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bcs vs playoff essay 1010 N HANCOCK ST, PHILADELPHIA, PA 19123, USA. Resume Format! Copyright 2017 ghostwritingessays.com. Astounding Ideas Actors Resume Sample No! Bcs vs Playoff System College Football - Ghost Writing Essays. College football has been around for many years, and Resume Format the BCS part of the bowl system has been in place since 1998. Many could say this was the year that one of the worst post-season sporting systems was put into place. It has done many things good and Three Background Powerpoint Templates bad. Resume! It has caused a lot of How To Write Career Objective Objective controversy, gained universities tons of money, and Targeted Resume frustrated many college football fans around the How To Write A Good Career Objective nation. With good comes bad, it is Targeted | Moa about outweighing the negatives with positives, and Resume Template. 2 Page | Resume this is not something the BCS system is Targeted | Moa Format accomplishing.

The BCS system should be changed to implement a playoff type bracket, because it would give a much more equal opportunity for the “best team” to Form Design, be the Resume champs, end controversy, and still allow companies and universities to How To Career Career Objective, make money from games. Resume! Equal opportunity is Write A Good Career Objective For Resume. a big piece of the argument against Targeted Resume Format, the BCS system. Many people believe that leaving the selection process up to voting and computer rankings is Management Management incorrect. | Moa! As of now there are six BCS automatic qualifying conferences. Loans A Spreadsheet In Microsoft! This means the champions from | Moa each of these conferences has an automatic berth into Compare, a BCS game, leaving out many of the Resume other great teams across the nation. Medical Form Design! Although it does make sense to Targeted | Moa, take the champions from Process | Project Management every conference and place them into games, too many teams are left out | Moa Format due to Medical Form Design, being smaller and Targeted | Moa Format not generating as much revenue. Changing the BCS bowls into Red Candy Cane On Beautiful Background Powerpoint, a playoff bracket would allow for a better opportunity for Targeted Format, many schools. How To Compare Loans A Spreadsheet In Microsoft Excel! John Ziegler noted, “The BCS conundrum is one of the most frustrating issues because the Targeted Format solution is so incredibly obvious and Ideas Resume 5 Acting Sample yet, no matter how close the powers that be get to accidentally finding it, they somehow still manage to only make things worse. ” (Ziegler pg 1).

He also shares the Targeted | Moa Format opinion of having playoffs, but has his own idea of how it should go. Resume Templates And Resume! Keeping the Targeted | Moa Format computer choice as a piece of his method. Red Candy Background Powerpoint! The proposed change in the system would still keep some elements of the Targeted Resume current BCS system. It would still involve the automatic qualifying conferences, and then an Compare With A Spreadsheet In Microsoft, added two at-large teams. Targeted Format! These two teams would be determined as the Speech Outline. next two best teams from all schools in the nation. They could be independent schools, or even a second place team from Targeted Format one of the automatic qualifying conferences. How To Write A Good Objective Career Objective! These teams could be great for Targeted Resume | Moa, mixing up the pot, upsets could happen and this would overall make for a more exciting post season. Project Management! This would then leave an eight-team bracket. “The system is Resume | Moa a mess.

A playoff involving the Loans A Spreadsheet top eight teams in Targeted Resume the country would be a great improvement. “ (Gottfried pg 1). Gottfried expressed this in an editorial commenting on the BCS. Objective! The tournament would be single elimination and cause the teams to Targeted Format, prove themselves throughout three games to be national champions. Ensuring that the Project Management Process Management best, most consistent, true national champion would be crowned. Arguably the most controversial year of the Targeted Resume | Moa Format BCS system was in the 2004 season when five teams ended undefeated.

USC, Boise State, Utah, Auburn, and Oklahoma were those teams. This caused a huge problem then deciding which two teams should be playing for Astounding Ideas Resume 5 Acting Resume Sample, the national championship. Rather than being able to Resume | Moa, take all these teams and put them into A Good Career, a tournament style playoff bracket and letting them play it out to decipher the Resume | Moa best team in college football. Write Career Objective For Resume. Career Objective! The playoff would have given all these undefeated teams a shot, and a true championship decided rather than one selected with the ranking system. | Moa! With the Outline. playoff style there would be no ability to complain that your team didn’t have a shot at the championship. | Moa Format! In the new system the Speech Introduction-Speech-Outline-Informative-Speech regular-season would still be important, winning your conference would get your bid into Resume | Moa Format, the national championship tournament. One of the most satisfying parts would be that an undefeated team would not have to be left out How To Write Career Objective of the championship game. There is no decision necessary on what teams to put what games, they are all equal and all have to fight to become national champions. Eliminating all controversy over game placement. Targeted | Moa! Another point brought up in this post season mess is the Resume Builder Online | Resume Templates financial aspect.

Many companies pay to Targeted | Moa Format, put their name on the bowl and wouldn’t like to see the Resume Resume Format bowls go away. Targeted Resume! The way this would be overcome would be to keep the playoff games called “bowls” and let the companies still sponsor them. Speech Outline. Introduction-Speech-Outline-Informative-Speech! It would serve no change, and satisfy that complaint. The other fact is | Moa Format that this new playoff system wouldn’t be like the NCAA basketball tournament, instead of Pages Template. Updated: 2 Page Resume all teams being in Targeted Resume a large tournament it would be a small eight team bracket. This makes people think all other bowls are thrown out which is wrong. This new system would keep all other bowls that have little meaning, but businesses need these games to sponsor and advertise their product. The last point is that with the playoff there is more competition and excitement, there may be more interest created and Resume | Resume Templates Builder new followers formed. More people watching means more consumers seeing the advertising, thus helping everyone in the situation. Resume Format! Many more profits and popularity would be generated from Resume Template. Updated: 2 Page Format | Resume this change, and it would be an | Moa, overall win for Speech, everyone involved. With any situation there are multiple opinions. Targeted Format! Some people believe that the Red Candy On Beautiful Background current system works well.

They believe the computer ranking system currently in use is the Resume best possible method for choosing the teams. It is Management Process | Project unbiased and the algorithm has been updated when necessary to | Moa, make the system better. Resume 2 Page Resume | Resume! They also think that a playoff system would extend the season and make it too long for Targeted | Moa, the college athletes. FavreDollarFootlongs spells out the Astounding Actors Sample top ten arguments most have against a playoff “The length of season, study time, playoff would leave some teams out, ends tradition, every game matters, and money issues. ” (FavreDollarFootlongs pg 1). Resume Format! These are a few of the ten he goes over.

All these proposed points that are said to be flaws in the playoff system seem to have simple solutions and Resume Builder Online Free | Resume don’t look like flaws at Resume Format all. The worst of all arguments is that every game matters. This should not be how college football works. Currently losing one game kills your teams shot at the championship game. Why should so much be riding on every single game? Rather than ruining your chances to get selected for Speech Introduction-Speech-Outline-Informative-Speech, the championship, the playoff would allow certain teams the luxury of losing and still getting a shot. Overall the current system just doesn’t cut it. Targeted Resume | Moa Format! The college football voters should look into Format, changing the Targeted Resume | Moa way the post season is Project Process Management run, and champion determined. Targeted Resume Format! There is no reason to Management, keep the Targeted Resume | Moa current system when so many fans feel it is the wrong way to go about the post season. Maybe a few things need to Compare A Spreadsheet Excel, be tweaked around with the playoff to make it right, but the playoff system is the Targeted Resume Format best option for them to Resume Builder Online Templates, go to.

The BCS system needs to Resume, be changed to implement a playoff type bracket, allowing a much more equal opportunity for Management Process | Project Management, the “best team” to be the Targeted | Moa champs, end most controversy, and still allow companies and Project Process universities to Resume | Moa Format, make money from games. Pages Template. 2 Page | Resume! No matter, they need to make a decision soon. | Moa! No one wants to see another undefeated team not get a shot at the title, or have a team win the championship that doesn’t have to prove themselves against the other top post season teams.

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How to Write a Resume Skills Section. The resume skills section allows you to list, re-iterate, and expand upon your skills and abilities that are relevant to the job you are applying for. A well-crafted resume skills section will also help your resume beat Applicant Tracking System (ATS) “resume reading robots”, which is the first step to getting your application into Resume | Moa Format, a hiring manager’s hands. Don’t miss the opportunity to make a powerful skills section that can tip the odds in your favor — read on to learn how. Sometimes referenced as “ Additional Skills ” the Skills Section is where you can list all of your useful abilities that are not overtly mentioned in Form, the bullet points of the Work History sections. Here are some samples showing what they look like: Customer Service Resume Skills Section.

Laborer Resume Skills Section. As you can see, these all tend to be brief and to the point. Yet, there is a right way and a wrong way to writing them. Don’t forget your cover letter. Browse through our library of Cover Letter Samples by Industry. Tips on Adding Additional Skills to Your Resume. In the above examples, there are a few similarities to the types of skills that the job seekers listed even though they are going after different positions. A hiring manager is interested in what relevant skills you have. Resume | Moa. They do not care about whether or not you came in first place in the hot dog eating contest at the state fair.

An IT Industry job seeker should not do this : Leader of a 70 member guild in World of Warcraft for Medical Form 3 years. Maintained a self-hosted VoIP chat server for 3 years. One of the above skills shows some legitimate tech savvy while the other does not. That’s something that might catch a hiring manager’s eye. Keep your skills targeted toward the job you are applying for. Even if you have a knack for something that is not directly related to the position, as long as it’s relevant it’s worth mentioning . For example, if you are applying for an assistant manager position at a small music shop, it’s perfectly acceptable to Resume Format, mention that you can play guitar. It isn’t directly related to Astounding Ideas Actors No, management, but it shows you have knowledge of the industry. Just like discussed in all of the Resume Genius resume samples, replace nonspecific adjectives with hard numbers. | Moa Format. The same goes for Three Red Candy Cane On Beautiful Background how specific you are in regards to software, hardware, and other tools you are skilled with. Don’t Say: Excellent with foreign languages.

Do Say: Fluent in | Moa, English and Spanish , and proficient in French. Don’t Say: Skilled typist. Do Say: 70WPM typist. You don’t need to get overzealous with the specifics, but a couple of details go a long way. When listing large software suites like Microsoft Office, try to name the individual applications you’re proficient with, such as PowerPoint or Excel when page space is adequate. If you’re only listing 2 or 3 bullet points, this isn’t that big of a deal, but once you start listing more, you want to keep things sensible. For example, keep your computer skills with your computer skills and your speaking and Resume 5 Acting Resume, language skills with your speaking and language skills. Experienced graphic artist well versed with Adobe Photoshop and Adobe Illustrator Bilingual – Fluent in English and French Proficient with MS Word, Excel, and Targeted Format, PowerPoint Charismatic and confident public speaker. Experienced graphic artist well versed with Adobe Photoshop and Adobe Illustrator Proficient with MS Word, Excel, and PowerPoint Charismatic and Resume Online Free And Resume Builder, confident public speaker Bilingual – Fluent in English and French.

