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Discrimination Against Disabled People Research Papers
basic essay layout Centre for Academic Success. A report is a systematic, well organised document which defines and research papers on disability analyses a subject or problem, and which may include: the record of a sequence of ncssm application, events. interpretation of the significance of these events or facts. evaluation of the research papers, facts or results of research presented. discussion of the outcomes of a decision or course of action. Essays Addiction! Reports must always be: Various courses require you to write reports (as opposed to essays), notably business and scientific or technical subjects. There are, however, different interpretations of research papers, what a report should look like, so it is important that you check with your course tutors and college course documentation as to the report format and content expected. Research! In addition, there is at times some blurring between what “essays”, “reports” and “assignments” are, so again check within your department. Much of the advice given in Guide 1.01, How to write an essay, also applies to reports. Always analyse your brief carefully, making sure that you fully understand the addiction, topic, question or case, that you know what the on disability, purpose of the report is, and who it is being written for. The clearer these things are in sabine leick your mind, the easier the report will be to research papers write and the more effective it will be. When you are researching, planning and eventually writing, continually ask yourself what the main purpose of the report is, what your objective is in movie writing it: is it to inform; to papers argue; to persuade; to evaluate? What does your reader want to see in the report and what will they do with it?
You first need to decide your basic framework. Thesis Binding! With your main topic or question as a central focus, jot down your initial thoughts and start to group these together. You may find the Mind Mapping technique useful: see Guide 2.11. Start to on disability divide key ideas from subsidiary information, and continually ask yourself if everything is relevant; if it isn’t, then delete it. From your prior knowledge (from reading and lectures), you should be able to put together a fairly basic structure. You will now be able to plan your research. Ask yourself what you need to find out, maybe in essay movie the form of questions that need to be answered, then approach your reading from this starting point. If you have specific information to look for, it will make your reading easier and less time consuming. (See Guide 2.02 Reading techniques). Try not to papers gather too much information. Again, keeping your topic or question in college essays mind, reject anything which is research papers not 100% relevant.
When you’re making notes, always try to summarise the main points as concisely as possible. Remember to make a comprehensive record of any sources consulted in order to be able to correctly reference these. Make a record of the research methods you used. Unlike essays, reports are written in sections with headings and ncssm essay sub-headings, which are usually numbered. Below are the possible components of a report, in the order in which they would appear. Check within your department which of these you should include. This should normally include the title, your name and the name of the tutor to whom it is being submitted, date of submission, your course/department, and if applicable, the name of the person and/or organisation who has commissioned the report. Avoid “fancy” fonts and effects and don’t include any clipart. Acknowledgements (usually just in long reports)
A list of people and organisations both within and outside Birmingham City University who have helped you. Contents page (always included in research papers on disability reports of 4+ pages) A clear, well-formatted list of all the addiction, sections and papers sub-sections of the report. Don’t forget to put the sabine leick dissertation, page numbers! If applicable, there should be a separate list of tables, figures, illustrations and/or appendices after the main index. Make sure that the headings in this list correspond exactly with those in your main body. It is best to do your list of contents right at the end. Terms of research, reference (sometimes included) A definition of the task; your specific objective and purpose of movie, writing. Even if you don't include this as a heading, it is a vital process to go through in your planning. If it is group work, who exactly is responsible for what? How long have you got?
What is your task timescale? Why are you writing the research papers on disability, report? What exactly are the assessment criteria? Who are you writing the report for? Are you actually playing a role? What does your reader want to addiction see?
Procedure (sometimes included) How your research was carried out; how the information was gathered. Materials and methods (included if applicable) Similar to papers procedure, but more appropriate to scientific or engineering report writing. Ncssm! The following advice comes from Robert Barrass' book Scientists Must Write (Chapman Hall,1978:135-136): Summary (usually included in longer reports; may be called Executive Summary, Abstract or Synopsis) This is a very brief outline of the report to research give the potential reader a general idea of what it’s about. A statement of: method/procedure used (unless included in separate section) main conclusions and recommendations. Introduction (always included) This should show that you have fully understood the task/brief and that you are going to cover everything required. Indicate the basic structure of the report. You should include just a little background/context and indicate the reasons for writing the titanic movie, report. You may include your terms of reference and procedure/research methods if not covered elsewhere. Your introduction will often give an indication of the conclusion to the report.
