of and pedagogy essay, bilinear forms . . . . . . . . . . . . . . . . . . . . . Best Essays. . . . . . . . . . 26 Discriminants . . . . . Play And Pedagogy. . . . . . . . . . . Usa. . . . . . . . . . . . And Pedagogy. . . . . . . . . . . 27 Rings of integers are finitely generated . . . . . . . . . . . . . . Deductive Reasoning Writing. . . . . . . . . . 29 Finding the ring of integers . . . . . . . . . Essay. . . . . . . . . . . . . . . . . . . . . 31 Algorithms for finding the ring of integers . . Dissertation. . . . . . . . And Pedagogy Essay. . . . . . . . . . . . . 34 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Essay. . . . . . Play And Pedagogy. . Spelling Masters. . 38. 3 Dedekind Domains; Factorization 40 Discrete valuation rings . . . . . . . . . . . . Essay. . . . . Caltech Books. . . . . . . . Play. . . . . . . . . 40 Dedekind domains . . . . . . . . . . . . . . Masters Thesis. . Play And Pedagogy. . . . . . . . . Books Essay. . . Play And Pedagogy. . . . . . . . . 42 Unique factorization of ideals . Best Essays. . . . . . . . Play And Pedagogy. . . . . . . . . . . . . . Reasoning Writing. . . . . . . . 43 The ideal class group . . . . . Play Essay. . . . . . . . . . . . . . . . . . . . . . . . College. . . . . 46 Discrete valuations . . . And Pedagogy Essay. . . . . College Essay Prompts. . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Integral closures of Dedekind domains . Play And Pedagogy. . . . . . . . . College Personal Prompts. . . Play Essay. . . . . . . . Dissertation Help. . Play And Pedagogy Essay. . . . . 51 Modules over Dedekind domains (sketch). . . . . . . Dissertation Help. . . . . Play. . . . . . . . . . . . Masters Thesis. 52.

Factorization in extensions . . . . . . . . . . . . . . . . . . . . . Play Essay. . . . . . . Help. . . 52 The primes that ramify . Play And Pedagogy. . . . . . . . . . Thesis Indian. . . . . . . . . . . . . . . . . . . . . . 54 Finding factorizations . . . . . . . . . . . . . Play Essay. . . . . . . . . . . . . . . . . . . . 56 Examples of factorizations . . . . . . . . Books Essay. . . . . . . . . . . . . Play. . . . . . . . . . 57 Eisenstein extensions . . . . . . . . . . . . . . Correct Thesis. . . Play. . . . . . . . . . . . . . . . . 60 Exercises . . . . . . . . . . Doctoral Dissertation Help. . . . . . Play Essay. . . Indian. . . . . . . And Pedagogy. . . . . . . . . . . . . . . . 61. Essay. 4 The Finiteness of the Class Number 63 Norms of ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Statement of the main theorem and its consequences . . . . . . . . . . . . . . . . 65 Lattices . . . . . And Pedagogy Essay. . . . . College Application Personal Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Some calculus . . . . . . . . . . And Pedagogy Essay. . . Correct Masters. . . . . Play Essay. . Essay. . . . . . . . . . . . . . . . . . . Play Essay. . 73 Finiteness of the class number . . . Thesis. . Play And Pedagogy Essay. . . . . . . . Management Thesis Banks. . . . . . . . . . . . . Essay. . . . . 75 Binary quadratic forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Exercises . . . Caltech Books. . Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78. 5 The Unit Theorem 80 Statement of the theorem . . . . . . . . . . . . . . . . . . . . . . . . . Correct Thesis. . . . . . Essay. 80 Proof that UK is finitely generated . . . . . . . . . . . . . . . . . . Caltech Books Essay. . . . . . Essay. . . 82 Computation of the rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . Management Thesis Indian. . . 83 S -units . . . . . . . Play And Pedagogy Essay. . . . . . . . . . . . . . . . Caltech Books. . . . Essay. . . . . . . . . . . . . . . . 85 Example: CM fields . . . . . . . . . . . . . . . . . . Best. . . Play Essay. . . . . . . . . . . . . . 86 Example: real quadratic fields . . . . Reasoning Writing. . . . . . . Play Essay. . . . . . . . . . . . . . . . . . 86 Example: cubic fields with negative discriminant . . . . . . . . . . . . . . . . . 87 Finding .K/ . . . . . . . . . . . Spelling Masters Thesis. . . . . . . . . . . Play And Pedagogy Essay. . . . . . . . . . . . . . . . 89 Finding a system of fundamental units . . . . . . . . . . . . . . . . . . . . . . . And Worst Essays. 89 Regulators . Play Essay. . . . . . . . . . . . . . . . . . . . . . . . . . Doctoral Dissertation Help. . . . . . . . . . . . Play And Pedagogy. . 89 Exercises . . . . . . . . . Doctoral Dissertation Help. . . . . Play Essay. . . . . . . . . Best. . . Essay. . . . . . . . . . . . . . . . 90. 6 Cyclotomic Extensions; Fermat’s Last Theorem. 91 The basic results . . . . . . . . . . . . . . . . . . . Caltech Books. . . . . . . . . . . . . . . . . 91 Class numbers of cyclotomic fields . . . . . . . . . . . . . . . . . . . . . . . . . 97 Units in cyclotomic fields . . . . . . . . . . . . . . . . . . . Essay. . . Dissertation. . . . . . Play And Pedagogy. . . . . 97 The first case of Fermat’s last theorem for regular primes . . . . . . . . . . . . . 98 Exercises . . . . . Thesis Banks. . . . . . . . . . . . . . . . . . . . . . . . . . . . Play And Pedagogy Essay. . . . Reasoning Essay. . . . 100. 7 Valuations; Local Fields 101 Valuations . . . Play And Pedagogy Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Nonarchimedean valuations . . . . . . . . . . . . . . . . . . . . . . Best Essays. . . . . . . . 102 Equivalent valuations . . Play And Pedagogy. . . . . . . . . . . . Management Indian. . . . . . . . . . . . . And Pedagogy. . . Deductive Essay Writing. . . . . . 103 Properties of play, discrete valuations . . . . . . Caltech Books Essay. . . . . . Essay. . . . . . Correct Spelling Masters. . . . . . . . . . . 105 Complete list of valuations for the rational numbers . . . . . . . . . . . . . . . . 105 The primes of a number field . . . Play And Pedagogy. . . . . . . . . . . . . . . . . College Essay. . . . . . . . . . 107 The weak approximation theorem . . . . . . . . . Play Essay. . . . . . . . . Best And Worst. . . . . . . . . 109 Completions . . . . And Pedagogy Essay. . Caltech Books. . . . . . . . . . . . . . . . . . . . Play. . . . . . . . . . . . . . 110 Completions in the nonarchimedean case . . . . . . . . . . . Essays. . Play And Pedagogy. . . . . . . . . . . 111 Newton’s lemma . . . . . . . . . . Deductive Reasoning. . . . . Play. . . . . . . . . . . Management. . . . . . . . . . . 115 Extensions of nonarchimedean valuations . . . . . . . Play And Pedagogy Essay. . . . . . . . . . . . . . . 118.

Newton’s polygon . . . . . . . . . . Application Personal. . Essay. . . . . . . . . . Doctoral Help Usa. . . . . . . . . . . . . . . 120 Locally compact fields . . Play And Pedagogy. . . . . . . . . . . . . . . . . . . Best Essays. . . . . . . . . . . . 122 Unramified extensions of a local field . . And Pedagogy. . . . . . . . . . . . . . Spelling Thesis. . . . . . . . . 123 Totally ramified extensions of K . . . . . . . . . . . . . . . . . . . . . . . . . Play And Pedagogy Essay. . 125 Ramification groups . . . . . . . Best. . . . . . . . . . . . And Pedagogy. . . . . . . . . . . . . . . . 126 Krasner’s lemma and applications . . . . . . . . . . . . . . . . . . . . . . . . . 127 Exercises . . . . . . . Caltech Essay. . . . And Pedagogy. . . . . . . . Books Essay. . . . . . . . . . . . . . . . And Pedagogy Essay. . . . . . . 129. 8 Global Fields 131 Extending valuations . . . . Reasoning Essay Writing. . . . . And Pedagogy. . . . . . College Application Essay Prompts. . . . . . . . . . . And Pedagogy. . . . . . . . . . 131 The product formula . . . . . . . . . . . . . . . . . . Essay Writing. . . . Play And Pedagogy. . . . . . . . Doctoral Dissertation Usa. . . . . And Pedagogy Essay. 133 Decomposition groups . . . . . . . . . . . College Application Essay Prompts. . . . . . . . Essay. . . . . . . . . . Help Usa. . . . . 135 The Frobenius element . . . . . . . . . . . . . . . Play And Pedagogy Essay. . . . . . . And Worst. . Play And Pedagogy. . . . . . . . . . 137 Examples . . . . . . . . Doctoral Usa. . . . . Play Essay. . Spelling Masters Thesis. . . . . . . . And Pedagogy. . . . . . . Correct Thesis. . . . Play And Pedagogy Essay. . . . . . . . . . Deductive Reasoning. 139 Computing Galois groups (the hard way) . . . . Play And Pedagogy. . Caltech Books Essay. . . . . Essay. . . . . . . . . . . Correct Masters Thesis. . . . 140 Computing Galois groups (the easy way) . . . . . . . . . . . . . . . . . . . . . . 141 Applications of the Chebotarev density theorem . . . . . . . . . . . . . . . . Play And Pedagogy. . Best And Worst Essays. . 146 Exercises . . . Essay. . . . . . . . . . . . . . . Dissertation Help. . . Essay. . . . . . . . . . Essays. . . . . . . And Pedagogy. . . . . Dissertation Usa. 147. A Solutions to the Exercises 149. B Two-hour examination 155. We use the standard (Bourbaki) notations: ND f0;1;2; : : :g; ZD ring of integers; RD field of real numbers; CD field of complex numbers; Fp D Z=pZD field with p elements, p a prime number. For integers m and n, mjn means that m divides n, i.e., n 2mZ. Throughout the notes, p is a prime number, i.e., p D 2;3;5; : : :. Given an equivalence relation, ?? denotes the equivalence class containing . The empty set is denoted by ;. The cardinality of a set S is denoted by jS j (so jS j is the number of elements in S when S is finite). Let I and A be sets; a family of elements of play and pedagogy, A indexed by I , denoted .ai /i2I , is a function i 7! ai WI ! A. X Y X is a subset of Y (not necessarily proper); X. def D Y X is defined to be Y , or equals Y by definition; X Y X is isomorphic to Y ; X ' Y X and Y are canonically isomorphic (or there is a given or unique isomorphism); ,! denotes an injective map; denotes a surjective map. It is standard to use Gothic (fraktur) letters for ideals: a b c m n p q A B C M N P Q a b c m n p q A B C M N P Q.

The algebra usually covered in dissertation help usa, a first-year graduate course, for and pedagogy essay example, Galois theory, group theory, and multilinear algebra. An undergraduate number theory course will also be helpful. Caltech Books. In addition to the references listed at the end and in footnotes, I shall refer to the following of my course notes (available at www.jmilne.org/math/): FT Fields and Galois Theory, v4.22, 2011. GT Group Theory, v3.11, 2011. CFT Class Field Theory, v4.01, 2011. I thank the following for providing corrections and comments for earlier versions of and pedagogy essay, these notes: Vincenzo Acciaro; Michael Adler; Giedrius Alkauskas; Francesc Castella?; Kwangho Choiy; Dustin Clausen; Keith Conrad; Paul Federbush; Hau-wen Huang; Roger Lipsett; Loy Jiabao, Jasper; Lee M. Goswick; Samir Hasan; Lars Kindler; Franz Lemmermeyer; Siddharth Mathur; Bijan Mohebi; Scott Mullane; Wai Yan Pong; Nicola?s Sirolli; Thomas Stoll; Vishne Uzi; and others. PARI is an open source computer algebra system freely available from http://pari.math.u- bordeaux.fr/. FERMAT (1601–1665). Stated his last “theorem”, and proved it for mD 4. He also posed the problem of finding integer solutions to the equation, X2?AY 2 D 1; A 2 Z; (1) which is essentially the problem1 of finding the units in Z? p A?.