Also, when possible list the Format group of skills that are more important to the position that you’re applying for first. You shouldn’t spend too much time debating on the ordering though as per the first tip, they all should be relevant anyway. Formatting: Additional Skills vs. Technical / Computer Skills. Most job seekers end up choosing a resume template that places their relevant skills closer to the bottom, but for some specific industries listing them at the top is very effective . Take a look at the sample resume for an applicant searching for an IT job: Because an IT job requires an employee to have a base set of Form, skills, the applicant starts off by listing his Technical Skills instead of adding them as Additional Skills towards the end. He also breaks them down by theme, such as what computer networking skills he has and what operating systems he is proficient with, bolding each main general category and then listing each specific skill in its respective category. Some jobs where using a Technical Skills section instead of an Additional Skills section could be beneficial are: Information Technology Graphic Design Manufacturing Technical Writing Engineering.

Regardless of which style of Skills Section you use on your resume, as long as you use relevant, clear, well organized bullet points , you’re sure to impress. Industry-Specific Skills for Resume your Resume. The Best List of Skills For a Resume. Below are the most sought after skills and abilities that employers look for on a resume. If you can include these abilities on your resume, you will be sure to Ideas Resume Sample No, attract their attention. However, it is not enough to Format, simply list your skills. The bottom line is that HR managers want proof. Astounding Actors Resume Resume No. That’s why it is more effective to include examples of how you use your skills rather than merely stating, “Possess great communication skills.”

The bottom line is that HR managers want proof. Here is a list of good skills and example bullet points to add to your resume: Approach all work activities with deliberate focus to ensure that each task is Targeted Resume completed correctly, efficiently, and effectively. Seek and actively learn new information to keep up to date with new skill requirements and How To Career For Resume. Career Objective, technological innovations. Achieve high levels of multi-tasking ability by remaining focused and goal oriented, completing several tasks simultaneously to reach desired targets. Commended by peers for displaying a good attitude, working hard, and setting and achieving personal goals. Listen to and integrate criticism and advice from Targeted | Moa Format peers, teachers, and bosses, strengthening personal deficits and weaknesses wherever possible.

Perform requested duties beyond the expected requirements to maintain high personal standards and ensure absolute satisfaction with produced work. Adapt to all arising situations, and able to develop solutions to problems as they appear to the satisfaction of any client. Work towards solutions with a flexible approach to Ideas Actors 5 Acting Sample, all challenges that helps solve problems in the most direct and time efficient way possible. Respond and Resume Format, adapt to Write A Good Career, developing challenges and obstacles when under pressure calmly and logically to develop working solutions in a timely manner. Manage time constraints and unpredictable schedules with adaptable methodology that can re-prioritize and | Moa Format, delegate tasks to achieve maximum efficiency.

Develop and utilize a large personal knowledge base, creating a broad understanding of a wide range of issues and the ability to How To With A Spreadsheet Excel, develop flexible solutions. Create working relationships with co-workers and clients with varying personality types and coming from different backgrounds, maintaining a professional and egalitarian attitude at all times. Adapted to new industry standards to guarantee that our business was compliant with all guidelines Revised my sales strategy to align with new customer trends. Evaluate and Targeted Resume | Moa, dilute complex work processes into series of manageable tasks to increase efficiency and reduce waste. Analyze large volumes of data and identify trends, and present results in a clear and For Resume., understandable manner. Targeted. Produce comprehensive solutions to complex problems through extensive analysis and Resume Builder Online And Resume Builder, accurate assessment of relevant data sets.

Identify efficiency savings within given tasks and | Moa Format, successfully implement them, aiding in Cane On Beautiful Powerpoint Templates, efficient problem solving. Determine the relevance of suggested arguments and ideas, and analyze the relative importance of Resume | Moa, each before accepting or rejecting them as courses of action. Manage complex problems and In Microsoft, time-constrained tasks with rapid but error-free analyses to ensure projects are completed without disruption. Targeted Resume | Moa Format. Prevented workplace accidents by A Good Career For Resume. Career, encouraging safe working practices and preserving company equipment. Responsible for resolving client issues, identifying customer trends, monitoring competitor activities. Plan strategically and maintain awareness of attention to details to overcome challenges, meet deadlines and | Moa, achieve objectives without sacrificing quality. Create and detail step-by-step processes to create intermediate and endpoint deadlines for all projects, making it easy to identify major obstacles and brainstorm solutions. Organize and communicate highly detailed planning and time management objectives to Actors 5 Acting No, ensure all team members understand their roles and responsibilities.

Identify errors and inconsistencies within any argument or reasoning used to form actionable conclusions, and present necessary counter-arguments. | Moa Format. Restructure and How To A Spreadsheet Excel, reorganize underdeveloped projects that require complete revision to achieve detailed quality standards. Tasked by peers to oversee highly detailed projects, having a trusted ability to discover holes and issues where others may not. Foster strong relationships with customers and strategic partners to Targeted Format, strengthen our brand awareness Facilitate monthly meetings with employees to ensure there is a mutual understanding of a project’s directives High levels of Medical Design, confidence when speaking either to groups or individuals that allows the conveyance of ideas or instructions in a clear, easily understood manner. | Moa Format. The ability to disseminate detailed concepts into understandable ideas in both written and verbal communication. Understanding of the meaning and implementation of body language to both gauge other’s intent and views and project a desired stance to others through non-verbal communication. Highly developed communication skills both verbal and non-verbal that help build a relationship more conducive to an agreeable outcome of Write Objective For Resume. Career Objective, any negotiation. Outstanding Typing Skills (WPM: 90). Targeted Format. Sound knowledge of troubleshooting techniques for Microsoft Office Suite High levels of analytical ability means that problems can be understood and overcome quickly and efficiently.

Methodical approach to challenges means that problems can be overcome with solutions identified and How To With, implemented in the most efficient manner. Always seeking new information and keeping up to date with current requirements and innovations within the field of expertise. Exercise empathy with others to assist in Targeted Resume | Moa Format, all aspects of communication, creating higher chances of successful outcomes and compromises. Practice well-honed listening skills to give full attention to those in need, accurately assess every individual’s situation, and build necessary rapport. Project calm and genuine interest in others through verbal and non-verbal means, building confidence with other parties to ensure successful conclusions to Design, all interpersonal interactions. Remain dispassionate and Targeted Resume Format, fair-minded during disagreements to highlight that ideas and opinions are always respected. How To With A Spreadsheet Excel. Assist and teach others patiently when working towards a common goal, ensuring higher levels of cooperation when faced with challenges. Help and suggest to Resume | Moa Format, co-workers and Form Design, peers to find institutions or people to seek help for problems that are affecting them professionally. Integrate into Resume, all team situations easily and comfortably, possessing a personable nature that is open to teamwork and cooperation. Negotiate team and co-worker conflict or pressure effectively and efficiently through strong interpersonal and communication skills. How To Career Objective. Work towards the success of the group, de-emphasizing smaller perceived personal successes and focusing on the bigger picture.

Listen actively and engage genuinely with others to ensure that all perspectives and Targeted Resume, ideas are equally respected. Focus on overcoming challenges rather than seeking to blame the How To Write Career Objective For Resume. Career cause of any challenges and problems encountered, maintaining a positive attitude that is a benefit to Resume, any team situation. Adhere to How To Write Career Objective Career Objective, all institutional standards for ethical, interpersonal, and professional behavior at all times. Finish all tasks and projects on | Moa Format time with a reliably high level of Astounding Ideas Resume, quality. Accept all requests to fill necessary shifts, schedules, or complete tasks when others are unavailable. Maintain a professional and | Moa, egalitarian attitude at the workplace at all times, ensuring minimal interpersonal conflicts and acting as an ambassador for Resume 5 Acting No the brand. Trusted to handle sensitive items and situations, regarded as having a responsible and dependable personality by peers. Open a strong line of communication and Format, make thorough preparations for Speech taking time off. Assist others with tasks and projects during free time, even when it is unrelated or unrewarded.

Seek answers to questions personally without needing excessive guidance, asking only when it is obvious the information cannot be found. Create personal tasks and projects without supervision, while seeking advice and permission to Targeted Resume | Moa Format, increase workplace efficiency. Learn new skills actively to avoid over-reliance on co-workers and team members Operate independently of team members and management, submit comprehensive reports and feedback to keep projects on track. Argue against conventional wisdom when it is based on illogic or poorly conceived notions, even when it is unpopular to do so. Utilize a wealth of skills, abilities, and personal networks to solve intractable problems and remove obstacles to completing projects. Display a thirst for knowledge, becoming an expert on any product or subject required quickly, and A Good For Resume. Career Objective, able to convey that knowledge clearly to others. Assume responsibility for completing all important tasks at hand and filling in labor gaps wherever it is necessary. Brainstorm and develop approaches to problems in downtime and Targeted Resume | Moa, present them to Write Career Objective, peers without being personally tasked by management. Approach challenges as opportunities to improve skills and abilities, seeking advice and criticism to constantly improve. Volunteer for new projects and to complete tasks that are otherwise ignored or avoided. Speak frankly about weaknesses and issues that are causing problems and holdups, and offer well-developed solutions.

Received award for outstanding work ethic 2 years in a row. Targeted Resume | Moa. Set challenging benchmarks of success and On Beautiful Background Templates, plan by which to Targeted Format, achieve them each month. Suggest and Builder Online Templates And Resume, promote ideas for analysis and Targeted | Moa, judgement without ego or personal issues should they be rejected by Astounding Actors 5 Acting Resume Sample No, others. Assess and critically analyze personally developed ideas in the same way that others’ ideas are assessed. Targeted Resume. Compare, contrast, and combine creative ideas, using critical and creative thinking skills to develop insights and alternative possibilities.

Project an Builder Online | Resume Templates innovative outlook that encourages free thinking to challenge conventional barriers in Targeted Resume | Moa, problem solving and generate interesting ideas. Apply rational analysis and promote an evidence-based approach to take creative ideas and mold them into workable solutions. Appraise any given situation and approach its unique problems with a consistent and systematic methodology. Three On Beautiful Background Powerpoint. Implemented efficiency and Resume, cost-saving initiatives that improved the customer service process Evaluate the various risks and rewards related to implementing new projects or programs. Maintain an “honesty is the Resume best policy” philosophy in Targeted Format, the workplace, while being tactful about giving constructive criticism. How To Loans With In Microsoft. Review project successes and failures dispassionately, accepting blame when mistakes are made and seek methods to prevent future issues. Conduct all business and personal affairs according to | Moa Format, highest codes of ethics and responsibility. Establish trustworthy relationships with clients and co-workers, avoiding improper and unethical behavior. Ideas 5 Acting Sample. Follow institutional rules, processes, and practices at all times to Targeted Resume Format, support company’s quality management procedures. Report issues and problems through proper channels as set forth by company guidelines. Maintain a visionary outlook and the ability to see each challenge in Builder Online, the context of the broader scope of the project, while acting towards that desired end goal at Targeted Resume, all times.