Main body/findings (always included) This is the substance of your report. Research! The structure will vary according to the nature of the material being presented, with headings and sub-headings used to clearly indicate the different sections (unlike an essay). A situationproblemsolutionevaluation approach may be appropriate. It is not sufficient to simply describe a situation. Your tutor will be looking for analysis and for essay movie, a critical approach, when appropriate. Charts, diagrams and tables can be used to papers reinforce your arguments, although sometimes it may be better to intelligence include these as an appendix (particularly if they are long or complicated). Do not include opinions, conclusions or recommendations in this section. Results (possibly included in scientific/engineering reports) This section records your observations (in the on disability, past tense) and would normally include statistics, tables or graphs.
Your conclusion should draw out the implications of your findings, with deductions based on the facts described in your main body. Don’t include any new material here. Recommendations (sometimes included) These should follow on logically from your conclusion and be specific, measurable and achievable. Thesis Binding! They should propose how the situation/problem could be improved by suggesting action to be taken. A “statement of cost” should be included if you are recommending changes that have financial implications. Recommendations can be numbered if you wish. Appendices (sometimes included) An appendix (plural=appendices) is detailed documentation of points you outline in papers your findings, for example, technical data, questionnaires, letters sent, tables, sketches, charts, leaflets etc. It is essay competitions supplementary information which you consider to be too long or complicated or not quite relevant enough to include in your main body, but which still should be of research papers, interest to your reader. Each appendix should be referred to in your text. You should not include something as an appendix if it is not discussed in oxford green the main body. This is a list giving the full details of all the sources to which you have made reference within your text.
By far the on disability, most common method in use at Birmingham City University is the Harvard method. Bibliography (sometimes included) This is either a separate list of essay movie, sources which you have used during your research, but have not actually made reference to research in your writing, or this list together with your list of references. Check in your department what you are expected to emotional use. Glossary (occasionally included) Include a glossary if the report includes a lot of research papers, specialised vocabulary or acronyms which may not be familiar to the reader. College Addiction! Always use clear and concise English, avoiding jargon and colloquial language. Write in fairly short sentences. Make sure you develop each paragraph sufficiently (usually a minimum of 5/6 sentences). Research! Most of college, your report should be impersonal, although it may be appropriate in your conclusion or recommendations to include more personal language. Be extra careful with verb tenses. Grammar, spelling and punctuation. Links to further resources on writing reports.
Last updated: 4 January 2011. Centre for Academic Success. Research Papers On Disability! City North : 0121 331 7685 Email. Millennium Point Learning Centre : 0121 202 2500 Email. Phd Thesis Emotional Intelligence! To book a tutorial at Millennium Point: 0121 202 2500.
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In . Titanic! particular, Ovid , a Roman poet born in 43 BC, retells and adjusts much of Greek mythology in a humorous yet personal style to suit himself and his audiences (Plant 2012, p. 298). A close comparison of Ovid and Hesiod calls for papers on disability similarities and differences in their accounts of the human races. In Book I of the essay, Metamorphoses, Ovid accounts four “Ages of Humankind”. Ancient Rome , Daphne , Gian Lorenzo Bernini 1331 Words | 2 Pages. Amores by Ovid: Use of the Domina Amoris and Servitium Amoris. Ovid’s use of the domina amoris and servitium amoris as the foundation his Amores was not unique, but rather reflected a theme created in the time of Plato. . Research! Plato wrote of the idea of a “ love lady” in his The Symposium.
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They all fit together to essay titanic . form one huge unifying story with a lot of different meanings and themes. Throughout the entire epic, one reoccurring theme that is papers prevalent to me is the agony of love . The tortures of love , if you will, and the resulting effects of that adoration towards another. Love is one thing that remains consistent throughout the entire epic. It doesn't arise as just. 2009 albums , Emotion , Epic poetry 1776 Words | 5 Pages. For a work of binding, art to be considered a portrait, the artist must have intent to portray a specific, actual person.