The English mathemati- cians found an algorithm for solving the problem, but neglected to prove that the algorithm always works. EULER (1707–1783). He introduced analysis into the study of the prime numbers, and he discovered an early version of the quadratic reciprocity law. LAGRANGE (1736–1813). He found the management thesis complete form of the quadratic reciprocity law: D .?1/.p?1/.q?1/=4; p;q odd primes, and he proved that the algorithm for solving (1) always leads to a solution, LEGENDRE (1752–1833). He introduced the “Legendre symbol” m p. , and gave an incom- plete proof of the quadratic reciprocity law. He proved the following local-global principle for quadratic forms in three variables over Q: a quadratic form Q.X;Y;Z/ has a nontrivial zero in Q if and only if it has one in R and the congruence Q 0 mod pn has a nontrivial solution for all p and n. GAUSS (1777–1855). He found the first complete proofs of the quadratic reciprocity law. He studied the Gaussian integers Z?i ? in order to find a quartic reciprocity law. He studied the classification of binary quadratic forms over Z, which is closely related to the problem of finding the class numbers of quadratic fields.

DIRICHLET (1805–1859). He introduced L-series, and used them to prove an analytic for- mula for the class number and a density theorem for the primes in an arithmetic progression. He proved the following “unit theorem”: let ? be a root of a monic irreducible polynomial f .X/ with integer coefficients; suppose that f .X/ has r real roots and 2s complex roots; then Z??? is a finitely generated group of and pedagogy, rank rC s?1. Best And Worst Essays. KUMMER (1810–1893). He made a deep study of the arithmetic of cyclotomic fields, mo- tivated by a search for higher reciprocity laws, and showed that unique factorization could be recovered by the introduction of “ideal numbers”. He proved that Fermat’s last theorem holds for regular primes.

HERMITE (1822–1901). He made important contributions to quadratic forms, and he showed that the roots of a polynomial of degree 5 can be expressed in terms of elliptic functions. EISENSTEIN (1823–1852). He published the first complete proofs for the cubic and quartic reciprocity laws. KRONECKER (1823–1891). He developed an and pedagogy essay, alternative to Dedekind’s ideals. He also had one of the most beautiful ideas in mathematics for generating abelian extensions of number fields (the Kronecker liebster Jugendtraum).

RIEMANN (1826–1866). Studied the Riemann zeta function, and made the Riemann hy- pothesis. 1The Indian mathematician Bhaskara (12th century) knew general rules for finding solutions to the equa- tion. DEDEKIND (1831–1916). Best And Worst Essays. He laid the modern foundations of algebraic number theory by finding the correct definition of the ring of integers in a number field, by proving that ideals factor uniquely into products of prime ideals in such rings, and by showing that, modulo principal ideals, they fall into finitely many classes. Defined the zeta function of a number field. WEBER (1842–1913). Made important progress in class field theory and the Kronecker Jugendtraum. Play Essay. HENSEL (1861–1941).

He gave the books essay first definition of the field of p-adic numbers (as the set of infinite sums. n, an 2 f0;1; : : : ;p?1g). HILBERT (1862–1943). He wrote a very influential book on algebraic number theory in 1897, which gave the first systematic account of the theory. Some of his famous problems were on number theory, and have also been influential. And Pedagogy Essay. TAKAGI (1875–1960). He proved the fundamental theorems of abelian class field theory, as conjectured by Weber and Hilbert. NOETHER (1882–1935). Together with Artin, she laid the foundations of modern algebra in which axioms and conceptual arguments are emphasized, and she contributed to the classification of central simple algebras over number fields. HECKE (1887–1947).

Introduced HeckeL-series generalizing both Dirichlet’sL-series and Dedekind’s zeta functions. ARTIN (1898–1962). Deductive Essay. He found the “Artin reciprocity law”, which is the main theorem of class field theory (improvement of play, Takagi’s results). Introduced the Artin L-series. HASSE (1898–1979).

He gave the caltech essay first proof of local class field theory, proved the Hasse (local-global) principle for all quadratic forms over number fields, and contributed to the classification of central simple algebras over number fields. BRAUER (1901–1977). And Pedagogy. Defined the Brauer group, and contributed to the classification of central simple algebras over number fields. WEIL (1906–1998). Defined the Weil group, which enabled him to give a common gener- alization of Artin L-series and Hecke L-series. CHEVALLEY (1909–84). The main statements of class field theory are purely algebraic, but all the earlier proofs used analysis; Chevalley gave a purely algebraic proof. With his introduction of ide?les he was able to give a natural formulation of class field theory for infinite abelian extensions. IWASAWA (1917–1998). He introduced an important new approach into algebraic number theory which was suggested by the theory of college application essay, curves over finite fields.

TATE (1925– ). He proved new results in group cohomology, which allowed him to give an elegant reformulation of class field theory. With Lubin he found an essay, explicit way of generating abelian extensions of reasoning, local fields. LANGLANDS (1936– ). The Langlands program2 is a vast series of conjectures that, among other things, contains a nonabelian class field theory. 2Not to be confused with its geometric analogue, sometimes referred to as the geometric Langlands pro- gram, which appears to lack arithmetic significance. Introduction It is greatly to be lamented that this virtue of the [rational integers], to be decomposable into prime factors, always the same ones for a given number, does not also belong to the [integers of cyclotomic fields].

Kummer 1844 (as translated by Andre? Weil) The fundamental theorem of arithmetic says that every nonzero integerm can be writ- ten in the form, mD?p1 pn; pi a prime number, and that this factorization is essentially unique. Consider more generally an play, integral domain A. An element a 2A is said to be a unit if. it has an inverse in A (element b such that ab D 1D ba). I write A for the multiplicative group of units in A. An element of A is doctoral help, said to and pedagogy essay prime if it is neither zero nor a unit, and if. Doctoral Usa. If A is a principal ideal domain, then every nonzero element a of A can be written in the form, aD u1 n; u a unit; i a prime element; and this factorization is unique up to order and replacing each i with an associate, i.e., with its product with a unit. Our first task will be to discover to what extent unique factorization holds, or fails to hold, in number fields. Three problems present themselves.

First, factorization in a field only makes sense with respect to a subring, and so we must define the “ring of integers” OK in essay, our number field K. Secondly, since unique factorization will fail in general, we shall need to reasoning essay writing find a way of measuring by how much it fails. Finally, since factorization is only considered up to units, in order to fully understand the arithmetic of K, we need to play essay understand the structure of the group of units UK in OK . THE RING OF INTEGERS. Let K be an algebraic number field. Each element ? of K satisfies an equation. ?nCa1? n?1 C Ca0 D 0. with coefficients a1; : : : ;an in Q, and ? is an algebraic integer if it satisfies such an equation with coefficients a1; : : : ;an in Z. We shall see that the algebraic integers form a subring OK of K. The criterion as stated is difficult to apply. We shall show (2.11) that ? is an reasoning essay writing, algebraic integer if and only if its minimum polynomial over Q has coefficients in Z. Consider for example the field K D Q? p d?, where d is a square-free integer. The. minimum polynomial of ? D aCb p d , b ¤ 0, a;b 2Q, is. .X ? .aCb p d//.X ? .a?b. p d//DX2?2aXC .a2?b2d/; and so ? is an algebraic integer if and only if. 2a 2 Z; a2?b2d 2 Z: From this it follows easily that, when d 2;3 mod 4, ? is an algebraic integer if and only if a and b are integers, i.e., and, when d 1 mod 4, ? is an algebraic integer if and only if a and b are either both integers or both half-integers, i.e., For example, the minimum polynomial of 1=2C p 5=2 is X2?X ?1, and so 1=2C. is an algebraic integer in Q? p 5?. Let d be a primitive d th root of 1, for example, d D exp.2i=d/, and letK DQ?d ?. Then we shall see (6.2) that. OK D Z?d ?D ?P.

as one would hope. A nonzero element of an and pedagogy essay, integral domain A is said to be irreducible if it is not a unit, and can’t be written as a product of two nonunits. For example, a prime element is (obviously) irreducible. A ring A is doctoral dissertation usa, a unique factorization domain if every nonzero element of A can be expressed as a product of irreducible elements in essentially one way. Is the ring of integers OK a unique factorization domain?

No, not in general! We shall see that each element of OK can be written as a product of irreducible elements (this is true for all Noetherian rings), and so it is the uniqueness that fails. For example, in Z? p ?5? we have. 6D 2 3D .1C p ?5/.1?. To see that 2, 3, 1C p ?5, 1?. p ?5 are irreducible, and no two are associates, we use the. p ?5 7! a2C5b2: This is multiplicative, and it is easy to see that, for ? 2OK , Nm.?/D 1 ” ? N? D 1 ” ? is a unit. (*) If 1C p ?5D ??, then Nm.??/D Nm.1C. p ?5/D 6. Thus Nm.?/D 1;2;3, or 6. In the. first case, ? is a unit, the second and third cases don’t occur, and in and pedagogy, the fourth case ? is a unit. A similar argument shows that 2;3, and 1?. p ?5 are irreducible. Next note that (*) implies that associates have the same norm, and so it remains to show that 1C p ?5 and.

1? p ?5 are not associates, but. has no solution with a;b 2 Z. Why does unique factorization fail in OK? The problem is that irreducible elements in. OK need not be prime. In the above example, 1C p ?5 divides 2 3 but it divides neither 2. nor 3. In fact, in an integral domain in which factorizations exist (e.g. a Noetherian ring), factorization is unique if all irreducible elements are prime. What can we recover? Consider. 210D 6 35D 10 21: If we were naive, we might say this shows factorization is not unique in Z; instead, we recognize that there is a unique factorization underlying these two decompositions, namely, The idea of Kummer and Dedekind was to enlarge the set of “prime numbers” so that, for example, in Z? p ?5? there is a unique factorization, 6D .p1 p2/.p3 p4/D .p1 p3/.p2 p4/; underlying the above factorization; here the pi are “ideal prime factors”.

How do we define “ideal factors”? Clearly, an ideal factor should be characterized. by and worst, the algebraic integers it divides. Moreover divisibility by a should have the following properties: aj0I aja;ajb) aja?bI aja) ajab for all b 2OK : If in addition division by a has the property that. ajab) aja or ajb; then we call a a “prime ideal factor”. Since all we know about an ideal factor is the play set of elements it divides, we may as well identify it with this set. Thus an ideal factor a is a set of elements of OK such that. 0 2 aI a;b 2 a) a?b 2 aI a 2 a) ab 2 a for all b 2OK I. it is prime if an addition, ab 2 a) a 2 a or b 2 a: Many of you will recognize that an ideal factor is what we now call an ideal, and a prime ideal factor is a prime ideal. There is an obvious notion of the product of two ideals: aibi ; ajai ; bjbi : In other words, abD. nX aibi j ai 2 a; bi 2 b. One see easily that this is again an ideal, and that if. aD .a1; . ;am/ and bD .b1; . ;bn/ then a bD .a1b1; . ;aibj ; . ;ambn/: With these definitions, one recovers unique factorization: if a ¤ 0, then there is an essentially unique factorization: .a/D p1 pn with each pi a prime ideal. In the above example, .6/D .2;1C p ?5/.2;1?.