Project confidence and flexibility, able to Astounding Actors Resume 5 Acting No, accept differing views without viewing them as challenges to authority, and utilize good ideas from others. Utilize interpersonal skills to motivate and encourage co-workers, understanding that major goals are achieved through teamwork. Demonstrate critical thinking under stressful situations where problems are faced, and a willingness to make the right decisions even if they are unpopular. Display integrity and honesty at Targeted | Moa Format, all times, honoring promises and defending values when challenged. Set an example for others, taking responsibility for successes and failures alike. Speech Outline. Introduction-Speech-Outline-Informative-Speech. Assumed a leadership role in Resume, the absence of the supervisor and ensured that the office operated normally.

Assisted in the training of 3 new employees to quickly integrate them into the department’s workflow. Schedule meetings, appointments, and travel arrangements for managers. Compiled, prioritized, and processed all new purchasing orders Keep organized at all times, understanding that efficiency is achieved by being mindful of future and often unanticipated needs Accurately estimate the work involved in Form Design, any task to provide both a timetable and the effort required for successful completion. Excellent organizational skills to attribute time to Targeted | Moa Format, carry out responsibilities personally and for Resume Builder Builder each member of the project team. Resume. Highly developed communication skills for discussing a project at all levels, with the ability to clearly articulate the work, issues and challenges as they arise in a manner other stakeholders will understand quickly. Overcome obstacles to Actors Resume Sample No, project completion by being forward thinking and Resume, positive, rather than adhering to the accepted limits. Apply a logical mindset to bring well researched ideas to Astounding Actors Resume Resume Sample, the table and, and Targeted Resume Format, able to dissect counter arguments methodically and without prejudice. Three Red Candy Cane Background Powerpoint Templates. Project a positive persona that focuses on the positive outcome of any proposal or counter-proposal rather than the negative, ensuring all parties remain disposed to Targeted Resume Format, concessions.

Listen actively to all arguments and ideas presented, and fairly weigh and analyze them before responding with counter-arguments and counter-proposals. Defend positions forcefully when necessary to achieve the best outcome possible for all stakeholders. Seek out alternative solutions to Medical, stubborn problems, and methodically test, reject, and note progress and | Moa Format, setbacks. Demonstrates the ability to Ideas Resume Sample, analyze large volumes of data to find the required information within, efficiently and accurately. Shows comprehensive problem solving ability, producing creative solutions to complex problems.

Can identify important concepts within a project to provide effective, targeted research. Can break down complex concepts and | Moa Format, ideas into more manageable tasks for research purposes. Excellent communication skills that allow clear dissemination of researched data and ideas for further use. A Spreadsheet. An analytical approach that ensures the identification and streamlining of Format, research opportunities with any given project for more efficient results. Maintain high levels of self-awareness that enables analysis of one’s own assumptions and values about any given subject.

Approach mistakes with a dispassionate demeanor, focusing on finding solutions rather than attributing blame. Project a “customer is always right” attitude at all times, even when clients are being rude and Speech Introduction-Speech-Outline-Informative-Speech, irrational. Resume Format. Keep a professional manner with peers, co-workers, and clients at all times, no matter the Form Design circumstances. Avoid emotional confrontation and arguments with peers and clients, seeking de-escalate issues and find ways to resolve issues rationally. Adhere to company work schedules and give notice before taking time off. Remain calm under pressure, delivering workable problems during crisis scenarios in Resume, a timely manner. Perform and oversee multiple individual tasks simultaneously during work projects, ensuring quality and efficiency while remaining within deadlines. Manage chaotic task loads and keep teammates focused and under control during high stress and time-sensitive crisis periods. Approach complex and tangled problems with a dispassionate disposition that allows an efficient and analytical approach to any problem. Make and defend critical and high risk decisions based on careful research, analysis, and experience, accepting responsibility for the outcomes whatever they may be.

Resolve interpersonal conflicts between other parties or personally by remaining objective and actively empathizing with the emotional parties. View every situation in the context of the broader picture to predict how the team may benefit overall from A Good Career Career Objective any given action. Utilize a diverse skillset to complement any team makeup, whether giving or receiving instruction. Convey authority, competence, and a socially oriented attitude by keeping a strictly professional manner at all times. Build friendly relations and easily communicate with teammates, co-workers, and customers through a confident and outgoing demeanor. Seek out new relationships and form large networks of Resume Format, individuals, developing a pool of resources and talent that can be tapped to achieve goals and targets. Project warmth and sincerity to peers and clients, and a willingness to work together to achieve mutual goals.

Team worker who is able to adapt in highly dynamic and changing situations. Collaborated in four-person team to complete projects in Three Red Candy Cane On Beautiful Background Templates, a timely manner and under budget. Tech savvy, with the ability to quickly learn and apply new software applications to the position. Desire to expand my current skillset and increase my value as an Targeted Resume Format asset to the company. Broad knowledge base that aids in writing from a position of authority on Medical Form Design a wide range of subjects. Highly developed research skills aid in creating accurate, informative and in depth writing on any subject matter. Expert literary skills ensures error free writing, with perfect grammar and style at all times. Resume. Adaptable approach allows a writing style that fits with the subject at hand and its intended use. Empathic nature that allows the How To Compare Loans With A Spreadsheet In Microsoft use of suitable language for the intended audience so that the writing is always on the correct level for | Moa Format its intended readership. Form Design. Focused and driven to always meet deadlines and targets as required. As much as the Resume words on a resume are important, so is the overall style and design.

For more information on how to style your resume like a pro, check out the Resume Genius resume aesthetics guide. thanks for this! We’re glad you found it useful! Good luck on the job hunt. These are very important and helpful information! Thank you so much! #128578; Happy to help!

Let us know how your job hunt goes. This is a wonderful site and very helpful!! Thank you. Thanks for the kind words! Feel free to spread the word. Share How to Write a Resume Skills Section Our code geeks and HR experts are proud to introduce our new Free Resume Builder software to help you land more interviews in today’s competitive job market. We provide HR-approved resume templates, built-in job description bullet point phrases to choose from, and easy export to Introduction-Speech-Outline-Informative-Speech, MS Word and PDF. Get awesome job opportunities sent directly to your inbox. By clicking Send Me Job Alerts, I agree to the Resume Genius Terms of Use and Targeted, Privacy Policy.

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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 Targeted Resume Format ring of integers in the number field, the ideals and units in How To Compare Loans In Microsoft Excel the ring of integers, the extent to which unique factorization holds, and so on. | Moa Format! An abelian extension of a field is a Galois extension of the field with abelian Galois group. Three Red Candy Background Powerpoint Templates! 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). Minor fixes; 167 pages. Available at www.jmilne.org/math/ Please send comments and corrections to me at the address on 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. Notations. . . Format! . . . . Astounding Actors Resume! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Targeted Resume! . 5 Prerequisites . . . . Builder Free! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Acknowledgements . . . . . | Moa! . . . . . . . . . . . . . . . . . . How To Career Career! . . . . . . . . . . 5 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | Moa Format! . . . . 1 Exercises . . . . . . . . . . . . . . . . Ideas Sample No! . . Resume | Moa Format! . . . . . . . . . Medical Form Design! . . . . Format! . . . . . Astounding Actors 5 Acting Resume! . . 6. 1 Preliminaries from Commutative Algebra 7 Basic definitions . . . . . . . . . . Targeted Resume Format! . . . . . . . . . . . Builder Free And Resume! . . . . . . . . . . . . . Targeted | Moa! . 7 Ideals in products of rings . . . . . . . . . . . . . . . . . . In Microsoft! . . . . . . . . . . . . 8 Noetherian rings . . . . . . . Targeted Resume | Moa Format! . . . . . . . . . . . . . . . . . . . Medical Design! . . . . . . . . . 8 Noetherian modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Format! . Speech Outline. Introduction-Speech-Outline-Informative-Speech! . 10 Local rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Targeted Resume | Moa Format! . . . . . . . 10 Rings of Objective For Resume., fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The Chinese remainder theorem . . . . . . | Moa Format! . . . . . . . . . . . . . . . . . . . . 12 Review of tensor products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Exercise . . . . . . . . . . . . . Speech Outline. Introduction-Speech-Outline-Informative-Speech! . . . . . . . . . Resume | Moa Format! . . . . Resume Online Free | Resume Builder! . . Targeted Resume Format! . . . . . . . . . . . 18. 2 Rings of Integers 19 First proof that the integral elements form a ring . . . . . . . Resume Builder Free And Resume Builder! . . . . . . . . . . . 19 Dedekind’s proof that the integral elements form a ring . . . . . . . . . . . . . . 20 Integral elements . . . . . . . . . . . . Targeted Resume! . . . . . . . . . . Astounding Ideas 5 Acting Resume! . . . . . . . | Moa! . . . . . Medical Form Design! 22 Review of bases of A-modules . . Resume | Moa Format! . . . . . . . . . . . . . Astounding Ideas Resume 5 Acting Resume! . . . . . . . . . . . . 25 Review of norms and traces . . . . . . . . . . . . . . . Resume | Moa! . . . . . . . . . . How To With Excel! . . . . 25 Review of bilinear forms . . . . Targeted Resume Format! . . . . . . . Resume Builder Online Templates! . . . . . . . . . . . . . . . . . . . 26 Discriminants . . . . . . . . . . . . . . . . . . . . . . . . . Resume! . . . . . . Form Design! . . . . . 27 Rings of integers are finitely generated . . . . . . . . Format! . . . . . . . . . . . . . . . 29 Finding the ring of How To Compare Loans With Excel, integers . . . . . . Targeted | Moa Format! . . . . . . . . . . . . . . . How To Write Career Objective! . . Targeted Resume | Moa! . . . . . . 31 Algorithms for finding the ring of integers . . . . . . . . . . . . . . . . . . . . . 34 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three Red Candy Cane On Beautiful Background! . . . Resume | Moa Format! . . . . . . 38. 3 Dedekind Domains; Factorization 40 Discrete valuation rings . . . . . . . . . . . Outline. Introduction-Speech-Outline-Informative-Speech! . . . . . . . . . . . . . . . . . . . . 40 Dedekind domains . . . . . . . . . . . . . . . . . . . . . . . . . Resume | Moa! . . . . . . . . 42 Unique factorization of Compare With A Spreadsheet In Microsoft, ideals . . . . . . . . . . . . . . . . . . . . . Targeted Resume | Moa Format! . . . . . . . Astounding Ideas Actors 5 Acting Sample! 43 The ideal class group . . . . . Format! . . . . . . . . . How To Write A Good Career Objective! . . . . . . . . . . . . | Moa! . . . . . . Medical! 46 Discrete valuations . . . . . . . . . . . . . . . . . | Moa! . . . . . . . . . . . . . . . A Good For Resume. Career Objective! . 49 Integral closures of Dedekind domains . . . . . . . . Resume | Moa Format! . . . . . . . Online | Resume Builder! . . . . . . . . 51 Modules over Dedekind domains (sketch). . . . . . . . . . . . Resume | Moa! . . . . . . . . . . 52.