This can be communicated . through such techniques as naming a specific person in the title of the work or creating an image in which the physical likeness leads to an emotional individuality unique to a specific person. While these criteria are not the only ways of connoting a portrait, they are just two examples of how Sherman carefully communicates to the viewer that these works are not. Anarcho-punk , Crass , Post-punk 1149 Words | 3 Pages. from interpersonal affection (I love my mother) to pleasure (I loved that meal). It can refer to an emotion of a strong attraction and . personal attachment. It can also be a virtue representing human kindness, compassion, and affection—the unselfish loyal and benevolent concern for the good of on disability, another. It may also describe compassionate and affectionate actions towards other humans, one's self or animals. Ancient Greeks identified four forms of binding green, love : kinship or familiarity (in Greek. Attachment theory , Friendship , Human bonding 942 Words | 4 Pages. Love is a variety of different feelings, states, and attitudes that ranges from interpersonal affection (I love my mother) to . pleasure (I loved that meal). It can refer to an emotion of a strong attraction and research papers on disability, personal attachment. It can also be a virtue representing human kindness, compassion, and affection—the unselfish loyal and benevolent concern for phd thesis intelligence the good of another. It may also describe compassionate and research on disability, affectionate actions towards other humans, one's self or animals. . Attachment theory , Friendship , Interpersonal relationship 1862 Words | 6 Pages.
(Singapore) Art , culture, and society; these three elements are closely linked. These three elements affect one another in one way or another. Essay! . Research Papers! There is often a conflict of interest between the artist, the audience, and the government body. The artist’s aim is to express art freely. College Essays! The audience’s aim is to view art in forms that are not offensive to them. The government’s aim is to mitigate the conflict of interest between the papers on disability, two parties by implementing policies and restrictions to art pieces that. Aesthetics , Art , Artist 1171 Words | 3 Pages. Metamorphoses, by Ovid , as the poet tells of the god Jupiter destroying all man kind (except for Deucalion and Pyrrha) because of the actions . of one, Lycaon.
Ovid describes Jupiter's destruction as an effort to phd thesis protect all the gods who do not live in the heavens. However, Jupiter's actions are not justified in any way presented in research, the book. In the story there are multiple cases where Jupiter and other gods cause danger and essays, torment on the lower class of gods. Examples of papers, rape, intervention of true love , and god’s. Daphne , Greek mythology , Human 1286 Words | 4 Pages. schoolmates from ncssm application essay Ateneo Municipal. | Plaza de Cataluna | * Where his friends held him a welcome party in Barcelona. | El Amor Patrio | * . Research Papers On Disability! Love of thesis binding oxford gloucester, Country * Essay he wrote when he was 21. * First nationalistic essay | Sacrifices | * Youth * Pleasures * Splendor of genius * Life | Laong Laan | * Pseudonym he used when he wrote Love of Country. Papers On Disability! | Tierra Extranjera | * Term he used to refer to application Spain. | Universidad Central de Madrid | * Where he enrolled in papers on disability, philosophy. Anthropology , Ateneo de Manila University , Jose Rizal 1253 Words | 4 Pages. The Art of Rhetoric in the Metamorphoses. The Art of Rhetoric in the Metamorphoses Among the numerous passages covered in The Metamorphoses of Ovid , there are many . stories regarding the origins of the Earth, the activities of the Roman gods, and some of Rome’s significant rulers and founders.
Within each of these stories, Ovid injects an overall idea that can be taken away from the text. Many of these overall ideas are themes and lessons, but also there are arts that are illustrated to the reader such as poetry, singing, or weaving. . Achilles , Greek mythology , Homer 1446 Words | 4 Pages. The English word love can refer to a variety of essay, different feelings, states, and attitudes that ranges from research on disability interpersonal affection to . pleasure . It can refer to an emotion of a strong attraction and personal attachment. It can also be a virtue representing human kindness, compassion, and phd thesis emotional, affection—the unselfish loyal and benevolent concern for on disability the good of another. As well, it may describe compassionate and affectionate actions towards other humans, one's self or animals. Four forms of leick, interpersonal. Attachment theory , Friendship , Interpersonal relationship 2133 Words | 6 Pages.
tale of the ages amongst the research, two storytellers as well. These similarities and emotional, differences allow the deciphering of the tales to papers on disability hold differences in application essay, the value . Research! of the ages of mankind. Ncssm! Raising key similarities in the Gold, Silver and on disability, Bronze Ages both Ovid and titanic, Hesiod tell a different meaning on how the ages that precede them affect the rest of mankind. The Heroic and Iron Ages are important in papers, the continuation of essays, both stories, the tale of creation and mankind, and the view of the world to the Greeks. Ages of Man , Bronze Age , Copper 944 Words | 3 Pages. ?Neidalina Ortiz Composition II Instructor Candace Peters Love Write your final draft analysis essay that evaluates a . specific concept (such as love , competition, or fame). Use the guidelines shown in Chapters 5 and papers on disability, 6 to develop your ideas and shape your essay. You should include 3-5 outside resources in your assignment. Love is defined as a deep tender, ineffable feeling of affection and solicitude toward a person, such as a rising from emotional intelligence kinship, recognition. Affection , Emotion , Friendship 597 Words | 3 Pages.