In fact, I claim. .2;1C p ?5/.2;1?. .3;1C p ?5/.3;1?. Spelling Thesis. .2;1? p ?5/.3;1?. For example, .2;1C p ?5/.2;1?. p ?5;6/. Since every gen- erator is divisible by 2, we see that. .2;1C p ?5/.2;1?. Conversely, 2D 6?4 2 .4;2C2. and so .2;1C p ?5/.2;1?. p ?5/ D .2/, as claimed. I further claim that the play and pedagogy essay four ideals. .2;1C p ?5/, .2;1?. p ?5/, and and worst .3;1?. p ?5/ are all prime.

For example, the obvious map Z! Z? p ?5?=.3;1?. p ?5/ is surjective with kernel .3/, and so. Z? p ?5?=.3;1?. which is an integral domain. How far is this from what we want, namely, unique factorization of elements? In other. words, how many “ideal” elements have we had to add to our “real” elements to get unique factorization. In a certain sense, only a finite number: we shall see that there exists a finite set S of ideals such that every ideal is of the form a .a/ for some a 2 S and play and pedagogy essay some a 2OK . Better, we shall construct a group I of “fractional” ideals in which the principal fractional ideals .a/, a 2K, form a subgroup P of finite index.

The index is called the class number hK of K. We shall see that. hK D 1 ” OK is a principal ideal domain ” OK is masters thesis, a unique factorization domain. Unlike Z, OK can have infinitely many units. For example, .1C p 2/ is a unit of infinite. order in Z? p 2? W. p 2/m ¤ 1 if m¤ 0: In fact Z? p 2? D f?.1C. p 2/m jm 2 Zg, and play and pedagogy essay so. Z? p 2? f?1gffree abelian group of rank 1g: In general, we shall show (unit theorem) that the roots of 1 in K form a finite group .K/, and that. OK .K/Z r (as an abelian group); moreover, we shall find r: One motivation for the development of algebraic number theory was the attempt to prove Fermat’s last “theorem”, i.e., when m 3, there are no integer solutions .x;y;z/ to the equation. with all of x;y;z nonzero. WhenmD 3, this can proved by the method of “infinite descent”, i.e., from one solution, you show that you can construct a smaller solution, which leads to caltech books essay a contradiction3. The proof makes use of the factorization. Play And Pedagogy. Y 3 DZ3?X3 D .Z?X/.Z2CXZCX2/; and it was recognized that a stumbling block to proving the theorem for larger m is correct, that no such factorization exists into polynomials with integer coefficients of degree 2. This led people to look at more general factorizations. In a famous incident, the French mathematician Lame? gave a talk at the Paris Academy in 1847 in which he claimed to prove Fermat’s last theorem using the following ideas. Let p 2 be a prime, and suppose x, y, z are nonzero integers such that.

Write xp D zp?yp D. Y .z? iy/; 0 i p?1; D e2i=p: He then showed how to obtain a smaller solution to the equation, and hence a contradiction. Liouville immediately questioned a step in Lame?’s proof in which he assumed that, in order to show that each factor .z ? iy/ is play, a pth power, it suffices to show that the factors are relatively prime in pairs and their product is a pth power. In fact, Lame? couldn’t justify his step (Z?? is not always a principal ideal domain), and Fermat’s last theorem was not proved for almost 150 years. However, shortly after Lame?’s embarrassing lecture, Kummer used his results on the arithmetic of the fields Q?? to prove Fermat’s last theorem for all regular primes, i.e., for all primes p such that p does not divide the class number of Q?p?. Another application is to finding Galois groups. The splitting field of a polynomial f .X/ 2Q?X? is a Galois extension of Q. In a basic Galois theory course, we learn how to compute the Galois group only when the degree is very small. By using algebraic number theory one can write down an algorithm to do it for any degree. For applications of algebraic number theory to elliptic curves, see, for example, Milne 2006. Some comments on the literature. COMPUTATIONAL NUMBER THEORY.

Cohen 1993 and Pohst and Zassenhaus 1989 provide algorithms for most of the construc- tions we make in this course. College Application Prompts. The first assumes the reader knows number theory, whereas the second develops the whole subject algorithmically. Cohen’s book is the more useful as a supplement to this course, but wasn’t available when these notes were first written. While the books are concerned with more-or-less practical algorithms for fields of small degree and small discriminant, Lenstra (1992) concentrates on finding “good” general algorithms. 3The simplest proof by infinite descent is that showing that p 2 is irrational. HISTORY OF ALGEBRAIC NUMBER THEORY.

Dedekind 1996, with its introduction by and pedagogy essay, Stillwell, gives an excellent idea of how algebraic number theory developed. Edwards 1977 is a history of algebraic number theory, con- centrating on the efforts to prove Fermat’s last theorem. The notes in Narkiewicz 1990 document the origins of most significant results in algebraic number theory. Lemmermeyer 2009, which explains the origins of “ideal numbers”, and other writings by the same author, e.g., Lemmermeyer 2000, 2007. 0-1 Let d be a square-free integer. Management Thesis Indian Banks. Complete the verification that the ring of integers in Q? p d? is as described. 0-2 Complete the verification that, in Z? p ?5?, .6/D .2;1C p ?5/.2;1?. is a factorization of .6/ into a product of prime ideals. CHAPTER 1 Preliminaries from Commutative.

Many results that were first proved for rings of integers in number fields are true for more general commutative rings, and it is more natural to prove them in that context.1. All rings will be commutative, and have an identity element (i.e., an element 1 such that 1a D a for all a 2 A), and play and pedagogy essay a homomorphism of rings will map the identity element to the identity element. A ring B together with a homomorphism of rings A! B will be referred to as an A-algebra. We use this terminology mainly when A is a subring of spelling thesis, B . In this case, for elements ?1; . ;?m of B , A??1; . ;?m? denotes the smallest subring of B containing A and the ?i . It consists of all polynomials in the ?i with coefficients in A, i.e., elements of the form X. ai1. im? i1 1 . ? im m ; ai1. im 2 A: We also refer to A??1; . ;?m? as the A-subalgebra of B generated by the ?i , and when B D A??1; . ;?m? we say that the ?i generate B as an play and pedagogy, A-algebra. For elements a1;a2; : : : of A, we let .a1;a2; : : :/ denote the smallest ideal containing the ai . It consists of finite sums. P ciai , ci 2 A, and it is called the ideal generated by. a1;a2; : : :. Books Essay. When a and b are ideals in A, we define. aCbD faCb j a 2 a, b 2 bg: It is play essay, again an ideal in A — in fact, it is the smallest ideal containing both a and b. If aD .a1; . ;am/ and bD .b1; . ;bn/, then aCbD .a1; . ;am;b1; . Doctoral Help. ;bn/: Given an ideal a in A, we can form the quotient ring A=a. Let f WA!

A=a be the homomorphism a 7! aCa; then b 7! f ?1.b/ defines a one-to-one correspondence between the ideals of A=a and the ideals of A containing a, and. 1See also the notes A Primer of Commutative Algebra available on my website. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. A proper ideal a of A is prime if ab 2 a) a or b 2 a. An ideal a is prime if and and pedagogy essay only if the help quotient ring A=a is an integral domain. A nonzero element of play and pedagogy essay, A is said to be prime if ./ is a prime ideal; equivalently, if jab) ja or jb. Dissertation Help Usa. An ideal m in A is maximal if it is maximal among the play and pedagogy proper ideals of application personal essay prompts, A, i.e., if m¤A and there does not exist an ideal a ¤ A containing m but distinct from it. An ideal a is maximal if and only if A=a is and pedagogy, a field. Every proper ideal a of deductive, A is contained in a maximal ideal — if A is Noetherian (see below) this is obvious; otherwise the proof requires Zorn’s lemma.

In particular, every nonunit in A is contained in a maximal ideal. There are the implications: A is a Euclidean domain) A is a principal ideal domain ) A is and pedagogy, a unique factorization domain (see any good graduate algebra course). Ideals in products of rings. PROPOSITION 1.1 Consider a product of rings AB . If a and b are ideals in A and B respectively, then ab is an ideal in AB , and every ideal in AB is of this form. The prime ideals of AB are the ideals of the form.

pB (p a prime ideal of A), Ap (p a prime ideal of B). PROOF. Let c be an ideal in AB , and let. aD fa 2 A j .a;0/ 2 cg; bD fb 2 B j .0;b/ 2 cg: Clearly a b c. Conversely, let .a;b/ 2 c. Then .a;0/ D .a;b/ .1;0/ 2 c and .0;b/ D .a;b/ .0;1/ 2 c, and so .a;b/ 2 ab: Recall that an ideal c C is prime if and only if C=c is an integral domain. The map. has kernel ab, and hence induces an isomorphism. Now use that a product of rings is an integral domain if and correct spelling only if one ring is zero and the other is an integral domain. 2. REMARK 1.2 The lemma extends in an obvious way to a finite product of rings: the ideals in A1 Am are of the form a1 am with ai an ideal in Ai ; moreover, a1 am is prime if and only if there is a j such that aj is a prime ideal in Aj and ai DAi for i ¤ j: A ring A is Noetherian if every ideal in A is finitely generated. PROPOSITION 1.3 The following conditions on a ring A are equivalent: (a) A is Noetherian. (b) Every ascending chain of ideals. eventually becomes constant, i.e., for some n, an D anC1 D . (c) Every nonempty set S of ideals in A has a maximal element, i.e., there exists an ideal in S not properly contained in any other ideal in S . Essay. PROOF. (a) (b): Let a D S. ai ; it is an ideal, and deductive reasoning essay hence is finitely generated, say a D .a1; : : : ;ar/. For some n, an will contain all the ai , and so an D anC1 D D a. (b) (c): Let a1 2 S . If a1 is not a maximal element of S , then there exists an a2 2 S such that a1 a2. If a2 is not maximal, then there exists an a3 etc.. From (b) we know that this process will lead to a maximal element after only finitely many steps. (c) (a): Let a be an ideal in A, and let S be the set of finitely generated ideals contained in a. Then S is nonempty because it contains the zero ideal, and so it contains a maximal element, say, a0 D .a1; : : : ;ar/.

If a0 ¤ a, then there exists an element a 2 ar a0, and .a1; : : : ;ar ;a/ will be a finitely generated ideal in a properly containing a0. This contradicts the definition of a0. 2. A famous theorem of Hilbert states that k?X1; . ;Xn? is Noetherian. In practice, al- most all the rings that arise naturally in algebraic number theory or algebraic geometry are Noetherian, but not all rings are Noetherian. For example, the ring k?X1; : : : ;Xn; : : :? of polynomials in an infinite sequence of symbols is not Noetherian because the essay chain of ideals. never becomes constant. PROPOSITION 1.4 Every nonzero nonunit element of a Noetherian integral domain can be written as a product of irreducible elements.

PROOF. We shall need to use that, for elements a and b of an integral domain A, .a/ .b/ ” bja, with equality if and only if b D aunit: The first assertion is obvious. For the second, note that if a D bc and b D ad then a D bc D adc, and so dc D 1. Hence both c and d are units. Deductive Reasoning. Suppose the statement of the proposition is false for a Noetherian integral domain A. Then there exists an element a 2 A which contradicts the statement and is such that .a/ is maximal among the ideals generated by play and pedagogy essay, such elements (here we use that A is Noetherian). Since a can not be written as a product of irreducible elements, it is not itself irreducible, and so a D bc with b and c nonunits.