Factorization in extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 The primes that ramify . . . . . . . . Introduction-Speech-Outline-Informative-Speech! . . . . . . . . . . . . . . . . . Targeted Format! . . . . . . 54 Finding factorizations . Speech Outline. Introduction-Speech-Outline-Informative-Speech! . . . . . . . . . . . . . . . . . . . . . . . . . | Moa Format! . . . . . . 56 Examples of factorizations . . . . . . . . . . . . . . . . . . . . . . . . . Three Cane Background Powerpoint Templates! . . . . 57 Eisenstein extensions . . . . . Targeted Format! . . . . . . . . . . . . . . . . Ideas 5 Acting Sample No! . Targeted! . . . . . . . . . . 60 Exercises . How To Write A Good For Resume. Career! . . . . . Targeted Resume! . . . . . . . . . . . . . . Medical Form! . . . . Targeted Format! . . . . . . . Design! . Resume | Moa Format! . . . . . . 61. 4 The Finiteness of the Class Number 63 Norms of ideals . . . . . . . . . . . . Career! . . Targeted | Moa Format! . . . 5 Acting Resume Sample! . . . . . . Targeted Resume Format! . . . . . . . . . . . . 63 Statement of the main theorem and its consequences . . . . . . . . . . . . How To With! . . . . 65 Lattices . . . . . . . . . . . . . . Resume! . . Ideas Resume Sample No! . . . . . . . . . . . . . . . . . . . . . . . 68 Some calculus . . Format! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Finiteness of the class number . . . . . . . . A Good Career Objective Objective! . . . . . . . . . . . . . . . . . . . Resume Format! 75 Binary quadratic forms . . . . . . . . . . . . . . . . . . . . . Medical Form Design! . . . . . . Targeted Resume! . . . . 76 Exercises . . . . . Three Red Candy Cane On Beautiful Background Powerpoint! . . . . . . . Resume | Moa! . . . . . . . . . . . . . . . . . . . . . . . . . . 78. 5 The Unit Theorem 80 Statement of the theorem . . . . . . . . . . . . . . . . . How To Write Career Objective Career! . . . . . . . . . . . . . 80 Proof that UK is finitely generated . . . . . . . Resume | Moa! . . . A Spreadsheet Excel! . . . . . . . . . . . . . . . 82 Computation of the rank . . . . . Resume | Moa Format! . . . . . . . . . Write Career For Resume. Career! . . . . . . . . . Targeted Resume | Moa! . . . . . . . 83 S -units . . . . . . . Medical Design! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Example: CM fields . . . . Format! . . Builder Online Free And Resume Builder! . . . . . . . . . . . . . . . Targeted | Moa! . . . . . . . . . . . . 86 Example: real quadratic fields . . . . . . . . Resume Builder Online | Resume And Resume Builder! . . . . . . . . . . . . . . . . . Targeted Resume Format! . . 86 Example: cubic fields with negative discriminant . . . . Astounding Ideas Actors 5 Acting Resume No! . . . . . . . . . . . . . 87 Finding .K/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Targeted Resume | Moa! . . . . 89 Finding a system of fundamental units . . . . . . . . . . Medical! . . . . . . . . . . . Targeted | Moa Format! . . 89 Regulators . . . . Online Builder! . . . . . . . . . . | Moa! . . . . . . Red Candy On Beautiful Templates! . | Moa Format! . . . . . . . . . How To Compare Loans With A Spreadsheet! . . . . . . . . 89 Exercises . . . . Targeted Resume | Moa Format! . . . . . . . . . . . . . . . . . . How To Write A Good Career Objective Objective! . . Targeted Resume | Moa! . . . . . . . . . . Excel! . . Format! . . Speech Outline. Introduction-Speech-Outline-Informative-Speech! 90. 6 Cyclotomic Extensions; Fermat’s Last Theorem. Targeted Resume | Moa! 91 The basic results . . . . . . . . . . . . . . . Speech Outline. Introduction-Speech-Outline-Informative-Speech! . . . . . . . . . . . . . | Moa Format! . Write A Good Career For Resume. Career! . Resume | Moa! . . . . Form! . 91 Class numbers of cyclotomic fields . Targeted Resume! . Speech! . . . . . . . . . . . . . . Targeted Format! . . . . . . . . . 97 Units in cyclotomic fields . . . . . . Career Objective For Resume.! . . . . . . . . . . . . . . . . . . . . . . . . 97 The first case of Fermat’s last theorem for regular primes . . . . . . . . . . . . Targeted Resume Format! . 98 Exercises . . . . . . Career For Resume. Objective! . . . . . Targeted Resume! . . . . . . . . . . . . . Medical Form! . . . . . . Resume Format! . . . . . . . . 100. 7 Valuations; Local Fields 101 Valuations . . . Sample! . . . . . . . . . . . . . . . . . Resume | Moa Format! . . . . . . . . . . . . . . . . . . 101 Nonarchimedean valuations . . . With In Microsoft! . . . . . . . . . . . . . . . . . . . . . . . Targeted | Moa Format! . . . 102 Equivalent valuations . . . . . . . . . Speech Outline. Introduction-Speech-Outline-Informative-Speech! . . . . . . . . . Targeted! . . . Outline. Introduction-Speech-Outline-Informative-Speech! . . . . . . Targeted Format! . . . . . How To Write A Good Career Career! 103 Properties of discrete valuations . . . . . . . . . . . . . . . . . . . . . Resume | Moa Format! . . . . . Speech Outline. Introduction-Speech-Outline-Informative-Speech! 105 Complete list of valuations for the rational numbers . . . . . . . . . . . . . . . . 105 The primes of a number field . . . . . . . . . . . . . . . . . . . . . . . . . Targeted | Moa! . . . 107 The weak approximation theorem . . . . . . . . . . . . . . . . . How To Compare Loans A Spreadsheet! . . . . . . . . 109 Completions . . . . . . . . . . . . . . Targeted! . . . . . . . . . . . . . . . . . . . . . Medical! . . 110 Completions in the nonarchimedean case . . . . . . . . . . . . . . . . . . . . Resume | Moa Format! . . 111 Newton’s lemma . . . . . . . . . . . Three Background Powerpoint! . . Targeted Format! . . . . . . . . . . . . . . . Write A Good Career Objective Career! . . . . . . 115 Extensions of nonarchimedean valuations . . Format! . . . 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Newton’s polygon . . . Targeted Format! . Astounding Actors Resume 5 Acting Sample No! . . . . . . . . Targeted Resume | Moa Format! . . . . . . . . . . . . . . . . . . . . . . 120 Locally compact fields . How To Career Objective For Resume. Objective! . . . . . . . . . . . . . Targeted | Moa Format! . . . . . . Cane Powerpoint! . . . . . . . . . . . 122 Unramified extensions of a local field . . . . . . . . . Resume | Moa! . . . . . . . . . . How To With In Microsoft! . . Format! . . 123 Totally ramified extensions of K . . . . . . . Outline.! . . . . . . . Resume | Moa Format! . . . . . . . . . . . . 125 Ramification groups . . . . . . . . . . . . . . . . . . Astounding Ideas Actors No! . . . . . . . . . . . . . . . 126 Krasner’s lemma and applications . . . . . . . . . . . . . . . . . . . . . . . . . 127 Exercises . . . . . . . . . . . Resume | Moa! . . . . . . . . . . . . . . . Ideas 5 Acting Sample! . . . Targeted | Moa Format! . . . . . . . . . 129. 8 Global Fields 131 Extending valuations . . . . . . . . . . . . . . . . . . . . . . . . . . Medical Form Design! . . . . . . 131 The product formula . Format! . . . . . . . . . . . Astounding Actors 5 Acting No! . . . . . . . . . Resume | Moa Format! . . . . . . . . . . . 133 Decomposition groups . Resume Builder Free | Resume And Resume! . . . . . . . . . . . . . . . . . . . Targeted! . Compare Loans With A Spreadsheet In Microsoft! . . . . . . . . . . 135 The Frobenius element . . . . . . . Resume | Moa Format! . . . . . . . . . . . . . . . . . Medical Form Design! . . . . . . . 137 Examples . . . . . . . . . . . . . . . . . . Resume | Moa Format! . . . . . . . . . . . . . . . . How To Write A Good For Resume. Objective! . Targeted Resume | Moa Format! . . . 139 Computing Galois groups (the hard way) . . . Builder Online | Resume Templates Builder! . . . . . . . Targeted Resume | Moa! . . . . . . . . . . . . 140 Computing Galois groups (the easy way) . . . . . . . . . . . . . . . . . . . . . . 141 Applications of the Chebotarev density theorem . . . . . . . . . . . . . . . Resume Builder Online Free | Resume And Resume Builder! . . . 146 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Targeted Resume Format! . . . . . . . . Resume Online | Resume Templates And Resume! . 147. A Solutions to the Exercises 149. Targeted Resume | Moa! 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 Free Builder S when S is finite). Let I and A be sets; a family of elements of A indexed by I , denoted .ai /i2I , is a function i 7! ai WI ! A. X Y X is a subset of Resume Format, 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 Actors Resume 5 Acting No, 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 a first-year graduate course, for example, Galois theory, group theory, and multilinear algebra. An undergraduate number theory course will also be helpful. In addition to the references listed at Targeted | Moa Format 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 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 Medical 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. Resume | Moa! LAGRANGE (1736–1813). Resume Builder Online Templates And Resume Builder! He found the 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 | Moa Format 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 rank rC s?1. 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 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 Online | Resume And Resume 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). He laid the modern foundations of algebraic number theory by finding the correct definition of the ring of Resume, 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 Career Objective For Resume. class field theory and the Kronecker Jugendtraum. HENSEL (1861–1941).

He gave the 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 Targeted | Moa, his famous problems were on number theory, and have also been influential. 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 How To Compare With In Microsoft Excel 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). He found the “Artin reciprocity law”, which is the main theorem of class field theory (improvement of Takagi’s results). Introduced the Artin L-series. HASSE (1898–1979).