circus. Waylon exhibits __________ while Mike exhibits __________. Papers On Disability! a. prejudice; discrimination b. discrimination; prejudice c. Addiction! subtyping; . prejudice d. subtyping; discrimination 4. Research Papers! Karen's roommate hung one of her paintings from art class in their dorm room. Upcoming Essay Competitions In India! Initially, Karen hated the painting and thought it was hideous. But by the end of the year, Karen had grown to research papers on disability like the painting and titanic movie, even wanted to take it home with her. The best explanation for Karen's change in attitude. Attitude change , Elaboration likelihood model , Interpersonal attraction 1794 Words | 7 Pages. Love : What It Really Means What is love ? When someone tells you that they love you, how are you supposed to . respond? There sometimes seems to research papers be no way to decipher the sabine leick dissertation, implication behind the words I love you. Research Papers On Disability! When one loves someone or something, to what extent is their desire? It would be ideal if the English language could have more words for love . Emotional! Love is so complicated in and of on disability, itself, that even if you were to have different words; it would still be challenging to dissertation clarify. Because the English.
Agape , Emotion , Friendship 905 Words | 3 Pages. is the theme of love . Research On Disability! Philia, Eros, and Agape are the three types of love present in the play and essay, are what represent the on disability, theme . of love . These three types of love , Philia, Eros, and gloucester green, Agape are expressed by the different characters in the play. The expression of the theme of love in the play is not just there by accident; William Shakespeare put it in this comedic and romantic play with a purpose. Philia is papers one of the three kinds of movie, love expressed in the play. The type of love that Philia represents. Agape , Friendship , Greek words for love 1173 Words | 3 Pages.
Love plays a significant role in every human beings life. There are many different forms of love in papers, a person’s life. A person . feels a different love for their friend then they do for an intimate lover. Dissertation! They feel different love for their families and parents then they feel for on disability animals or objects. An individual usually learns what love is from a young age, and gloucester, it progresses as they get older.
Some people have trouble experiencing some forms of love because they feel like they are unable to research due to past. Agape , Friendship , Interpersonal relationship 2175 Words | 6 Pages. Running Head: LOVE What’s Love Got to Do with It? Kathryn Barr Dr. Salome Dubenetzky PSY 301 . January 7, 2013 LOVE Attraction is defined as a person or thing that draws, attracts, allures, or entices; a characteristic or quality that provides pleasure, an attractive feature. Initially because of this attraction two people who are mutually attracted will begin or a friendship.
In the ncssm essay, beginning of a relationship love is strong and it. Interpersonal attraction , Interpersonal relationship , Love 1594 Words | 5 Pages. was inspired by papers on disability, that relationship. “The Passionate Shepherd to His Love ” by Christopher Marlowe is competitions in india most likely the most famous pastoral poem of . the carpe diem or “seize the day” style. Its inspiration was most likely to research papers convince a girl that life would be beautiful and filled with pleasures if she would be with him—his goal being seduction. Ever since the beginning of time, males and females have been looking for someone to love , someone they van spend their entire life with; and someone to accept. Christopher Marlowe , English-language films , Friendship 1096 Words | 3 Pages. ?Introduction – Part 1: In writing this statement I will explore the ideas and customs associated with what love is known to be, with reason . and competitions in india, argument. Research On Disability! I will mostly be analyzing romantic love , in relation to lovers. Intelligence! However with too much reasoning and argument comes confusion, so more argument than reasoning will be my approach. If you are not open to the negativities of love then my opinion has no value to you. For the positives of any topic are pleasing whether or not one can assimilate.
Idea , Interpersonal relationship , Irrationality 1253 Words | 3 Pages. non-living object. That feeling is love . However, when one is forced to define love , he or she often turns to romance to find the . Papers! meaning. Intelligence! It is described to be everything pink and pretty, full of hearts, roses, cuddly stuffed animals, chocolates, kisses, and hugs. Love is also expressed as the butterflies in the stomach, hair on the back of the neck rising to the occasion, hesitant lump in the throats, giddiness in the eyes, and fireworks in the hearts. However, love exists outside the realm of research papers, romance. Emotion , Love , Outline of self 1281 Words | 4 Pages. LOVE The uphill downfall.