Clearly .b/ .a/, and the ideals can’t be equal for otherwise c would be a unit. From the maximality of .a/, we deduce that b can be written as a product of irreducible elements, and similarly for c. Thus a is a product of irreducible elements, and we have a contradiction. 2. REMARK 1.5 Note that the proposition fails for the ring O of all algebraic integers in the algebraic closure of dissertation usa, Q in C, because, for example, we can keep in extracting square roots — an algebraic integer ? can not be an irreducible element of O because. p ? will also be. an algebraic integer and ? D p ? p ?. Thus O is not Noetherian. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. Let A be a ring. An A-module M is essay, said to be Noetherian if every submodule is finitely generated.

PROPOSITION 1.6 The following conditions on an A-module M are equivalent: (a) M is Noetherian; (b) every ascending chain of submodules eventually becomes constant; (c) every nonempty set of submodules in correct masters, M has a maximal element. PROOF. Similar to the proof of Proposition 1.3. 2. PROPOSITION 1.7 Let M be an A-module, and let N be a submodule of M . If N and M=N are both Noetherian, then so also is M . PROOF. I claim that if M 0 M 00 are submodules of M such that M 0N DM 00N and M 0 and M 00 have the same image in M=N , then M 0 DM 00. To see this, let x 2M 00; the second condition implies that there exists a y 2M 0 with the same image as x inM=N , i.e., such that x?y 2N . Then x?y 2M 00N M 0, and so x 2M 0. Now consider an ascending chain of submodules of M . If M=N is Noetherian, the play and pedagogy essay image of the chain in M=N becomes constant, and if N is Noetherian, the spelling intersection of the essay chain with N becomes constant. Now the claim shows that the deductive chain itself becomes constant. 2. Play. PROPOSITION 1.8 Let A be a Noetherian ring.

Then every finitely generated A-module is Noetherian. PROOF. If M is generated by a single element, then M A=a for some ideal a in A, and the statement is obvious. We argue by induction on the minimum number n of generators ofM . SinceM contains a submoduleN generated by n?1 elements such that the quotient M=N is generated by a single element, the statement follows from (1.7). 2. A ring A is said to local if it has exactly one maximal ideal m. In this case, A D Arm (complement of m in A). LEMMA 1.9 (NAKAYAMA’S LEMMA) Let A be a local Noetherian ring, and let a be a proper ideal in A. Let M be a finitely generated A-module, and define. aM D f P aimi j ai 2 a; mi 2M g : (a) If aM DM , then M D 0: (b) If N is a submodule of M such that N CaM DM , then N DM: Rings of fractions. PROOF. (a) Suppose that aM D M but M ¤ 0. Choose a minimal set of generators fe1; : : : ; eng for M , n 1, and write. e1 D a1e1C Canen, ai 2 a: Then .1?a1/e1 D a2e2C Canen: As 1? a1 is not in m, it is a unit, and so fe2; . ; eng generates M , which contradicts our choice of fe1; : : : ; eng. (b) It suffices to show that a.M=N/DM=N for doctoral dissertation help then (a) shows that M=N D 0. Con- sider mCN , m 2M . From the assumption, we can write. aimi , with ai 2 a, mi 2M: and play so mCN 2 a.M=N/: 2. The hypothesis that M be finitely generated in the lemma is essential. For example, if A is a local integral domain with maximal ideal m ¤ 0, then mM DM for any field M containing A but M ¤ 0. Rings of fractions.

Let A be an integral domain; there is a field K A, called the field of fractions of A, with the property that every c 2K can be written in the form c D ab?1 with a;b 2A and b ¤ 0. For example, Q is the field of fractions of Z, and k.X/ is the field of fractions of k?X?: Let A be an college application, integral domain with field of fractions K. A subset S of A is said to be multiplicative if 0 … S , 1 2 S , and S is closed under multiplication. If S is a multiplicative subset, then we define. S?1AD fa=b 2K j b 2 Sg: It is obviously a subring of K: EXAMPLE 1.10 (a) Let t be a nonzero element of A; then. St def D f1,t ,t2. g. is a multiplicative subset of A, and we (sometimes) write At for S?1t A. For example, if d is a nonzero integer, then2 Zd consists of those elements of Q whose denominator divides some power of d : Zd D fa=dn 2Q j a 2 Z, n 0g: (b) If p is play and pedagogy, a prime ideal, then SpDArp is a multiplicative set (if neither a nor b belongs to p, then ab does not belong to p/. We write Ap for S?1p A. For example, Z.p/ D fm=n 2Q j n is not divisible by pg:

2This notation conflicts with a later notation in which Zp denotes the ring of p-adic integers. Caltech Books Essay. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. PROPOSITION 1.11 Consider an integral domainA and a multiplicative subset S ofA. For an ideal a of A, write ae for the ideal it generates in S?1A; for an ideal a of S?1A, write ac for aA. Then: ace D a for all ideals a of S?1A aec D a if a is a prime ideal of A disjoint from S: PROOF. Let a be an ideal in S?1A. Clearly .aA/e a because aA a and a is an ideal in S?1A. For the reverse inclusion, let b 2 a. We can write it b D a=s with a 2 A, s 2 S . Then aD s .a=s/ 2 aA, and so a=s D .s .a=s//=s 2 .aA/e: Let p be a prime ideal disjoint from S . Clearly .S?1p/A p. For the reverse inclu- sion, let a=s 2 .S?1p/A, a 2 p, s 2 S . Consider the equation a. s s D a 2 p. Both a=s. and s are in A, and so at least one of a=s or s is in p (because it is prime); but s … p (by assumption), and so a=s 2 p: 2. Play. PROPOSITION 1.12 Let A be an integral domain, and let S be a multiplicative subset of essays, A. Play. The map p 7! pe defD p S?1A is a bijection from the set of prime ideals in A such that pS D? to reasoning essay writing the set of prime ideals in S?1A; the inverse map is p 7! pA. PROOF. It is easy to see that. p a prime ideal disjoint from S) pe is a prime ideal in S?1A, p a prime ideal in S?1A) pA is a prime ideal in A disjoint from S; and (1.11) shows that the two maps are inverse.

2. EXAMPLE 1.13 (a) If p is a prime ideal in A, then Ap is a local ring (because p contains every prime ideal disjoint from Sp). (b) We list the essay prime ideals in some rings: Note that in general, for thesis t a nonzero element of an integral domain, fprime ideals of Atg $ fprime ideals of A not containing tg. fprime ideals of A=.t/g $ fprime ideals of A containing tg: The Chinese remainder theorem. Recall the classical form of the theorem: let d1; . ;dn be integers, relatively prime in pairs; then for play any integers x1; . ;xn, the congruences. The Chinese remainder theorem. have a simultaneous solution x 2 Z; moreover, if x is one solution, then the other solutions are the integers of the form xCmd with m 2 Z and d D. We want to translate this in terms of ideals. Management Indian Banks. Integersm and n are relatively prime if and only if .m;n/D Z, i.e., if and only if .m/C .n/D Z. Play And Pedagogy Essay. This suggests defining ideals a and b in a ring A to be relatively prime if aCbD A. If m1; . ;mk are integers, then T .mi / D .m/ where m is the least common multiple. of the mi . Thus T .mi / . Caltech Essay. Q mi /, which equals. Q .mi /. If the mi are relatively prime in. pairs, then mD Q mi , and so we have. Q .mi /. Note that in general, a1 a2 an a1a2 . an; but the two ideals need not be equal. These remarks suggest the essay following statement. THEOREM 1.14 Let a1; . ;an be ideals in a ring A, relatively prime in pairs. Then for any elements x1; . ;xn of A, the congruences. have a simultaneous solution x 2 A; moreover, if x is one solution, then the other solutions are the elements of the form xC a with a 2. Q ai . In other words, the. natural maps give an exact sequence.

PROOF. Suppose first that n D 2. As a1C a2 D A, there are elements ai 2 ai such that a1Ca2 D 1. The element x D a1x2Ca2x1 has the required property. For each i we can find elements ai 2 a1 and bi 2 ai such that. And Worst. ai Cbi D 1, all i 2: The product Q i2.ai Cbi /D 1, and lies in a1C. Q i2 ai , and play and pedagogy so. We can now apply the theorem in the case nD 2 to obtain an element y1 of A such that. y1 1 mod a1; y1 0 mod Y. These conditions imply. y1 1 mod a1; y1 0 mod aj , all j 1: Similarly, there exist elements y2; . ;yn such that. yi 1 mod ai ; yi 0 mod aj for j ¤ i: The element x D P xiyi now satisfies the requirements. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. It remains to prove that T. ai . We have already noted that T. ai . First suppose that nD 2, and let a1Ca2 D 1, as before. For c 2 a1a2, we have. c D a1cCa2c 2 a1 a2. which proves that a1 a2 D a1a2.

We complete the proof by induction. This allows us to assume that. T i2 ai . We showed above that a1 and. Q i2 ai are relatively. prime, and so a1 . The theorem extends to A-modules. THEOREM 1.15 Let a1; . ;an be ideals in A, relatively prime in correct spelling masters, pairs, and let M be an play and pedagogy essay, A-module. There is an exact sequence: This can be proved in the same way as Theorem 1.14, but I prefer to use tensor products, which I now review. Review of tensor products. Let M , N , and P be A-modules. A mapping f WM N ! P is said to be A-bilinear if. f .mCm0;n/D f .m;n/Cf .m0;n/ f .m;nCn0/D f .m;n/Cf .m;n0/ f .am;n/D af .m;n/D f .m;an/ 9=; all a 2 A; m;m0 2M; n;n0 2N: i.e., if it is best essays, linear in each variable. A pair .Q;f / consisting of an A-module Q and an A-bilinear map f WM N !Q is called the tensor product of M and N if any other A- bilinear map f 0WM N ! P factors uniquely into f 0 D ? ?f with ?WQ!

P A-linear. The tensor product exists, and is unique (up to a unique isomorphism making the obvious diagram commute). We denote it by M ?AN , and we write .m;n/ 7! m?n for f . Play And Pedagogy Essay. The pair .M ?AN;.m;n/ 7!m?n/ is characterized by each of the following two conditions: (a) The mapM N !M ?AN is A-bilinear, and any other A-bilinear mapM N ! P is of the caltech form .m;n/ 7! ?.m?n/ for a unique A-linear map ?WM ?AN ! P ; thus. BilinA.M N;P /D HomA.M ?AN;P /: (b) TheA-moduleM?AN has as generators them?n,m2M , n2N , and as relations. 9=; all a 2 A; m;m0 2M; n;n0 2N: Tensor products commute with direct sums: there is a canonical isomorphism. Review of tensor products.

It follows that if M and N are free A-modules3 with bases .ei / and .fj / respectively, then M ?AN is a free A-module with basis .ei ? fj /. In particular, if V and W are vector spaces over a field k of dimensions m and n respectively, then V ?kW is a vector space over k of dimension mn. Let ?WM !M 0 and ?WN !N 0 be A-linear maps. Play And Pedagogy Essay. Then. .m;n/ 7! ?.m/??.n/WM N !M 0?AN 0. is A-bilinear, and therefore factors uniquely through M N !M ?AN . Thus there is a unique A-linear map ???WM ?AN !M 0?AN 0 such that. REMARK 1.16 The tensor product of two matrices regarded as linear maps is called their Kronecker product.4 If A is doctoral dissertation help, mn (so a linear map kn! km) and B is r s (so a linear map ks! kr ), then A?B is the mr ns matrix (linear map kns! kmr ) with. 0B@ a11B a1nB. : : : . am1B amnB. 1CA : LEMMA 1.17 If ?WM !M 0 and ?WN !N 0 are surjective, then so also is. ???WM ?AN !M 0 ?AN. PROOF. Essay. Recall that M 0?N 0 is generated as an A-module by the elements m0?n0, m0 2 M 0, n0 2 N 0. By assumption m0 D ?.m/ for some m 2M and n0 D ?.n/ for some n 2 N , and som0?n0 D ?.m/??.n/D .???/.m?n/. Therefore the image of ??? contains a set of generators for spelling masters M 0?AN 0 and so it is equal to it.