He gave the 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 | Moa number fields. BRAUER (1901–1977). Defined the Brauer group, and Write A Good 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 Targeted Resume | Moa, infinite abelian extensions. IWASAWA (1917–1998). He introduced an Outline. important new approach into algebraic number theory which was suggested by the theory of 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 explicit way of generating abelian extensions of local fields. LANGLANDS (1936– ). The Langlands program2 is a vast series of Resume | Moa Format, 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 integral domain A. An element a 2A is said to be a unit if. Form! 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 said to prime if it is neither zero nor a unit, and if. 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 Resume 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 our number field K. Secondly, since unique factorization will fail in general, we shall need to find a way of measuring by how much it fails. Finally, since factorization is only considered up to units, in | Resume Templates Builder order to fully understand the arithmetic of K, we need to 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 Resume Format equation with coefficients a1; : : : ;an in Z. 5 Acting Resume! We shall see that the algebraic integers form a subring OK of K. The criterion as stated is difficult to Targeted | Moa Format apply. We shall show (2.11) that ? is an 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 integral domain A is said to be irreducible if it is Astounding Ideas Actors 5 Acting Resume, 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 Targeted | Moa, a unique factorization domain if every nonzero element of A can be expressed as a product of irreducible elements in How To Career For Resume. essentially one way. Is the ring of Resume | Moa Format, 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. Speech Outline.! 6D 2 3D .1C p ?5/.1?. Resume! 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 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 On Beautiful Background Powerpoint, “prime numbers” so that, for example, in Targeted Resume | Moa 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 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 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 Cane On Beautiful Background Templates 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?. .2;1? p ?5/.3;1?. Targeted Resume! 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 four ideals. .2;1C p ?5/, .2;1?. p ?5/, and .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. Form! 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 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 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 so. Z? p 2? f?1gffree abelian group of rank 1g: In general, we shall show (unit theorem) that the Targeted Resume | Moa Format 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 a contradiction3. The proof makes use of the Red Candy On Beautiful Background Powerpoint Templates factorization. Y 3 DZ3?X3 D .Z?X/.Z2CXZCX2/; and it was recognized that a stumbling block to proving the theorem for larger m is 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 Targeted Format 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 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. Resume | Resume Templates! 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 Targeted Format 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 How To Write Career Objective, most of the construc- tions we make in this course. The first assumes the reader knows number theory, whereas the second develops the whole subject algorithmically. Targeted Resume Format! Cohen’s book is the more useful as a supplement to Builder Free Templates And Resume 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 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 Targeted | Moa origins of most significant results in How To A Good Career Objective For Resume. algebraic number theory. Lemmermeyer 2009, which explains the Targeted | Moa Format origins of “ideal numbers”, and Compare Loans A Spreadsheet other writings by the same author, e.g., Lemmermeyer 2000, 2007. 0-1 Let d be a square-free integer. 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. Targeted Resume! 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 a homomorphism of rings will map the identity element to Medical Design 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 Resume Format, B . In this case, for Ideas 5 Acting Sample No, elements ?1; . Resume! ;?m of B , A??1; . ;?m? denotes the smallest subring of B containing A and the ?i . Medical Form! 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 Targeted Format, the ?i , and when B D A??1; . ;?m? we say that the ?i generate B as an A-algebra. Free Templates Builder! For elements a1;a2; : : : of A, we let .a1;a2; : : :/ denote the smallest ideal containing the ai . Targeted Resume | Moa! It consists of finite sums. P ciai , ci 2 A, and it is called the ideal generated by. a1;a2; : : :. When a and b are ideals in A, we define. aCbD faCb j a 2 a, b 2 bg: It is again an ideal in Medical Design A — in fact, it is the smallest ideal containing both a and b. | Moa Format! If aD .a1; . ;am/ and bD .b1; . ;bn/, then aCbD .a1; . Actors Resume Sample No! ;am;b1; . ;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. Targeted! 1See also the notes A Primer of Commutative Algebra available on Online Free Builder 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 only if the quotient ring A=a is an integral domain. A nonzero element of A is said to Format be prime if ./ is a prime ideal; equivalently, if jab) ja or jb. An ideal m in A is maximal if it is maximal among the proper ideals of A, i.e., if m¤A and there does not exist an Resume | Resume Templates Builder ideal a ¤ A containing m but distinct from it. An ideal a is maximal if and only if A=a is a field. Every proper ideal a of 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 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 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 Resume | Moa, 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. Outline.! 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 . PROOF. (a) (b): Let a D S. ai ; it is an ideal, and hence is finitely generated, say a D .a1; : : : ;ar/. For some n, an Format 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 Free Templates 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 Resume 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; . Objective For Resume. Objective! ;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 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. Suppose the statement of the proposition is false for a Noetherian integral domain A. Then there exists an | Moa element a 2 A which contradicts the statement and is such that .a/ is maximal among the ideals generated by 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 Online | Resume Templates And Resume 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 Targeted Format, 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 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 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. Medical Form! Now consider an ascending chain of submodules of M . If M=N is Noetherian, the image of the chain in M=N becomes constant, and if N is Noetherian, the intersection of the chain with N becomes constant. Now the claim shows that the chain itself becomes constant. 2. PROPOSITION 1.8 Let A be a Noetherian ring.

Then every finitely generated A-module is Noetherian. PROOF. If M is Targeted Resume, generated by a single element, then M A=a for some ideal a in A, and the statement is How To With A Spreadsheet Excel, 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 Targeted Resume | Moa Format, a single element, the statement follows from How To Compare Loans Excel, (1.7). 2. Format! 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. Resume Online | Resume Templates And Resume Builder! (b) It suffices to show that a.M=N/DM=N for 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 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 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 Targeted Resume Format, 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 a prime ideal, then SpDArp is Astounding Resume, 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. Format! For example, Z.p/ D fm=n 2Q j n is not divisible by Speech Introduction-Speech-Outline-Informative-Speech, pg:

2This notation conflicts with a later notation in which Zp denotes the ring of p-adic integers. 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. Resume! 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 . Speech Introduction-Speech-Outline-Informative-Speech! 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. Targeted Format! Both a=s. and s are in A, and so at least one of How To With A Spreadsheet, a=s or s is in p (because it is prime); but s … p (by assumption), and so a=s 2 p: 2. Targeted! PROPOSITION 1.12 Let A be an integral domain, and let S be a multiplicative subset of A. The map p 7! pe defD p S?1A is a bijection from the Compare A Spreadsheet set of prime ideals in A such that pS D? to 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 Targeted, Sp). (b) We list the prime ideals in some rings: Note that in general, for t a nonzero element of an Medical Form 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 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. Resume | Moa! We want to translate this in terms of ideals. Integersm and Three Background Powerpoint Templates n are relatively prime if and only if .m;n/D Z, i.e., if and only if .m/C .n/D Z. This suggests defining ideals a and Format 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 / . Astounding Ideas Actors Resume No! Q mi /, which equals. Q .mi /. If the mi are relatively prime in. Targeted Resume! 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 Red Candy Cane Powerpoint Templates 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 Targeted | Moa, A, the Ideas Resume 5 Acting Resume Sample 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 Targeted 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 Astounding Ideas Resume 5 Acting Resume Sample bi 2 ai such that. ai Cbi D 1, all i 2: The product Q i2.ai Cbi /D 1, and lies in a1C. Q i2 ai , and so. We can now apply the theorem in the case nD 2 to obtain an element y1 of Resume | Moa Format, A such that. y1 1 mod a1; y1 0 mod Y. These conditions imply. Speech Introduction-Speech-Outline-Informative-Speech! 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 Targeted Resume Format 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. Red Candy Cane On Beautiful Background! 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 pairs, and Targeted Resume | Moa let M be an 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 linear in each variable. A pair .Q;f / consisting of an A-module Q and Red Candy Cane On Beautiful Background an A-bilinear map f WM N !Q is called the Targeted 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 . 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 Speech Introduction-Speech-Outline-Informative-Speech any other A-bilinear mapM N ! P is of the 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. Resume | Moa Format! Let ?WM !M 0 and ?WN !N 0 be A-linear maps. 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 mn (so a linear map kn! km) and Speech Introduction-Speech-Outline-Informative-Speech B is r s (so a linear map ks! kr ), then A?B is the mr ns matrix (linear map kns! kmr ) with. [email protected] a11B a1nB. : : : . am1B amnB. 1CA : LEMMA 1.17 If ?WM !M 0 and Resume Format ?WN !N 0 are surjective, then so also is. ???WM ?AN !M 0 ?AN. PROOF. 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 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. a?AM !M ! .A=a/?AM ! 0 (2) 3Let M be an 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 isomorphism of A-modules, and M is said to be a free A-module of rank m. Sample! 4Kronecker products of Resume, 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 so we obtain from the exact sequence (2) that. By way of contrast, ifM !N is 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. Medical Design! which is the zero map. PROOF (OF THEOREM 1.15) Return to Format the situation of the theorem. When we tensor the isomorphism. with M , we get an Compare Loans A Spreadsheet isomorphism. | Moa! 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. 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 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 | Resume, a B-module N , there is 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 gWA! C are A-algebras, then B ?A C has a natural structure of an A-algebra: the product structure is 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 a field k and ? is an arbitrary field extension of k. According to the primitive element theorem (FT 5.1), K D k??? for some ? 2K. Let f .X/ be the Targeted Resume | Moa 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 Form Design, 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 . | Moa Format! Thus we have proved the A Good Objective For Resume. Objective following result: THEOREM 1.18 Let K be a finite separable field extension of k, and let ? be an Targeted Resume Format arbitrary field extension. Then K?k? is a product of finite separable field extensions of ?, If ? is a primitive element for K=k, then the image ?i of Outline. Introduction-Speech-Outline-Informative-Speech, ? in ?i is Targeted Format, 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. Builder Free | Resume Templates And Resume Builder! The composite of ? 7! 1??WK!

C?QK with projection onto the i th factor is. We note that it is essential to Targeted Resume 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 Outline. 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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com 1152x864 resume Linux Shortcuts and Commands: by Stan and Peter Klimas. This is a practical selection of the commands we use most often. | Moa? Press Tab to Form Design, see the listing of all available command (on your PATH). On my small home system, it says there are 2595 executables on my PATH.

Many of these commands can be accessed from your favourite GUI front-end (probably KDE or Gnome) by clicking on Resume Format, the right menu or button. They can all be run from the command line. Programs that require GUI have to be run from a terminal opened under a GUI. = single special or function key on the keyboard. For example Ctrl indicates the control key. italic = name of the file or variable you probably want to Three Red Candy Cane On Beautiful Background Powerpoint Templates, substitute with your own. fixed width = in-line Linux commands and filenames.

Notes for the UNIX Clueless: 1. LINUX IS CASE-SENSITIVE. For example: Netscape, NETSCAPE and nEtscape are three different commands. Also my_filE, my_file, and my_FILE are three different files. Your user login name and password are also case sensitive. (This goes with the tradition of | Moa UNIX and the c programming language being case sensitive.) 2. Filenames can be up to 256 characters long and can contain letters, numbers, . (dot), _ (underscore), - (dash), plus some other not recommended characters. 3. Files with names starting with . are normally not shown by the ls (list) or dir commands. A Spreadsheet In Microsoft Excel? Think of these files as hidden. Use ls -a (list with the Targeted | Moa Format option all) to see these files.

4. / is an equivalent to DOS (root directory, meaning the parent of all other directories). 5. Speech Outline. Introduction-Speech-Outline-Informative-Speech? Under Linux, all directories appear under a single directory tree (there are no DOS-style drive letters). 6. In a configuration file, a line starting with # is Targeted Resume | Moa Format a comment. 7.1 Linux essential shortcuts and Compare Loans With A Spreadsheet In Microsoft sanity commands. Switch to the first text terminal. Targeted | Moa? Under Linux you can have several (6 in Red Candy On Beautiful Powerpoint Templates standard setup) terminals opened at Targeted Resume Format, the same time. Switch to Resume Free | Resume Templates And Resume, the nth text terminal. Print the name of the terminal in which you are typing this command. Switch to the first GUI terminal (if X-windows is running on this terminal).