What is love ? Is it scientific, humanistic, or is it holistic? We may never know, but we can . know what causes it and how it is created. Everyone wants an insight on how to keep the firing passion in their relationship, but what motivated me to learn more about upcoming essay competitions in india, this topic was my past relationship experiences; I wanted to figure out how I fell in love and on disability, have an idea on why things ended the way they did. Of course, there is no exact scientific reason why things. Emotion , Greek words for love , Interpersonal relationship 1256 Words | 4 Pages. Art 1030: ART APPRECIATION Dr. Carol Ventura Study Guide for First Test Spring 2015 You do not have to know the names of . artists or their work for this test. Oxford! The first test will be multiple choice and on disability, will cover terms and media only. These words are from the oxford gloucester green, text, lectures, and videos. I suggest you make a flashcard for each word with the word and a photocopy of the example from the book (if there is one) on one side and on disability, the meaning and context on the other.
When you study with the flash cards. Arch , Barrel vault , Color 487 Words | 2 Pages. ? Is It Love ? Jazmine M Hawkins Georgia Perimeter College Abstract This paper explores the findings of . multiple researchers’ theories of love ? It breaks down what we can be classified as passionate love and compassionate love ? What does love have to do with your attention span? Some researches define love scientifically saying that love is a production of a mixture of hormones and sabine dissertation, chemical reactants while others say love is self-defined and can only be judged. Attachment theory , Developmental psychology , Human bonding 1362 Words | 4 Pages.
Love Love is something that most humans look for in life because it comes with one of the research on disability, greatest amount of application essay, pleasure a . Papers On Disability! human being can experience. The love for our mother and our entire families is one of the first thing a baby feels and as the years goes by we know that life is about two big thing: success in work field and being able to find people that will love you for who you are. Being able to love is one of the most important thing because it can lead to ncssm essay a great amount of trust and. English-language films , Family , Homosexuality 2815 Words | 7 Pages. one-word topic Love . Papers On Disability! This piece was written in 45 minutes (actually I had more time, I but I wasted too much time - some of it unnecessary - . to think of what to write), so mind you, I was in quite a hurry. Personally, I don't think it's that good. I really wish they gave us more time for this written paper for thesis English. Could've produced a better essay with more time, I think. On Disability! So anyway, here you go. Comments will be appreciated.
Love (SPM Trial Exams Essay) by Lee Zhi Wei Love . It is the upcoming essay competitions, one. Doubt , Heart , Human 959 Words | 3 Pages. “ Love for another often hides a greater love for oneself” By a close comparison of your two texts, discuss the representation of . sex and seduction. In both Milton’s ‘Paradise Lost’ and Ford’s ‘Tis Pity She’s a Whore’ sex is papers on disability represented as a catalyst for sin. The love which is promised by many of the central characters in the poem and the play often has a falsehood and is used as a facade for the character’s true egotistic needs within. One can see a falsehood in Giovanni’s admitted love for.
Adam and Eve , Garden of college addiction, Eden , Interpersonal relationship 1102 Words | 3 Pages. people would not imagine how Valentine’s day affect America and other countries from economical to emotional. Valentine’s day is easy to recognize for its . many symbols: cupid which represents an on disability, angel who helps mates get together or fall in love , hearts, arrows, love cards, letters and the colors white and red representing purity and blood.(Thompson) There are many legends about the origin of Valentine’s day, but there are two that are more realistic and important. This holiday started in one place and. Chocolate , Love , Lupercalia 1480 Words | 4 Pages. February 1st 2012 True Love and thesis binding gloucester, its Obstacles Love is one of the most important things to the survival of the human race, . because it allows humans to research on disability work together and ncssm application, connect with each other.
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This essay will discuss how the on disability, internet has affected this art but it has not been lost but simply modified. Communication. Communication , History of the Internet , Instant messaging 1060 Words | 4 Pages. were a truthful man, he would haveinformed me that the lumber not included in the account werebad”. 17. Rizal Challenges A French To A DuelWhen Carnicero . heard thisdispleasing news, he informedMr. Juan Lardet that Dr.Rizal was an expert inMartial Arts speci?cally inthe ?eld of Fencing and sabine, PistolShooting.Mr. Juan Lardet gave it athought and later apologized.Dr. Rizal and Mr. JuanLardet’s relationship becamestable afterwards. Research Papers! 18.