2. One can also show that if M 0!M !M 00! 0. is exact, then so also is. M 0?AP !M ?AP !M 00 ?AP ! 0: For example, if we tensor the exact sequence. with M , we obtain an exact sequence. Play. a?AM !M ! .A=a/?AM ! 0 (2) 3Let M be an correct spelling masters thesis, A-module. Elements e1; : : : ; em form a basis for M if every element of M can be expressed uniquely as a linear combination of the ei ’s with coefficients in A. Then Am!M , .a1; : : : ;am/ 7! an essay, isomorphism of A-modules, and M is said to be a free A-module of rank m. Essays. 4Kronecker products of matrices pre-date tensor products by about 70 years.

1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. The image of a?AM in M is. P aimi j ai 2 a, mi 2M g ; and play and pedagogy essay so we obtain from the exact sequence (2) that. By way of contrast, ifM !N is deductive reasoning, injective, thenM ?AP !N ?AP need not be injective. For example, take A D Z, and note that .Z. m ! Z/?Z .Z=mZ/ equals Z=mZ. which is the and pedagogy essay zero map. PROOF (OF THEOREM 1.15) Return to the situation of the theorem. When we tensor the isomorphism. with M , we get an isomorphism. Personal. M=aM ' .A=a/?AM ' ! Q .A=ai /?AM ' EXTENSION OF SCALARS.

If A! B is an A-algebra and M is an A-module, then B?AM has a natural structure of a B-module for which. Play And Pedagogy Essay. b.b0?m/D bb0?m; b;b0 2 B; m 2M: We say that B?AM is the B-module obtained from M by best, extension of scalars. The map m 7! 1?mWM ! B ?AM has the following universal property: it is A-linear, and for any A-linear map ?WM ! N from M into a B-module N , there is and pedagogy, a unique B-linear map ?0WB?AM !N such that ?0.1?m/D ?.m/. Thus ? 7! ?0 defines an isomorphism. HomA.M;N /! HomB.B?AM;N/, N a B-module: For example, A?AM DM . If M is a free A-module with basis e1; : : : ; em, then B?AM is a free B-module with basis 1? e1; : : : ;1? em. TENSOR PRODUCTS OF ALGEBRAS.

If f WA! B and management indian banks gWA! C are A-algebras, then B ?A C has a natural structure of an A-algebra: the product structure is play essay, determined by the rule. .b? c/.b0? c0/D bb0? cc0. and the map A! B?AC is a 7! f .a/?1D 1?g.a/. For example, there is a canonical isomorphism. a?f 7! af WK?k k?X1; : : : ;Xm?!K?X1; : : : ;Xm? (4) Review of tensor products. TENSOR PRODUCTS OF FIELDS. We are now able to compute K?k? if K is a finite separable field extension of deductive reasoning writing, a field k and ? is an arbitrary field extension of k. According to play and pedagogy essay the primitive element theorem (FT 5.1), K D k??? for some ? 2K. Let f .X/ be the minimum polynomial of ?. By definition this means that the map g.X/ 7! g.?/ determines an isomorphism.

Hence K?k? ' .k?X?=.f .X///?k? '??X?=.f .X// by (3) and (4). Because K is separable over k, f .X/ has distinct roots. Therefore f .X/ factors in ??X? into monic irreducible polynomials. that are relatively prime in pairs. We can apply the Chinese Remainder Theorem to deduce that. Finally, ??X?=.fi .X// is a finite separable field extension of ? of degree degfi . Thus we have proved the following result: THEOREM 1.18 Let K be a finite separable field extension of k, and let ? be an arbitrary field extension. Then K?k? is application essay prompts, a product of finite separable field extensions of ?, If ? is a primitive element for K=k, then the image ?i of ? in ?i is a primitive element for?i=?, and if f .X/ and fi .X/ are the minimum polynomials for ? and ?i respectively, then. EXAMPLE 1.19 Let K DQ??? with ? algebraic over Q. Then. C?QK ' C?Q .Q?X?=.f .X///' C?X?=..f .X//' Yr. iD1 C?X?=.X ??i / Cr : Here ?1; : : : ;?r are the conjugates of ? in C. The composite of ? 7! 1??WK!

C?QK with projection onto the i th factor is. We note that it is essential to assume in (1.18) that K is separable over k. If not, there will be an ? 2K such that ?p 2 k but ? … k, and the ring K?kK will contain an element ? D .??1?1??/¤ 0 such that. ?p D ?p?1?1??p D ?p.1?1/??p.1?1/D 0: Hence K?kK contains a nonzero nilpotent element, and so it can’t be a product of fields. NOTES Ideals were introduced and studied by Dedekind for rings of algebraic integers, and later by others in polynomial rings. It was not until the 1920s that the theory was placed in its most natural setting, that of arbitrary commutative rings (by Emil Artin and Emmy Noether). Embed this document on your website. If you don't receive any email, please check your Junk Mail box.

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essay times Nicholas Handler, is a junior at Yale University majoring in history. Handler is play and pedagogy essay, active in social justice organizations and hopes to become a human rights lawyer. I never expected to deductive writing, gain any new insight into the nature of my generation, or the changing landscape of American colleges, in and pedagogy, Lit Theory. Lit Theory is supposed to deductive, be the class where you sit at the back of the room with every other jaded sophomore wearing skinny jeans, thick-framed glasses, an and pedagogy essay, ironic tee-shirt and over-sized retro headphones, just waiting for lecture to be over correct masters thesis, so you can light up a Turkish Gold and walk to lunch while listening to Wilco. That’s pretty much the way I spent the course, too: through structuralism, formalism, gender theory, and post-colonialism, I was far too busy shuffling through my iPod to see what the patriarchal world order of capitalist oppression had to do with Ethan Frome. But when we began to study postmodernism, something struck a chord with me and made me sit up and look anew at the seemingly blase college-aged literati of and pedagogy essay which I was so self-consciously one. Letter: Fortunately, College Has Changed. This is in regard to your college essay contest that took place last year. The essay entitled Fortunately, College Has Changed by Matthew Bender from the University of Arkansas has several factual errors and insinuations.

Then entire first and reasoning second paragraphs are neither chronologically or factually correct. Play And Pedagogy? How do I know that there are errors? Because I am Mervin Jebaraj, the person referred to in the opening paragraph. 1. A committee of students wrote the actual text of a proposed bill not a note. The idea began in November of personal essay 2007 and play essay not in the spring. 2. There was no staying up all night, and there was no on campus bbq. The committee obtained a meeting with Sen.

Madison after a lot of work and didn’t just pass a note to reasoning, her. The committee also spent months working with her and other legislators. to see the resolution passed. We don’t appreciate the trivialising narrative of our work. 3. The resolution never asked for the creation of socially aware investments, the options already existed. 4. The conference I went to play, was well after the divestment process and was to correct spelling, share ideas about divestment with others as opposed to receiving inspiration for play essay divestment.

5. There is an implication that I was skinny dipping and correct spelling masters smoking marijuana in Belize. Neither is true. I hold the New York times in the highest regard and hope that you will take this seriously. In the and pedagogy, future, I hope you check the. veracity of statements made before you publish them. Mervin Jebaraj, Research Assistant, Center for Business and Economic Research.

Liz Addison , 38, is a biology major whose goal is to personal, become a large animal veterinarian. She has trained a winning racehorse and is interested in American presidential history. Oh, the hand wringing. “College as America used to understand it is coming to an end,” bemoans Rick Perlstein and his beatnik friend of fallen face. Those days, man, when a pretentious reading list was all it took to lift a child from suburbia. When jazz riffs hung in the dorm lounge air with the essay, smoke of books essay a thousand bongs, and college really mattered. Really mattered? Rick Perlstein thinks so. It mattered so much to him that he never got over his four years at the University of Privilege. So he moved back to live in its shadow, like a retired ballerina taking a seat in the stalls. But when the curtain went up he saw students working and essay studying and working some more.

Adults before their time. Today, at the University of Privilege, the student applies with a Curriculum Vitae not a book list. Shudder. Frankie Thomas , is a junior majoring in cinema-television critical studies, with a minor in gender studies. Her immediate plans include dropping out at the end of the year to write and/or travel. She is a film maker and a blogger, with interests ranging from the social history of the Victorian era to doctoral usa, birdwatching to the novels of play and pedagogy Dawn Powell. I had the kind of college experience most people only writing, dream about. Charged by play and pedagogy, the atmosphere of management banks intellectual exploration, inspired by professors who pushed me farther than I’d ever imagined I could go, I made fascinating new friends at Skidmore; together we discovered Nabokov and Kafka, Citizen Kane and Dr. Strangelove, and our own literary voices. It was a three-week summer program.

I was fifteen. Now I’m twenty, halfway toward graduating from University of Southern California, and if I had a thousand dollars for and pedagogy essay every college student I know who Struggles With Depression…well, I still wouldn’t have enough money to pay my full tuition. But it would keep me going for a semester or two, assuming I didn’t lose my own struggle and drop listlessly out. As our SATs would have put it, “depression” is to “college campus” as “consumption” is to “Victorian orphanage,” and ours is a generation of wheezing waifs. Max Lance , 23, is a freshman at USC’s School of caltech books Cinematic Arts, majoring in writing for film and television. He hopes to and pedagogy, make his mark either with a “life-changing TV show” or by “marrying someone rich.” When I dropped out of college three years ago I would have completely agreed that college isn’t the best and worst essays, cultural experience that it was hyped up to be. As I return this September, I’ve realized that it’s a good thing it isn’t. I completely agree that college as America used to know it has come to an end, but I believe that schools have changed for the better.

The problem I had when I quit school the first time around was that I never adjusted to how schools have changed. I dropped out because of my mislaid expectations; the play, same ones that Rick Perlstein is nostalgic for. I’m going back to school because I’ve realized what the best and worst, college experience is like today and I’m now more than prepared to abuse it. Like nearly everyone in my graduating class, I attended higher education because that’s what we did next. College seemed more like 13th grade rather than a place where I would be opened up to radical people and ways of thinking. I spent my freshman and and pedagogy sophomore years doing what I needed to do to get good grades because that’s all I had done since kindergarten. And even though I worked hard to earn a 3.7 GPA, I dropped out of spelling thesis New York University because of a complete lack of passion for and pedagogy essay what I was studying (journalism, via process of elimination).

Travis Weinger , 21, is a senior majoring in history, with a concentration in war, revolution and social change. His minor is political science. And Worst? He is a founder of the Triton, a newspaper at UCSD, and of the Symposium, an on-campus discussion group. Rick Perlstein’s article, boiled down, is simply an extended version of the bitching that every generation hears from the one that preceded it: “Back when I went to school, we walked uphill in the snow both ways…” In sum, college mattered back when Mr. Perlstein went to it because that was when he went to it. Since college has changed from when he remembered it, he wants us to play essay, believe that it has somehow degenerated into personal prompts, irrelevance.

The vast majority of essay Perlstein’s complaints fit under the above rubric. Our college experience is spelling thesis, not as liberating as his was (no longer can we simply phone public intellectuals and bully them into visiting our dorms). Our activists are not as radical as his were (we don’t take over enough buildings). Our connection to the Sixties isn’t as strong as his was (our band members aren’t former revolutionaries). And Pedagogy? We are not as alienated from society as he was (we engage our world, not whine about it). Perlstein’s claim that his experience was in some way both richer and and worst harder than the next generation’s is an old one, and is continuously echoed by every generation. Like most complaints of this type, it is largely groundless and and pedagogy essay mildly insulting. Caltech Books? To respond to play essay, it bit by bit would validate his nostalgic whining to best essays, a degree it does not deserve. The Cultural Contradictions of and pedagogy American Universities. For the past twenty to thirty years, we have seen the great degradation of post-secondary education. Conventional wisdom suggests that the reasoning writing, problem lies simultaneously within the hands of the politicians and the students.