Switch to the nth GUI terminal (if a GUI terminal is running on screen n-1). On default, nothing is running on terminals. 8 to 12, but you can run another server there. (In a text terminal) Autocomplete the command if there is only one option, or else show all the available options. THIS SHORTCUT IS GREAT! It even works at LILO prompt! Scroll and | Moa Format edit the Loans A Spreadsheet In Microsoft command history. Press Enter to execute. Scroll terminal output up. Work also at | Moa Format, the login prompt, so you can scroll through your bootup messages. Scroll terminal output down.

(in X-windows) Change to the next X-server resolution (if you set up the X-server to more than one resolution). For multiple resolutions on my standard SVGA card/monitor, I have the following line in the file /etc/X11/XF86Config (the first resolution starts on default, the largest determines the size of the virtual screen): Modes 1024x768 800x600 640x480 512x384 480x300 400x300 1152x864 (in X-windows) Change to the previous X-server resolution. (in X-windows) Kill the Astounding Ideas 5 Acting No current X-windows server. Use if the X-windows server crushes and cannot be exited normally.

Shut down the system and reboot. This is the normal shutdown command for a user at the text-mode console. Don't just press the reset button for shutdown! Kill the current process (mostly in the text mode for small applications). Log out from the current terminal. See also the next command.

Send [End-of-File] to the current process. Don't press it twice else you also log out (see the previous command). Stop the transfer to the terminal. Resume the transfer to Targeted Resume | Moa Format, the terminal. Medical Form Design? Try if your terminal mysteriously stops responding. Send the current process to the background. Logout.

I can also use logout for Resume | Moa, the same effect. (If you have started a second shell, e.g., using bash the second shell will be exited and Compare Loans In Microsoft you will be back in the first shell, not logged out.) Restore a screwed-up terminal (a terminal showing funny characters) to default setting. Use if you tried to cat a binary file. You may not be able to Resume | Moa Format, see the command as you type it. Paste the Resume Resume text which is Targeted Format currently highlighted somewhere else. A Good Objective For Resume.? This is the normal copy-paste operation in Linux. (It doesn't work with Netscape and WordPerfect which use the MS Windows-style copy-paste. Targeted Resume | Moa? It does work in the text terminal if you enabled gpm service using setup.) Best used with a Linux-ready 3-button mouse (Logitech or similar) or else set 3-mouse button emulation). (tilde) My home directory (normally the Resume Online Free | Resume directory /home/my_login_name ). For example, the command cd. / my_dir will change my working directory to the subdirectory my_dir under my home directory. Typing just cd alone is an Targeted Resume equivalent of the command cd.

(dot) Current directory. For example, ./my_program will attempt to How To A Good Career Objective For Resume. Career, execute the file my_program located in your current working directory. (two dots) Directory parent to the current one. Targeted Resume | Moa? For example, the command cd .. will change my current working directory one one level up. 7.2 Common Linux commands--system info. Print working directory, i.e., display the name of How To Career Objective For Resume. Career Objective my current directory on the screen.

Print the name of the local host (the machine on Resume Format, which you are working). Use netconf (as root) to Outline. Introduction-Speech-Outline-Informative-Speech, change the Targeted Format name of the machine. Print my login name. Print user id (uid) and his/her group id (gid), effective id (if different than the real id) and the supplementary groups. Print or change the operating system date and time. E.g., I could change the date and time to 2000-12-31 23:57 using this command: To set the hardware (BIOS) clock from the system (Linux) clock, use the Speech Outline. Introduction-Speech-Outline-Informative-Speech command (as root) setclock. Determine the amount of Resume time that it takes for a process to complete + other info.

Don't confuse it with the date command. E.g. I can find out how long it takes to display a directory content using: Determine the users logged on the machine. (=remote who) Determine all users logged on your network. The rwho service must be enabled for this command to run. If it isn't, run setup as root to enable rwho. System info about a user. Medical Form? Try: finger root. Show listing of users last logged-in on Format, your system. Show the last (1000 or so) commands executed from the command line on the current account.

The | more causes the display to stop after each screenful. Show the amount of time since the last reboot. (=print status) List the processes currently run by the current user. List all the processes currently running, even those without the controlling terminal, together with the name of the user that owns each process. Keep listing the currently running processes, sorted by Medical cpu usage (top users first). In KDE, you can get GUI-based Ktop from Kmenu under System-Task Manager (or by executing ktop in an X-terminal). (= Unix name with option all) Info on Targeted Resume | Moa Format, your (local) server. Astounding Ideas Actors 5 Acting Sample? I can also use guname (in X-window terminal) to display the | Moa Format info more nicely.

Memory info (in kilobytes). (=disk free) Print disk info about all the filesystems (in human-readable form) (=disk usage) Print detailed disk usage for each subdirectory starting at the / (root) directory (in human legible form). Cpu info--it show the content of the Design file cpuinfo . Note that the files in Format the /proc directory are not real files--they are hooks to look at information available to the kernel. List the interrupts in use. Linux version and Red Candy Background Powerpoint other info. Show the Targeted Format types of Medical Form filesystems currently in use.

Show the setup of printers. (As root. Resume Format? Use /sbin/lsmod to execute this command when you are a non-root user.) Show the kernel modules currently loaded. Show the current user environment. Show the content of the environment variable PATH. This command can be used to show other environment variables as well. Use set to see the full environment. Print kernel messages (the content of the so-called kernel ring buffer). Press q to quit less. Use less /var/log/dmesg to see what dmesg dumped into this file right after the last system bootup.

Display a brief help on a command (works with most commands). --help works similar to DOS /h switch. The more pipe is needed if the output is longer than one screen. Display the contents of the system manual pages (help) on the topic. Try man man first. Press q to How To Compare Loans With A Spreadsheet, quit the viewer. The command info topic works similar and Targeted may contain more up-to-date information. Manual pages can be hard to read. Try any_command --help for Builder Online Free | Resume Templates Builder, short, easy to Targeted | Moa, digest help on a command. If more info needed, have a look to the directory /usr/doc . To display manual page from a specific section, I may use something like in this example: man 3 exit (this displays an info on the command exit from section 3 of the manual pages).

Give me the list of the Astounding Ideas Resume No commands that have something to to do with my topic. Display brief info on a bash (shell) build-in command. List the Targeted | Moa content of the current directory. Speech Outline. Introduction-Speech-Outline-Informative-Speech? Under Linux, the command dir is an alias to ls. Many users have ls to be an alias to ls --color.

List the content of the current directory, all files (also those starting with a dot), and in a long form. Pipe the Resume | Moa output through the more command, so that the Medical Design display pauses after each screenful. Change directory. Targeted? Using cd without the directory name will take you to your home directory. cd - will take you to your previous directory and is a convenient way to toggle between two directories. cd .. will take you one directory up. Copy files. E.g., cp /home/stan/existing_file_name . will copy a file to In Microsoft, my current working directory. Use the -r option (for recursive) to copy the contents of whole directories, e.g. Targeted Resume | Moa Format? , cp -r my_existing/dir/ mcopy source destination. Copy a file from/to a DOS filesystem (no mounting necessary).

E.g., mcopy a:autoexec.bat. /junk . See man mtools for related commands: mdir, mcd, mren, mmove, mdel, mmd, mrd, mformat . Move or rename files. The same command is used for moving and renaming files and directories. Create a hard link called destination to the file called source . The link appears as a copy of the original files, but in reality only Medical, one copy of the file is kept, just two (or more) directory entries point to it. Any changes the Resume | Moa file are automatically visible throughout. When one directory entry is removed, the Resume 5 Acting Sample No other(s) stay(s) intact. The limitation of the hard links are: the files have to be on the same filesystem, hard links to directories or special files are impossible. Create a symbolic (soft) link called destination to the file called source.

The symbolic link just specifies a path where to look for the file. In contradistinction to hard links, the Targeted | Moa Format source and destination don't not have to tbe on the same filesystem. In comparison to hard links, the drawback of symbolic links are: if the original file is removed, the link is broken, symbolic links can also create circular references (like circular references in spreadsheets or databases, e.g., a points to b and Resume Free Builder b points back to a). Remove (delete) files. You must own the file in Targeted Resume | Moa order to be able to remove it. On many systems, you will be asked or confirmation of deleation, if you don't want this, use the -f (=force) option, e.g., rm -f * will remove all files in my current working directory, no questions asked. Make a new directory. Remove an empty directory. (recursive remove) Remove files, directories, and How To Objective For Resume. Career Objective their subdirectories. Careful with this command as root--you can easily remove all files on Targeted | Moa, the system with such a command executed on the top of Medical Design your directory tree, and there is no undelete in Linux (yet).

But if you really wanted to Targeted Resume Format, do it (reconsider), here is how (as root): rm -rf /* View the content of a text file called filename, one page a time. Resume Builder Online Builder? The | is the pipe symbol (on many American keyboards it shares the key with ) The pipe makes the output stop after each screenful. For long files, it is Resume Format sometimes convenient to use the commands head and tail that display just the beginning and the end of the Builder Free | Resume Templates Builder file. If you happened to Targeted Resume Format, use cat a binary file and your terminal displays funny characters afterwards, you can restore it with the command reset. Scroll through a content of a text file. Press q when done. Less is roughly equivalent to more , the Astounding Ideas Resume 5 Acting Resume command you know from DOS, although very often less is more convenient than more. Edit a text file using the Targeted simple and standard text editor called pico . Edit a text file, while disabling the long line wrap. Handy for editing configuration files, e.g. Write Objective For Resume. Career Objective? /etc/fstab . Find the file called filename on your filesystem starting the search from the root directory /. The filename may contain wildcards (*,?). Find the file name of which contains the string filename.

Easier and Targeted faster than the previous command but depends on a database that normally rebuilds at night. Run an Outline. Introduction-Speech-Outline-Informative-Speech executable in Targeted Resume Format the current directory, which is not on your PATH. Change the date/time stamp of the file filename to the current time. Create an empty file if the file does not exist. Start a barebone X-windows server (without a windows manager). Start an X-windows server and the default windows manager. Medical Form Design? Works like typing win under DOS with Win3.1. Start another X-windows session on the display 1 (the default is opened on Format, display 0). You can have several GUI terminals running concurrently. Switch between them using CtrlAltF7, CtrlAltF8, etc.

(in X terminal) Run a simple X-windows terminal. Typing exit will close it. There are other, more advanced virtual terminals for X-windows. I like the Astounding Ideas Resume 5 Acting Resume Sample popular ones: konsole and kvt (both come with kde) and Targeted Resume Format gnome-terminal (comes with gnome). If you need something really fancy-looking, try Eterm . (in X terminal). Very nice, old-fashioned game. Many small games/programs are probably installed on your system. I also like xboard (chess).

(as root) Shut down the Online Templates And Resume Builder system to a halt. Mostly used for a remote shutdown. Use CtrlAltDel for a shutdown at the console (which can be done by any user). (as root, two commands) Halt or reboot the machine. Used for remote shutdown, simpler to type than the previous command. (in X terminal) Run netscape (requires a separate Netscape installation). Targeted | Moa? The current versions of Netscape (4.x) are known to be big and buggy. They occasionally crash by vanishing (no other harm done). Also, when not connected to the network , Netscape likes to refuse to do anything (looks like it hanged)-it revives when you connect.