This narrative does not account for the history of college. Throughout the modern age, the and pedagogy essay, role college played in management banks, the national debate was minimal. To this date, there has only been one president with a Ph.D., and both The New Deal and Truman’s Fair Deal did relatively little for college and education in essay, general (with the dissertation, exception of the G.I. Bill). And even today, most candidates on play and pedagogy essay, both sides of the deductive essay writing, isle have the same prescription for college: the problem is lack of funding, therefore, the solution is to increase funding. It usually ends at and pedagogy that. In order to doctoral dissertation help usa, find the true crisis of college, we must first look at its true purpose.

A few months ago, Charles Murray wrote a controversial series of columns in the Wall Street Journal arguing, not that college had been written out of the play, national debate, but that its role is too great. Correct Masters? Essentially, too many people are going to college who did not need college, but instead needed vocational training. There are serious problems with his logic to be sure, not the essay, least of correct thesis which is his obvious IQ-ism. Essay? While it is true that college is in need of some serious reforming, focusing solely on caltech books, IQ will not solve them, for IQ is not the only purpose of college. For example, there are, what a professor of mine called, “latent overtones.” That is, those unexpected, and unintended consequences of college learning. For example, one might discover a great philosopher that he’s never heard of, or another collegiate finds that they enjoy a field of study which they did not expect.

But this is, of course, part of the intellectual journey of students. And Pedagogy Essay? College exists not, as conventional wisdom suggests, to best, change the culture. It exists to create a new breed of intellectuals. All politics aside, students should exit college not knowing simply what to think, but how to think. This is where Mr. Murray and and pedagogy I agree. Personal Essay? He hits the nail on the head when he describes the purpose of college, that college is created to train the elites to play, do their jobs. However, this purpose has been lost in a quagmire of watered-down curricula and fluff courses. And this brings us to the real problem of college: the searing anti-intellectualism of the youth.

Education is the single most important factor in the growth of our country. Specifically, higher education paves a future and provides opportunity for students that attend college and gives them a shot at caltech books a career. 50 years ago, college was strictly for play and pedagogy essay the elite, high class Americans. Now, it seems that every common household has at least one family member attend college. But with the help, increasing drop out rate today, students seem less interested in learning at college and their priorities change from their original goal of play and pedagogy graduating. Essay? The importance of essay education today is a growing factor because the correct spelling thesis, future of this country depends on essay, the students in college today. College is misunderstood by many incoming freshman.

All of the television advertisements and billboards encouraging students to attend college are used as bait to reel in student’s tuition. Parents encourage their kids to attend college after graduating high school because they want to see their kids have a shot at management thesis indian banks success. However, college is essay, not cut out for everyone. More freshman than ever are dropping out after their first year because college can be overwhelming through everything that takes place within campus boundaries. The pressures of college whether it’s to personal essay prompts, impress parents or maintain a high GPA grasps hold of many students while they are in college, freezing them from work and attending class regularly. Back in the 50’s and 60’s when college was becoming so popular, people attended college solely to play essay, improve their education and learn through the caltech books essay, college experience, in hopes of obtaining a career after graduation. Now, people attend college because their friends or girlfriend go there. Essay? Many people attend college just to party as much as possible. College can be misleading for teenagers fresh out of high school, and people who feel that continuing their education isn’t the most important factor in attending college should not apply. College matters because without a thoroughly educated society, America would fall to its knees and regress into deep depression. Jobs would flounder because the people applying for them wouldn’t get accepted without college degrees.

Pat Brown expanded university development in California in essay, 1966 to encourage people of every social class to attend college and gain a higher education. The reason for his rapid expansion was because the essay, number of deductive reasoning college students doubled from and pedagogy essay 1957 to 1967, and Brown decided in caltech, order to improve society and keep America running, more universities should be built to attract new students. However, in 1997, only 54 percent of students that attended college as freshmen graduated with a degree six years later, 30 percent not even finishing their freshman year. Once students enroll in college, dropping out play and pedagogy essay, is the worst decision they can make. The opportunity cost of dropping can be detrimental to a student’s financial standing. Dropping out also means dropping tuition, and correct spelling masters students are often left with debt to pay off depending on which year they dropped out. Entering in a low paying job, drop outs must slowly pay back student loans, which is why college is so important to stick to and graduate once enrolled.

The likelihood of students being able to pay off student loans quickly after graduating is much greater than the likelihood of a drop out paying off loans. Essay? Drop outs sometimes will only and worst essays, make enough money per paycheck to pay off previous college debts, not leaving any left over cash for leisure activities. Once choosing the decision to attend college, remaining in college is the most important decision a student can make, in order to and pedagogy, avoid living a below average lifestyle. Young adults are fed by change. Best Essays? No matter how resistant or welcoming I am to change, when all is said and done change sustains me. Two years as an undergraduate student at Fordham University have been made slightly easier by knowing this about myself, because college means change. Even with the and pedagogy, still shrinking cyber community and the ‘real world’ opportunities offered to many young people today, nothing can replace the rush of change attached to the college experience. College students are encouraged to make noise. When interviewed by Rick Perlstein for an article entitled ‘What’s the Matter With College” students were very vocal. Hamilton Morris, a New York bred college student, described a college experience where many students hate school “with a passion” and “don’t leave”. Perlstein writes that Morris’s feelings are proof of a “culture of enervation” which overwhelms many campuses today.

Instead of seeing what Perlstein describes, students without hope or the will to pursue their studies, I see Morris as describing a culture of restlessness. Correct Spelling? Students who claim to hate college but still do not leave are experiencing a kind of restlessness which comes with the package. Students experience change so quickly–changes of passions, opinions and interests. Play? They are bound to become restless, especially when the off-campus world is within arm’s length. I often smile to think the world is at my fingertips when I am surfing the internet, but the truth is my fingers are touching my keyboard, and I am planted in my kitchen chair drinking Diet Coke.

College offers me the thesis, opportunity to shake hands with the leaders of and pedagogy business, art, science and medicine–something the internet can not give me. College professors do not want students to doctoral dissertation, be excited about school and theory alone–they want them to take their passion into play and pedagogy essay, the world beyond the campus. Thesis? I am not writing this commentary for my school newspaper. And Pedagogy Essay? I am writing it for New York Times Magazine, a publication Journalism majors like me aspire to work for. College urges me to aspire, to voice my opinions, and yes, to change. The problem with colleges in the 21st century is convoluted with many deciding factors, resulting in management thesis banks, a more complex position for current college students to experience, unlike any previous generation of college students.

In my opinion, being a college graduate student and play one who has been involved in my school, I can honestly say that the biggest problem with our generation is the spelling, sense of nihilism, which is plaguing the our very core of our being. Play And Pedagogy? It is important to realize that this comes not only from writing college campuses, but the society in general; people just don’t care. If they do care and want to be involved, societal pressures, mostly economic, is what keeps them from being invoked with the spirit of the previous generations. There seems to be no sense of urgency when it comes to our generation. Nihilism will do that to play essay, everyone.

I also find it interesting that the people who do want to be involved do not necessarily know what to best essays, get involved with. In the 60s, it seemed to be clear cut what the problem was; racism, sexism, or the war in Vietnam. A contrast between the 60s generation and us now is that people do not what the problems really are. The mentality when speaking to college students; they seem to focus more on trying to get that 80K a year job then the socio-political issues affecting us. It is essay, evident that we value the dollar more so than we value the human struggle. So apathy also plays a role. It is important to realize that we must do something, otherwise everyone suffers. Sending your child to college is not an option in American society, and it’s hardly a privilege at that. In today’s fierce and essay prompts fast paced world it is a necessity For most parents, thought goes into how they will even fund such a venture within the and pedagogy essay, first few months of the child’s conception. College funds and savings bonds, money from relatives and graduation parties, this all gets stored until an caltech books, entire portion of that funding goes towards expensive college visits. Not only play essay, does the child want to go to spelling, college, that child has picked out 10 in which there is an orientation at and pedagogy essay each for prospective parents.

They want to see where their money is going, as well as where their child will sleep, learn, and become the successful adult they were meant to be. What is wrong with college? As a successful student at caltech books a prominent Chicago school, I, for one, have plenty of opinions on the matter. Let’s look at “our war” by first taking a retrospective glance at Vietnam. My father, a student at and pedagogy essay the time of Vietnam, was a conservative at a very conservative Indiana school. Help Usa? He still wore his GDI shirt most days of the play essay, week and talked highly of the camaraderie between fellow students. There were protests that were actually allowed on application prompts, his campus. When the students died in play and pedagogy, the Kent incident he remembers rallies against the war in their honor. He also remembers reading the names of the dead soldiers with the rest of his class, keeping in somber memory the caltech books essay, fight his country was in. Bands of students were scared, there was a draft in effect. Everyone had war on the mind and as those 18 year olds took on their first years of college, they had a lot more to worry about than where the weekend’s keg party was taking place.

They were learning, growing, and forming opinions on the world they were entering by knowing their current events and being passionate about them. Of course, without the internet, their local papers brought them more world events and less Lindsay Lohan. Being passionate about the world takes a certain naivety that forms when someone does not already have the opinions of others so easily accessible. The internet has taken so much of this away from current students. In my experience, you only play, have to make a choice on which websites to read. Looking at our war today, many students walk away from books it, choosing not even to recognize that it affects their daily world.

There are many more cliques, many more places to falter, and many more reasons not to care. Hold a pen in play and pedagogy essay, front of you and look at it; notice its size and color in particular. Now, slowly move it away until you have your arm fully extended. Deductive Reasoning Essay Writing? Notice anything different? Probably not, and that is play essay, how it should be. If we remember back to correct masters, middle school science class, color is partially dependent upon the angle that light hits an object. But we just moved an object, causing the angle to change from our perspective, and play did not notice any change in color. The pen also moved further away without any apparent change in size.

I forgot the intricate details that explain why this happens, something to caltech books essay, do with a portion of the brain that keeps our perceptions fluid . What I do remember, and will never forget, is how cool this all seemed and how much more there is to the world when you get past the play, surface. College is a pretty different place today than it was for my parents thirty years ago. Then again, so were the two worlds in dissertation help usa, which we were raised. Most kids in my generation were not raised in the Sandlot. We did not hang out at the malt shop after school.

And we definitely did not attend any sock hops (or if we did, best believe we did not call them that). And Pedagogy? Instead, we started out playing on jungle gyms with woodchips and protective rubber flooring underneath. Eventually, we found ourselves being chauffeured to organized baseball practice, in a minivan. By high school, the importance of getting into a good college had been seared into us and serious attention had to be allocated toward after-school activities and other kinds of essay enriching events to play and pedagogy, make sure that we were “well- rounded”. Here’s a fun game that anyone my age can play: ask your parents what they got on their SATs. If they can, you win! Basically, it is like hitting the lottery, since your parents have to be like one out of a million.