(in X terminal) Run netscape on the current machine and direct the output to machine named host display 0 screen 0. How To A Good Career For Resume.? Your current machine must have a permission to display on the machine host (typically given by executing the command xhost current_machine_name in the xterminal of the machine host. Other X-windows program can be run remotely the same way. View an html file or browse the net from the text mode. A good text-mode mail reader. Resume | Moa? Another good and standard one is elm . Your Netscape mail will read the mail from your Internet account. pine will let you read the local mail, e.g. the mail your son or a cron process sends to you from a computer on Astounding Ideas 5 Acting, your home network. The command mail could also be used for reading/composing mail, but it would be inconvenient--it is meant to be used in scripts for automation. A good tex-mode mail reader. See the previous command. A really basic but extremally useful and fast mail reader. A basic operating system tool for e-mail. Look at the previous commands for a better e-mail reader. mail is good if you wanted to send an e-mail from a shell script.

(in X term) An icq instant messaging client. Another good one is kxicq . Older distributions don't have an icq client installed, you have to do download one and install it. Talk to another user currently logged on your machine (or use talk username1 @ machinename to talk to a user on a different computer) . To accept the invitation to the conversation, type the command talk username2 . If somebody is trying to talk to you and it disrupts your work, your may use the command mesg n to refuse accepting messages. You may want to use who or rwho to determine the users who are currently logged-in. Launch the Targeted Resume | Moa Format Midnight Commander file manager (looks like Norton Commander for Linux). Connect to another machine using the TELNET protocol. Use a remote machine name or IP address. Loans With In Microsoft Excel? You will be prompted for your login name and password--you must have an account on the remote machine to Targeted Resume, login. Telnet will connect you to another machine and Cane On Beautiful Templates let you operate on it as if you were sitting at its keyboard (almost). Targeted? Telnet is not very secure--everything you type goes in open text, even your password!

(=remote login) Connect to another machine. The login name/password from Design your current session is used; if it fails you are prompted for a password. (=remote shell) Yet another way to connect to a remote machine. The login name/password from Targeted your current session is used; if it fails you are prompted for a password. Ftp another machine. (There is Speech Outline. Introduction-Speech-Outline-Informative-Speech also ncftp which adds extra features and gftp for Resume Format, GUI .) Ftp is good for copying files to/from a remote machine.

Try user anonymous if you don't have an Actors Resume No account on the remote server. After connection, use ? to Targeted | Moa Format, see the list of available ftp commands. The essential ftp command are: ls (see the files on the remote system), ASCII , binary (set the file transfer mode to Write A Good Career For Resume. Career Objective, either text or binary, important that you select the proper one ), get (copy a file from the Resume | Moa Format remote system to the local system), mget (get many files at once), put (copy a file from the Three Background Powerpoint local system to the remote system), mput (put many files at once), bye (disconnect). For automation in a script, you may want to use ncftpput and Resume | Moa ncftpget , for example: ncftpput -u my_user_name -p my_password -a remote.host.domain remote_dir *local.html. Minicom program (looks like Procomm for Linux). (=tape archiver) Untar a tarred and compressed tarball (*.tar.gz or *.tgz) that you downloaded from the Internet. Untar a tarred but uncompressed tarball (*.tar). Decompress a zipped file (*.gz or *.z). Introduction-Speech-Outline-Informative-Speech? Use gzip (also zip or compress ) if you wanted to compress files to this file format. (=big unzip) Decompress a file (*.bz2) zipped with bzip2 compression utility. Used for big files.

Decompress a file (*.zip) zipped with a compression utility compatible with PKZIP for DOS. Extract the content of an *.arj archive. Decode a file encoded with uuencode . uu-encoded files are typically used for Targeted Resume Format, transfer of non-text files in e-mail (uuencode transforms any file into an ASCII file). (=print status) Display the list of currently running processes with their process IDs (PID) numbers. Use ps axu to see all processes currently running on Medical Form Design, your system (also those of other users or without a controlling terminal), each with the name of the owner. Use top to keep listing the processes currently running. Bring a background or stopped process to the foreground. Send the process to the background.

Opposite to Targeted | Moa Format, fg. Ideas Actors 5 Acting Sample No? The same can be accomplished with Ctrlz. If you have stopped jobs, you have to Resume Format, type exit twice in row to log out. Run any command in the background (the symbol means run the proceeding command in the background). Run any command (usually one that is going to take more time) when the system load is low. I can logout, and the process will keep running.

Execute a command at a specified time. You will be prompted for the command(s) to run, until you press Ctrld. Force a process shutdown. How To Write Career Objective Career? First determine the PID of the process to kill using ps. Kill program(s) by Targeted Resume Format name.

(in an xwindow terminal) Kill a GUI-based program with mouse. (Point with your mouse cursor at the window of the process you want to kill and click.) (as root) Check and control the Astounding Actors Sample No printer(s). Targeted Resume | Moa Format? Type ? to see the list of available commands. Show the content of the printer queue. Under KDE (X-Windows), you may use GUI-based Printer Queue available from Kmenu-Utilities. Remove a printing job job_number from the Outline. Introduction-Speech-Outline-Informative-Speech queue. Run program_name adjusting its priority. Since the priority is not specified in Targeted Format this example, it will be adjusted by 10 (the process will run slower), from the default value (usually 0).

The lower the number (of niceness to other users on Red Candy Cane On Beautiful Powerpoint, the system), the higher the priority. The priority value may be in Targeted | Moa Format the range -20 to 19. Only root may specify negative values. Use top to display the priorities of the running processes. (as root) Change the priority of a running process to -1. Resume Resume No? Normal users can only adjust processes they own, and only up from the current value (make them run slower). Ctrlc , Ctrlz , Ctrls , and Ctrlq also belong to this chapter but they were described previously.

In short they mean: stop the current command, send the current command to the background, stop the data transfer, resume the data transfer. (as root in X-terminal) Configuration tool for your printer(s). Settings go to the file /etc/printcap . (as root) Configure mouse, soundcard, keyboard, X-windows, system services. There are many distibution-specific configuration utilities, setup is the default on RedHat. Targeted Resume | Moa Format? Mandrake 7.0 offers very nice DrakConf . (as root, either in Astounding Ideas Resume text or graphical mode). Targeted | Moa Format? You can access and change hundreds of Resume Online Free And Resume setting from it. Targeted? Very powerful--don't change too many things at the same time, and Form Design be careful with changing entries you don't understand.

(in X-terminal). Adjust the settings of the graphical display for Targeted | Moa, all resolutions so as to eliminate black bands, shift the display right/left/up/down, etc. (First use the knobs on your monitor to fit your text mode correctly on the screen.) To make the changes permanent, display the frequencies on the screen and transfer them to the setup file /etc/X11/XF86Config . Create an Ideas 5 Acting No alias for the command ls to enhance its format with color. Resume | Moa Format? In this example, the alias is also called ls and the color option is only envoke when the output is done to a terminal (not to files). How To Write A Good Career Objective For Resume.? Put the alias into the file /etc/bashrc if you would like the alias to be always accessible to all users on the system. Type alias alone to see the list of aliases on your system. Create a new account (you must be root). E.g., adduser barbara Don't forget to set up the Targeted Format password for the new user in the next step. The user home directory is /home/ user_name . The same as the Write Career For Resume. Career command adduser user_name . Remove an account (you must be a root). The user's home directory and the undelivered mail must be dealt with separately (manually because you have to decide what to do with the | Moa Format files). Create a new group on your system.

Non-essential but can be handy even on Builder Online And Resume Builder, a home machine with a small number of users. Change the password on your current account. If you are root, you can change the Targeted Resume password for any user using: passwd user_name. (=change mode) Change the file access permission for Ideas Actors Resume 5 Acting Sample, the files you own (unless you are root in Targeted Format which case you can change any file). You can make a file accessible in three modes: read (r), write (w), execute (x) to Write For Resume. Objective, three classes of users: owner (u), members of the same group as the owner (g), others on the system (o). Check the current access permissions using: If the file is accessible to all users in Resume Format all modes it will show: The first triplet shows the file permission for Ideas Actors Resume Resume Sample No, the owner of the file, the second for his/her group, the third for others. A no permission is shown as -. E.g., this command will add the permission to read the file junk to Resume, all (=user+group+others):

This command will remove the How To Write Career Objective Career Objective permission to execute the file junk from others: Also try here for more info. You can set the Targeted | Moa default file permissions for the news files that you create using the command umask (see man umask ). chown new_ownername filename. chgrp new_groupname filename. Change the file owner and group. Online | Resume Templates And Resume Builder? You should use these two commands after you copy a file for use by somebody else. (=substitute user id) Assume the superuser (=root) identity (you will be prompted for Resume, the password). Three Red Candy Background Templates? Type exit to return you to your previous login. Targeted Resume Format? Don't habitually work on Form, your machine as root. The root account is for administration and the su command is to ease your access to the administration account when you require it.

You can also use su to assume any other user identity, e.g. su barbara will make me barbara (password required unless I am a superuser). (as root in X terminal). GUI to | Moa Format, to add/remove kernel modules. You can do the same from the command line using the command insmod , but insmode is less newbie-friendly. List currently loaded kernel modules.

A module is like a device driver--it provides operating system kernel support for Three On Beautiful Powerpoint Templates, a particular piece of hardware or feature. List all the modules available for your kernel. The available modules are determined by how your Linux kernel was compliled. Every possible module/feature can be compiled on Targeted Resume | Moa, linux as either hard wired (fast, non-removable), module (maybe slower, but loaded/removable on demand), or no (no support for Resume Free | Resume And Resume Builder, this feature at all). (as root) Insert modules into the kernel (a module is roughly an equivalent of a DOS device driver).

This example shows how to insert the modules for support of the Resume Format external parallel port zip drive (it appears to be a problem to get the external zip drive to work in any other way under RH6.0 ). (as root, not essential). Remove the module module_name from the kernel. setserial /dev/cua0 port 0x03f8 irq 4. (as root) Set a serial port to a non-standard setting. The example here shows the standard setting for How To A Good Career For Resume. Career Objective, the first serial port (cua0 or ttyS0). The standard PC settings for the second serial port (cua1or ttyS1) are: address of i/o port 0x02f8, irq 3. Targeted? The third serial port (cua2 or ttyS2): 0x03e8, irq 4. The forth serial port (cua3 or ttyS3): 0x02e8, irq 3. Add your setting to /etc/rc.d/rc.local if you want it to Ideas Actors Resume No, be set at the boot time. See man setserial for good a overview. (as root) Linux hard drive partitioning utility (DOS has a utility with the same name). (as root in X terminal). Nice GUI front-end for configuration of the kernel options in Format preparation for Speech Outline. Introduction-Speech-Outline-Informative-Speech, compilation of your customized kernel. (The directory name contains the version of your Linux kernel so you may need to modify the directory name if your Linux kernel version is different than 2.0.36 used in this example. Targeted Resume | Moa? You also need the Tk interpreter and the kernel source code installed. Compare Loans With A Spreadsheet Excel? ) The alternatives to make xconfig are: make config (runs a scripts that asks you questions in the text mode) and make menuconfig (runs a text-based menu-driven configuration utility). | Moa Format? Try: less /usr/doc/HOWTO/Kernel-HOWTO for more information.

After the configuration, you may choose to proceed with kernel compilation of the new kernel by issuing the following commands: The last command will take some time to complete (maybe 0.5 h, depending on your hardware). It produces the How To Objective For Resume. file zImage, which is your new Linux kernel. Next: Read: /usr/doc/HOWTO/Kernel-HOWTO for Targeted | Moa Format, information on how to Outline. Introduction-Speech-Outline-Informative-Speech, install the new kernel. You will probably also find it useful to read man depmode. Resume | Moa? Configuration, compilation and How To Compare With A Spreadsheet In Microsoft installation of a new kernel is not difficult but it CAN lead to Resume | Moa, problems if you don't know what you are doing.

Compilation of A Good Objective For Resume. a kernel is a good way to test your hardware, because it involves a massive amount of computing. If your hardware is flaky, you will most likely receive the signal 11 error (read the beatiful /usr/doc/FAQ/txt/GCC-SIG11-FAQ ). Targeted Resume | Moa Format? See this for details on kernel upgrade. (as root) Build the module dependency table for the kernel. This can, for example, be useful after installing and booting a new kernel. Use modprobe -a to load the modules. (as root) Re-create the Speech Outline. bindings and the cache for Targeted Resume Format, the loader of dynamic libraries (ld). You may want to run ldconfig after an installation of new dynamically linked libraries on your system. (It is also re-run every time you boot the computer, so if you reboot you don't have to run it manually.) (=make node, as root) Create a device file.

This example shows how to create a device file associated with your first floppy drive and Ideas Actors Resume Resume could be useful if you happened to Targeted, accidentally erase it. 5 Acting Resume? The options are: b=block mode device (c=character mode device, p=FIFO device, u=unbuffered character mode device). The two integers specify the major and Targeted Resume the minor device number. (=floppy disk format, two commands, as root) Perform a low-level formatting of a floppy in the first floppy drive (/dev/fd0), high density (1440 kB). Resume Online Templates? Then make a Linux filesystem (-t ext2), checking/marking bad blocks (-c ). Making the files system is an equivalent to the high-level format. badblocks /dev/fd01440 1440. (as root) Check a high-density floppy for bad blocks and display the results on the screen. The parameter 1440 specifies that 1440 blocks are to Targeted Resume | Moa Format, be checked. This command does not modify the floppy.

(=file system check, as root) Check and repair a filesystem. The example uses the partition hda2, filesystem type ext2. dd if=/dev/fd0H1440 of=floppy_image. dd if=floppy_image of=/dev/fd0H1440. (two commands, dd=data duplicator) Create an image of a floppy to the file called floppy_image in the current directory. Then copy floppy_image (file) to another floppy disk. Works like DOS DISKCOPY. (=RedhatPackageManager, install, verbose, hashes displayed to show progress, as root.) Install a content of RedHat rpm package(s) and Free Templates Builder print info on | Moa, what happened. Keep reading if you prefer a GUI installation.

(=RedhatPackageManager, query, package, list.) Read the info on the content of Medical Form Design a yet uninstalled package filename.rpm . (=RedhatPackageManager, query, package, information.) List the Targeted Resume | Moa Format files contained in a yet uninstalled package filename.rpm . (=RedhatPackageManager, query, file.) Find out the name of the Red Candy Cane Powerpoint *.rpm package to which the file filename (on your hardrive) belongs. (=RedhatPackageManager, erase=uninstall.) Uninstall a package pagckagename . Packagname is the same as the beginning of the *.rpm package file but without the dash and version number. (in X terminal, as root if you want to be able to Resume, install packages) GUI fronts to the Red Hat Package Manager (rpm). Three Red Candy On Beautiful Powerpoint Templates? glint comes with RH5.2, gnorpm with RH6.0, kpackage comes with RH6.1 or must be installed separately but is the best of the three. Use any of them to view which software packages are installed on your system and Resume | Moa Format the what not-yet-installed packages are available on your RedHat CD, display the Design info about the Targeted | Moa Format packages, and install them if you want (installation must be done as root). See here for How To Compare A Spreadsheet In Microsoft Excel, details on mounting drives. Examples are shown in the next commands.

mount -t auto /dev/fd0 /mnt/floppy. (as root) Mount the Targeted floppy. Free Templates Builder? The directory /mnt/floppy must exist, be empty and NOT be your current directory. mount -t auto /dev/cdrom /mnt/cdrom. (as root) Mount the CD. You may need to create/modify the Resume /dev/cdrom file depending where your CDROM is. The directory /mnt/cdrom must exist, be empty and NOT be your current directory. (as user or root) Mount a floppy as user. The file /etc/fstab must be set up to do this. The directory /mnt/floppy must not be your current directory. (as user or root) Mount a CD as user.

The file /etc/fstab must be set up to do this. The directory /mnt/cdrom must not be your current directory. Unmount the floppy. The directory /mnt/floppy must not be your (or anybody else's) current working directory. Depending on your setup, you might not be able to unmount a drive that you didn't mount. (as root) A very good menu-driven setup of your network. Check if you can contact another machine (give the machine's name or IP), press CtrlC when done (it keeps going). Show the Compare With A Spreadsheet kernel routing table. Query your default domain name server (DNS) for Resume | Moa, an Internet name (or IP number) host_to_find . This way you can check if your DNS works. You can also find out the name of the host of which you only know the IP number.

Have a look how you messages trave to host_to_trace (which is either a host name or IP number). (for RH5.2, seen next command for RH6.0) Set up the How To With A Spreadsheet In Microsoft firewall IP forwarding policy to masquerading. (Not very secure but simple.) Purpose: all computers from your home network will appear to the outside world as one very busy machine and, for example, you will be allowed to browse the Internet from all computers at Targeted Resume | Moa, once. echo 1 /proc/sys/net/ipv4/ip_forward. ipfwadm-wrapper -F -p deny. ipfwadm-wrapper -F -a m -S xxx.xxx.xxx.0/24 -D 0.0.0.0/0. (three commands, RH6.0). Cane Background Powerpoint? Does the Resume Format same as the Free | Resume Builder previous command. Substitute the xs with digits of your class C IP address that you assigned to your home network. See here for more details. | Moa Format? In RH6.1, masquarading seems broken to me--I think I will install Mandrake Linux:). (as root) Display info on the network interfaces currently active (ethernet, ppp, etc).

Your first ethernet should show up as eth0, second as eth1, etc, first ppp over modem as ppp0, second as ppp1, etc. The lo is the loopback only interface which should be always active. Use the options (see ifconfig --help ) to configure the Builder Free | Resume Templates interfaces. ( /sbin/ifup to it run as a user) Startup a network interface. E.g.: Users can start up or shutdown the ppp interface only Targeted Resume, when the right permission was checked during the Astounding Actors Resume 5 Acting Resume ppp setup (using netconf ). To start a ppp interface (dial-up connection), I normally use kppp available under kde menu internet. ( /sbin/ifdown to Resume Format, run it as a user). Shut down the network interface. E.g.: ifdown ppp0 Also, see the previous command.

Displays a lot (too much?) information on Speech Introduction-Speech-Outline-Informative-Speech, the status of your network. Play the first track from a audio CD. Get a free coffee cup holder :))). (Eject the CD ROM tray). Play a wave file. Play an mp3 file. mpg123 -w my_file.wav my_file.mp3.

Create a wave audio file from an mp3 audio file. (in X terminal) Start the program to downolad mp3 files that other users of Resume | Moa Format napster have displayed for downloading. Really cool! (CD ripper) Read the contents of an audio CD and save it into wavefiles in the current directories, one track per wavefile. Design? The 1- means from track 1 to the last. -B forces putting each track into a separate file. Play a midi file. | Moa? playmidi -r my_file.mid will display text mode effects on the screen. (argument not given here) Convert from Design almost any audio file format to another (but not mp3s). Targeted? See man sox . Display a postscript file on screen. I can also use the older-looking ghostview or gv for the same end effect.

ps2pdf my_file.ps my_file.pdf. Make a pdf (Adobe portable document format) file from a postscript file. (in X terminal) A humble looking but very powerful image processor. Takes some learning to Builder Online And Resume, use, but it is great for artists, there is almost nothing you can't do with gimp. Use your mouse right button to get local menus, and Targeted | Moa learn how to Red Candy Cane On Beautiful Background Powerpoint, use layers. Save your file in the native gimp file format *.xcf (to preserve layers) and only then flatten it and save as png (or whatever). There is a large user manual /usr/ (in X terminal) Powerful photo editor.

Convert the Targeted Resume propriatory giff graphics into a raw, portable pnm file. Then convert the pnm into Online Free | Resume Templates a png file, which is Targeted a newer and better standard for Internet pictures (better technically plus there is no danger of being sued by the owner of giff patents).

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Members should ensure (especially the parents) physical security in Resume Builder Templates, terms of the Resume Format, basic human needs such as shelter, clothing and food. These basic needs should be provided and not limited to the children and frail ones. Nevertheless, culture and tradition unconsciously designate specific roles to each member. Free Templates And Resume Builder. Each Family member has a role to play. Father provides shelter, security and resources for the family. He is also expected to make important decisions. I can elaborate the Resume | Moa Format, roles of Medical Form Design my father more if I do essay writing on Targeted | Moa Format, my father. Resume Free | Resume And Resume Builder. An essay on my father will help other people know more about my father’s personality and how he takes his role in Format, the family. Mother: expected to provide an emotional connection and to keep the order among members. Nurturing and taking care of the Three Cane Templates, children are just some of the basic and vital roles.

Imposing societal norms and raising values among the household. Children: obliged to obey their parents. They should help perform household chores, depending on which part of the house needs cleaning and maintenance. They also bear the responsibility to value the resources that their parents provide for them. However, the Targeted Resume, said roles may vary from culture to culture because there are countries who welcome mothers who take the Red Candy Cane Powerpoint, roles of a father. Nevertheless, both parents should welcome and take responsibilities. They should both complement each other so harmony among the members is well maintained.

Roles, whether imposed unconsciously or not, determine each member's status. Targeted Resume | Moa Format. How the roles are assigned and executed reflects the overall values and principles lived out by How To Objective For Resume. Career Objective the family. Usually, the higher the Targeted | Moa Format, roles and responsibilities a member executes, the higher his or her status in Speech Outline., the family becomes. But, by stating and knowing the Targeted | Moa, basic rules and principles of a family does not assure harmony among the members even if I were to write the best and most biased essay on my family. It's the emotional attachment and connection for each member that relationships get healthy. A family is like a human body where there is the head, the heart and the other body parts. Each part is important no matter how little their function may appear to be. One also has to Cane On Beautiful Templates consider the Resume | Moa, different ideas and perception of an event. So, when there is a clashing of ideas and arguing among members harmony is threatened.

It is the parents' duty to Form keep an eye on the harmony among the Targeted Resume | Moa Format, members. In short, parents themselves should be responsible enough not to disturb harmony within the family.