High school students in caltech books, the 60’s did not pay $1,000 for an SAT class and play and pedagogy definitely did not go to any Independent College Consultants. As Mr. Perlstein stated, college was seen as a place sort of apart from the caltech books essay, rest of the world. Kids went there and and pedagogy essay were met with new people, ideas, and situations. Back then, as I understand it, college was not seen as a stepping stone or a rung on the ladder. You did not go with the mindset that it was simply a means to end, a place to dissertation help, simply collect good grades and then experience the ‘director’s cut redux edition’ of college admissions in the form of graduate school, an internship or a job. Why College Matters: A Response to “What’s the Matter With College”

I suppose I should begin by saying that I don’t go to a real college. I mean, I don’t feel like I go to play and pedagogy, a real college. I don’t take real classes. I don’t live on a real campus. I’m a music major and doctoral usa attend the Peabody Institute in Baltimore, Maryland. Peabody is an established music conservatory, one of the play and pedagogy essay, schools of Johns Hopkins University (despite what I say about thesis, it not being a “real” school). In his essay, Perlstein is making it seem that today’s college undergraduates and the ideals we pursue are somehow deficient. That we’re missing out. He’s especially concerned that we’re nothing like the students of the 60s and 70s. He’s right about that, but that is nothing to be ashamed of. We’re students who want (or carry) the iPhone.

We are environmental activists. We’re more technologically savvy than Perlstein’s generation. Play? We get our information and communicate in a totally different way. We’re amazing jugglers. We’re a new breed. It is interesting to caltech essay, read that the defining issue for play essay the 1966 California gubernatorial race was college. Management Thesis Banks? For my sake, and I’m sure for and pedagogy essay the sake of essay a lot of my peers, I wish it were still that way.

College sounded romantic and fun. My friends argue that things have changed in the past 40 years, and that there are bigger fish to fry. The war, for example. Play And Pedagogy Essay? Making a living once college ends. When they start complaining, however, about classes and stress, I ask them, “aren’t there bigger fish to fry?” at which they sigh outwardly, roll their eyes, and throw their hands up in the air.

I understand where their frustration lies. We still feel young in the scheme of things, and not ready to plan out our lives after college. It feels like we’ve been doing nothing but planning since freshman year of high school. Who has time to worry anyway? Right now, I am worrying if I have enough money to pay the college application personal essay, rent this month. Many of my classmates worry how to pay for the next semester.

To be honest, when it came to play and pedagogy, college, most of us never really had a choice. Where I grew up, in caltech essay, Greenwich, Connecticut, there was never the option of play and pedagogy “college vs. no college.” The choice was “Ivy League vs. state school,” or something along those lines. The whole getting-ready-for-college experience was important. As you thumb these pages, reader, loyal subscriber, conscious citizen with an appetite for inquiry and thoughtfulness, or may I say fellow American, you tell yourself that you want to sample a young student’s intellect. Certainly I do believe that my own college experience has been important, even critical, to thesis indian, my life and to my thoughts here and now, but young and play and pedagogy impressionable does not necessarily partner with a tame, meaningful sense of hindsight… My college experience has fostered some growth. But for the nation? Lend me some relevance. Am I to best, accurately describe my confusion with you over coffee to tell you how this all breaks down–I fit in the puzzle and play and pedagogy I’m one of the corners, right? Politics. We don’t have movements, and we don’t have causes.

A choice between higher education and higher purpose has been made; show me one text message, fellow student, that you have wanted the whole country to read. Children live at school. Especially if they don’t have much of management thesis indian a home life to live in the afternoon or evening, kids live and and pedagogy essay learn at school. College isn’t so different, only first graders aren’t expected to shape up all by themselves when they appear to be wasting time. Oh, college students aren’t either?

Pity. I guess higher education isn’t all that important. Personal? Maybe the problems of higher education are just fronds atop a mirage of public schooling. Talk to Herbert Kohl, Jonathan Kozol, John Taylor Gatto, men who are trying to wake this country up, and play they’ll show you what’s happening to my younger brothers and sisters. Content in the shade, college students loaf, while in more dangerous environs, under the pretext that they are to learn, children sit down in their desks each morning in college, the arms of a crumbling system. In college, we choose to sleep in, not to participate, excel, regress, etc. If higher education is important to the nation, why don’t more people act like it? Better yet, if education is so important to the nation’s future, why is play, it neglected? Important as it is, I feel proud to remember the words of Thomas Jefferson, who often can remind us of politicians’ and citizens’ true responsibilities: “It is highly interesting to college application personal essay prompts, our country, and it is the duty of its functionaries, to provide that every citizen in it should receive an education proportioned to the condition and pursuits of his life.” He speaks to play, the politician, tells him to best, take a good look at his fellow Americans.

What sort of education will he provide to match the essay, condition, the quality of life? If the quality be poor, will he stick to poor schooling until lifestyles rise to the occasion? Try downtown Anywhere, where elementary schools have been forced to remove social studies and arts in favor of apparently year-round test preparation, for standards in English and prompts mathematics. The “need to know” world and the world of standardization are one in the same, and columns of darkened bubbles are in no short supply, though there’s still a need to live. The Problem with College: Why We No Longer See Ourselves As “Part of” a Community. One anomaly of American society is and pedagogy, that our universities play only a marginal role in our culture. In other nations, like France where intellectual life is doctoral dissertation, not centered on their institutions of education, this may come as no surprise, but the virtues of American universities are indisputable. Academics wonder why they are allowed to play essay, be the nation’s intellectual leaders, but not its leaders, or even advisors, in the political or ethical arenas. Some are resentful of the mainstream society, thinking it apostate, as though they were priests of some outworn creed, but this alienation, which has developed in tandem with the evolution of academia, did not come because the reasoning writing, society rejected the university as a social or moral authority, but rather because the university ran out of the energy it took to function in this role. This occurred, at least partially, because those of us in college found that the values we shared were not strong enough to unite us. From the time of Plato, the purpose of the university has not been to represent the society or culture in which it exists but to pursue truth.

Most academics, who may disagree on what truth is in essence, would agree that it is a noble and worthy objective. Play And Pedagogy Essay? And, since truth is their goal, many of them think themselves justified in being alienated from mainstream society. Reasoning Writing? This does not mean their views are homogenous; I can testify that, at play essay the University of Idaho (to name one example), the best and worst, politics of professors in the College of Business are not shared by the English instructors; but what the two departments have in common is their distance from America’s political center. And Pedagogy Essay? This is doctoral help usa, largely because specialists in and pedagogy, any field, whether that field is indian banks, philosophy or political science, tend to feel invalidated if anyone could reach the same conclusions that they do. Play Essay? It is a telling fact that, at least until recent years, there was a higher percentage of deductive reasoning self-described Marxist literary critics than blue-color workers. Nonetheless, this desire for essay academic innovation benefits the university in that it makes professors’ research original; it is for this reason that, whenever universities are rated according to prestige, the United States constantly is found to have the greatest number of correct masters thesis prestigious institutions. Even so, there is another facet to a professor’s job, teaching. And Pedagogy? This requirement creates a dilemma for many professors: their strenuous educations and meticulous research has caused many of them to become opinionated, but, at the same time, they need to keep their students pacified while educating them in accordance with principles which the management indian, students may not share. Play And Pedagogy Essay? Thus, they (and the students) learn that it is easier to ignore worldview-related issues.

In searching for reasoning essay writing the least common ethical denominator among the group, the instructors and and pedagogy essay the instructed clandestinely agree that the values which they hold as specific to their Weltanschauungs do not apply to everyone, and, if they do, the value of placidity applies even more. As Allan Bloom wrote in 1987, “[A]lmost every student entering the correct, university . . . says he believes . . . that truth is and pedagogy, relative” (1). While this outlook may work in as far as it prevents conflicts, it is an ineffective communal bond. This is because the reasoning writing, values of the classroom are provisional and–most students cannot help but feel–artificial. They haven’t the and pedagogy essay, power to masters, unite the students and faculty in a community, which requires common interests and mores.

In July, The Magazine published What's the Matter With College, an essay by the historian Rick Perlstein, online and invited college students across the United States to respond. Some 600 undergraduates did -- many agreeing with Perlstein's assertion that college as America used to understand it is coming to an end, many dismissing his argument as so much nostalgic pap, still others taking the play and pedagogy, occasion to critique higher education from an insider's perch. To continue the conversation, we're featuring the winning student essay and four runners-up, and posting another 450 of the entries in a searchable format. (The other entries were withdrawn by their authors or did not follow the contest's rules.)

Here Are The Most Ridiculous Laws In Every State. This iconic (read: horrifying) scene in last year's megahit Wolf of and pedagogy, Wall Street shows Jordan Belfort and company tossing a little person at a Velcro-covered target. Fortunately for Leo's character, they weren't in college application essay prompts, the Sunshine State. In Florida, owners of and pedagogy, commercial establishments (where alcohol is sold) may be fined up to $1,000 if they participate in or permit any contest of dwarf-tossing. The law makes sense, but the fact that the state has to college application, spell it out might make you scratch your head. We've all heard urban legends and rumors about absurd laws in America, but you can't believe everything you read on play and pedagogy the Internet. Sites like dumblaws.com €” which rarely link to prompts, states' current statutes or may misinterpret them €” only perpetuate the myths. We decided to undertake some legal legwork and identify the strangest statute still on the books in every state. Alabama residents commit unlawful bear exploitation if they purchase, possess, or train a bear for the purpose of bear wrestling. It's a Class B felony, punishable by a fine, confiscation of the bear, and restitution to a humane society for animals.

Apparently, man versus bear wrestling took hold in the early 1800s €” a byproduct of and pedagogy essay, Greco-Roman displays of masculinity. A person cannot get drunk in a bar and reasoning, remain on and pedagogy the premises. (Kind of defeats the purpose of a bar, doesn't it?) The statute states an intoxicated person may not knowingly enter or camp out dissertation usa, where alcohol is sold €” so maybe if you're inebriated enough, you can get away with it. In 2012, police in Alaska reportedly started aggressively enforcing the law, sending plainclothes officers to play, bars to dissertation help usa, identify and arrest suspects. No one can feed garbage to pigs without first obtaining a permit, which requires annual renewal. You can, however, swap out the and pedagogy essay trough for doctoral dissertation, a waste basket if the swine are raised for essay, your own consumption. A pinball machine can't give more than 25 free games to a player who continues to win. Some restaurant-gaming chains €” like Chuck E. Writing! Cheese €” are exempt from certain anti-gambling statutes because they award free games, toys, and novelties that don't constitute an exchange of play, valuable things. A frog that dies during a frog-jumping contest can't be eaten. This health code likely made its way into the books to protect competitors at doctoral dissertation help the Calaveras County Fair and Frog Jumping Jubilee, an play essay 80-year-old tradition in the gold mining town of Angels Camp. Each year, tourists and experienced jockeys compete to and worst essays, see how far their bullfrogs can leap. You have to get a permit to modify the weather.

Weather modification is not only possible, but it's actually a lucrative business. In select states, it's legal to perform activities that produce artificial changes in the composition or behavior of the and pedagogy atmosphere €” such as burning silver iodide, which carries into the clouds to stimulate rain. The permit requirement ensures minimal harm to the land and maximum benefit to the people. In Connecticut, letting other people copy your academic work isn't just a no-no in school €” it's also illegal. The general statutes explicitly prohibit selling a term paper, essay, dissertation, etc . at any education facility supervised by the state. The punishment isn't specified, but it's probably more than detention. It's a Class B misdemeanor to sell, barter, or offer the fur of deductive writing, a domestic dog or cat. Any products made in whole or in and pedagogy, part from the hair, say a coat of 101 Dalmatians, also result in a fine of $2,500 and a ban on reasoning essay writing owning a dog or cat for 15 years after conviction. Grumpy cat is still grumpy though. Owners of play, commercial establishments where alcohol is sold may be fined up to $1,000 if they participate in or permit any contest of dwarf-tossing.

In 1989, Florida outlawed this Australian bar fad of caltech essay, tossing little people when it caught on in southern parts of the state. A Florida state legislator tried to and pedagogy essay, repeal the law in 2011 but wasn't successful. Those engaging in llama-related activities, such as riding, training, or goofing around at a county fair or performance, are accountable for any and writing, all personal injuries incurred. Play And Pedagogy Essay! The llama professional is immune from liability for harm or death with few exceptions. Injured participants have a shot in court if they were just spectating from an management indian banks authorized area.

The urban beautification initiative dates back to and pedagogy essay, 1927, when an all-white circle of Hawaii's power wives created the Outdoor Circle Club and lobbied for the ban. Today, the group exists as a watchdog on ever-threatening, jumbo-size advertisements. Cannibalism is writing, strictly prohibited and punishable by up to 14 years in prison in essay, Idaho. But it's okay to willfully ingest the flesh or blood of a human being in life-or-death situations, if it's the only apparent means or survival. The only state to declare cannibalism illegal, Idaho erected the ban in 1990 as a reaction to spreading fear that eating humans would pop-up in ritualized practices. Urban legend says it's a crime to possess more than $600 worth of salamanders. (That's 75-plus salamanders, according to fair market value.) In reality, it's illegal to doctoral help usa, keep any variety of aquatic life in excess of $600 in Illinois if it was captured or killed in violation of the state's law.

Liquor stores can't sell cooled water or soda, but they can sell uncooled soda. Essay! In fact, they can't sell milk either. The code specifically lists what types of beverages (and at doctoral dissertation what temperatures) permit-holding businesses can have in and pedagogy, stock. Anyone trying to pass off margarine (or oleo or oleomargarine) as real butter is guilty of a misdemeanor. The great butter vs. And Worst! margarine battle rages on though, so we understand Iowa's desire for transparency.

Liquor may not be sold by the glass in 26 counties. In Kansas €” a state that outlawed alcohol sales until 1948, a full 15 years after Congress repealed Prohibition €” individual counties may, by play and pedagogy, resolution or petition, prohibit the sale of booze in public places where 30% or less of their gross comes from the sale of food. There's no place like home to get tipsy. Every legislator, public officer, and lawyer must take an management banks oath stating that they have not fought a duel with deadly weapons. When it entered the essay Kentucky Constitution in management thesis indian banks, 1849, the law was meant to deter men who might aspire to public office from participating in the once-rampant Southern tradition.

Some evidence suggests, however, that trial-by-combat might technically be legal on a federal level even today. According to play and pedagogy, the public health and safety codes, this Creole stir-fry, made with rice, meat, and vegetables, may be prepared for public consumption in the open, using iron pots and wood fires. An early version of the chance game of Bingo, called Beano, is legally regulated in this New England state. Best And Worst! The legal rules dictate that a person conducting or assisting in the conduct of the game may assist players by playing their cards while they take a restroom break. This allowance does not apply in high-stakes Beano, which apparently, is also a thing. A person who sells non-latex condoms by means of a vending machine is guilty of a misdemeanor and subject to a fine up to $1,000. Whether you're in and pedagogy, Gillette Stadium or Fenway Park, you'll probably never hear just half of the Star Spangled Banner. Singing or playing the national anthem other than as a whole and separate composition is punishable by a fine no more than $100. You'll pay the same price for dancing (at all) to it, too.

A statute on the books since 1931 makes adultery a felony €” punishable by a maximum of four years in prison and a $5,000 fine. In 2012, Portage police Sgt. James Myers was fired for on-the-job misconduct, including allegedly cheating on his wife and furthering a relationship with a local waitress using a city-issued cellphone and email account while on books essay the clock. He was neither fined nor imprisoned, suggesting Michigan doesn't take the law too seriously. In Minnesota, any game in which participants attempt to capture a greased or oiled pig is illegal. The same laws also prohibits turkey scrambles. Let's assume legislators were more concerned with animal cruelty than human stupidity. Using profanity in front of essay, two or more persons in a public place might land you in the county jail for up to 30 days. Or you could pay a hefty fine to the state swear jar, no more than $100. While this law appears to caltech books, be a direct assault on the First Amendment, it's thought to have been conceived in order to protect the essay public.

If any bull or ram over the age of 1 year old runs rampant for more than three days, any person may castrate the animal without assuming liability for damage. Three town residents must attest in writing that the essay animal is loose, and its owner must fail to reclaim or confine the beast after notice is given. Guiding sheep onto play and pedagogy a railroad track with intent to injure the train, not the sheep, can stick you with a whopping fine up to and worst essays, $50,000 and play and pedagogy essay, a stay at the state prison not exceeding five years. The locomotive corporation or owners of the railroad must be harmed, in addition to Dolly and friends. No person who is afflicted with a venereal disease can marry. Application Personal Essay Prompts! While it's nearly impossible to enforce, this health code could prevent marital bliss for more than 8,000 Nebraskans who reported cases of chlamydia or gonorrhea to play and pedagogy essay, the Centers for Disease Control and Prevention in best and worst, 2012. In the only state where prostitution won't get you arrested in essay, most counties, using x-rays to determine shoe size could.

That may sound strange, but a device with that exact purpose actually exists: a shoe-fitting fluoroscope also known as a pedoscope or foot-o-scope. With the knowledge that exposure to radiation harms people in awful ways, this practice went by the wayside. Caltech Books Essay! But at essay one point, the state had to books essay, spell it out. Anyone who didn't get the message is play and pedagogy, guilty of a misdemeanor. As of 1973, it's illegal to carry away or collect seaweed at night. Breaking most of the management thesis indian banks general provisions about fish and game will land you a violation €” with an and pedagogy essay unspecified punishment. Seaweed is routinely used in fertilizer and animal feed. It's also considered a good source of alginate, which gives liquid solutions a thicker texture (think Jell-O).

Just last year, Maine and its fisherman grappled over a similar set of regulations. In the college prompts Garden State, anyone wearing a body vest a.k.a. bullet-proof armor while committing murder, manslaughter, robbery, sexual assault, etc. is guilty of another crime. And attempting to flee while wearing this unlawful piece of clothing, after committing the initial act, bumps up the crime from third-degree to second- or first-degree. As stated in the New Mexico Constitution, idiots can't vote in state elections. Traditionally, the word idiot has referred to someone (rather politically incorrectly) mentally disabled or with an IQ below 30. But read the comments section on any website, and you'll see the term is more loosely applied now. The vagueness in these statutes could cause problems someday. Currently, Kentucky, Mississippi, and Ohio uphold the same idea in their constitutions. Even if you have a mental disability though, if you understand what voting means, federal law protects your right to cast a ballot, according to the National Alliance on Mental Illness. It's unlawful for three or more people wearing masks to gather in public for a demonstration or a march. Originally enacted in play and pedagogy essay, 1845, it entered the books when local tenant farmers disguised themselves as Native American and attacked and caltech essay, killed their landlords.

The law includes exceptions for masquerade parties and play and pedagogy essay, similar events. For certain organizations in North Carolina, bingo games can last only up to doctoral dissertation help usa, five hours. Play And Pedagogy Essay! The state's administrative code even contains a few more explicit restrictions on dissertation usa the game: only one in a 48-hour period and no more than a $500 prize. Our best guess as to the motivation behind this law? Retirement homes needed to play essay, crack down on geriatric bingo sharks. All members of college application personal prompts, North Dakota's Dry Pea and Lentil Council must be citizens. The organization was created in play and pedagogy essay, 1997 to to promote the dry pea, lentil, chickpeas, lupins, and and worst essays, fava bean industries, and the legislature clearly didn't want someone with just a green card wielding all that power.

A national version of the Dry Pea and play essay, Lentil Council also exists. Caltech Books! But North Dakota obviously decided it needed a more state-focused group. Every operator of an play essay underground coal mine must provide adequate supply of correct masters thesis, toilet paper with each toilet. This law clearly makes sense, but the fact that it exists at all raises some questions about play and pedagogy essay, basic human decency.. According to best, the most recently updated version of the Oklahoma statutes in play, 2013, McCarthyism is alive and caltech, well. We quote: It is essay, here now found and correct masters, declared to be a fact that there exists an International Communist conspiracy which is committed to the overthrow of the government of the United States and of the several states, including that of the play and pedagogy essay State of Oklahoma, by force or violence . In Oregon, leaving a container of best and worst, urine or fecal matter on essay the side of the road is a Class A misdemeanor. Best! And you can't throw it from the vehicle either.

Again, we understand the logic. But who tried to leave urine or excrement on play essay the side of the road in the first place? Human trafficking in general violates too many international laws to count. Spelling Masters! But Pennsylvania felt the need to specify that you can't barter a baby. But if you do find yourself swapping goods or services for your precious bundle, it's only a misdemeanor, which is usually punished less harshly than felonies. Rhode Islanders who bite off someone else's limb will face no more than 20 years in prison (but no less than one) €” but only if they maimed the victim on purpose. If you fall and play, your teeth accidentally dismember somebody, you will have a legitimate defense. Don't worry.. A male over the age of 16 can't seduce a woman by falsely promising to marry her. If found guilty, he'll be charged with a misdemeanor, fined at the court's discretion, and/or imprisoned for no longer than one year €” with a decent number of best and worst essays, exceptions.

For example, if the woman was already married or considered lewd or unchaste (which the law doesn't define), the court can't convict the play male of the misdemeanor. The offender will also walk if no one can corroborate the woman's testimony. And no law exists with the masters gender roles reversed. Agricultural producers may set off fireworks and and pedagogy, other explosives to safeguard their sunflower crops. Crows and other birds can wreak havoc on a blossoming field, and pyrotechnics are farmers' first defense €” so long as they're not used within 600 feet of an occupied home, church, or schoolhouse. If you do, the fish and wildlife commission will charge you with a Class C misdemeanor (punishable by fine only.) White deer, as people often call these mammalian anomalies, are extremely rare. Only about deductive reasoning essay writing, one in every 30,000 deer is born albino. Some even consider the animal the play essay modern unicorn and believe it has magical powers. In Texas, people wishing to caltech, run for office must acknowledge the Supreme Being. Play! If not, they could be subjected to religious tests.

In other words: No atheists allowed. In Utah, no one may hurl a missile at a bus or bus terminal €” except elected or appointed peace officers or commercial security personnel. Anyone outside those positions is guilty of masters thesis, a third-degree felony. The Vermont legislature created a law that prohibits outlawing clotheslines €” proof that governments don't always abuse their powers. Essay! The same statute also states that no law can ban solar collectors, listing both items as energy devices based on renewable resources. Except for married couples, sex is deductive reasoning essay writing, completely banned in Virginia. No matter your age or your partner's, breaking this law results in a Class 4 misdemeanor. Doors to and pedagogy essay, nearly all public buildings must open outwardly. Anyone who violates this will face a misdemeanor charge.

The statute does explain why though: to avoid congestion during emergencies, like fires. Don't attempt to substitute a hunting dog for a ferret in West Virginia. Anyone who hunts, catches, takes, kills, injures, or pursues a wild animal or bird with a ferret will face a fine of no less than $100 (but no more than $500) and no less than 10 (but no more than 100) days in jail. Not to college application, stereotype, but in play, Wisconsin (also known as America's Dairyland), many different kinds of masters, state-certified cheeses (Muenster, cheddar, Colby, Monterey Jack) must be highly pleasing. In Wyoming, you can't cut, sever, detach, or mutilate more than one-half of and pedagogy essay, a sheep's ear. Violations are felony offenses, punishable by up to essay, five years in prison. But less than one-half? Totally fine.

And if the sale document or title approves said mutilation, go ahead then. SEE ALSO: Here's What All 50 State Names Actually Mean. Recommended For You Powered by Sailthru. Here Are The Most Ridiculous Laws In Every State. This iconic (read: horrifying) scene in last.

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