Rizal And Fr. SanchezFr. Sanchez was the Jesuitpriest who taught Dr. Andres Bonifacio , Ateneo de Manila University , El filibusterismo 1680 Words | 5 Pages. ? Love Everyone has felt love at one point in leick dissertation, their life. It could have been between two people, a pet or even a non-living . object. You could have experienced it as a little crush or the real thing as a whole. Some people sometimes will go a lifetime without finding that one person for papers on disability them, but then there’s other times people fall in and out of love like it’s nothing to college essays addiction them. On Disability! You can love many things but the love between two people is upcoming priceless. Different types of people experience different. English-language films , Friendship , Interpersonal relationship 1262 Words | 4 Pages.
?Jalissa Goolsby Professor Rhodes English 29 January 14 Fatherless Love The vision of my Fatherless Love have . became more and more of a blur to my past childhood memories of not having him there in research on disability, my life as a young girl. This is my life not a story I always wanted to be daddy’s girl growing up. Not having my father there when I became mature or when I had my first break up played a major impact in my young life. ‘‘Dance With My Father’’ by Luther Vandross is a song that is very. 2006 albums , American films , Emotion 1309 Words | 4 Pages. disguised as a feast Rollin’ in sabine leick, the Rolls-Royce Corniche Only the research, doctors got this, I’m hidin’ from police Cocaine seats All white like I got the leick, whole . thing bleached Drug dealer chic I’m wonderin’ if a thug’s prayers reach Is Pious pious cause God loves pious? Socrates asks, “Whose bias do y’all seek?” All for Plato, screech I’m out here ballin’, I know y’all hear my sneaks Jesus was a carpenter, Yeezy, laid beats Hova flow the research papers on disability, Holy Ghost, get the hell up out application your seats Preach [Frank Ocean] . Christianity , Holy Spirit , Jay-Z 562 Words | 3 Pages. The Characterization of Medea in Euripides and Ovid.
Heroides XII: Medea to Jason by Ovid Both Fifth century B.C. playwright Euripides and Roman poet and dramatist Ovid tell the research papers on disability, . story of Jason ditching Medea for intelligence another woman; however, they do not always share a perspective on the female matron's traits, behavior, and purpose. Euripides portrays a woman who reacts to injustice by beginning a crusade to avenge all who harmed her which she is prepared to research on disability see through even if it means resorting to the most contemptible methods. Ovid , on upcoming in india the other hand, tells. Argonauts , Colchis , Emotion 1553 Words | 5 Pages. you in Drama, you have been the one person I really couldn’t stop thinking about. At the same time you have managed to keep my feet on research the ground, you were . never like those other “fan girls”. You always had something different about you and intelligence, I really love that about you. “You have kept my feet on the ground and yet showed me how beautiful the stars and research, skies are” – Read that somewhere one time, figured could be applied here. Lol I somehow always thought whatever you did was somehow simply “amazing. 2002 singles , 2006 albums , 2006 singles 1702 Words | 4 Pages. the visual aspects of art and architecture, line, shape, color, light, texture, space, math, volume, and composition. Style – the combination . of form and sabine, composition that makes a work distinctive.
Content – includes subject matter or meaning and papers on disability, a work of art . School of essays addiction, artists – a group of artist usually working at the same time and sharing similar style influences and ideas Iconography – identify and research papers, studying and subject matter and conventional symbols and works of arts . Representational –. 2nd millennium BC , Babylon , Borobudur 1106 Words | 9 Pages. The Art of Living As everyone knows, ink is something that can never be undone. It is something permanent and is very difficult to cover . up or remove. It can be in a form as simple as a pen caressing a piece of paper or as complex as a needle drenched in ink, piercing through skin to form a different kind of art , known as a tattoo. Essay Movie! As times are changing, tattoos seem to be getting a lot more common in my generation compared to previous ones. As tattoos become more popular, so do the criticisms. Family , Permanent makeup , Tattoo 1508 Words | 3 Pages. president in the history of the United States.
He had a strong moral vision of where his country must go to preserve and enlarge the rights of all her . people, but he was also a good man with a strong sense of character and a great discipline in the art of law; and research, he sought to continue the great and mighty legacy of the Constitution. He believed that the Founding Fathers had drawn up the Constitution without the mention of slavery because they felt that it would later die of a natural death. . Abraham Lincoln , American Civil War , President of the United States 1112 Words | 3 Pages. and the poor have to submit to it. 3. Religion and moral- Religion is oxford gloucester only represented by padre Estaban who cares about men’s souls but the majority of . the characters in the novel such as Galante, Gaspar, Andujar, Deblas, Marta lack compassion, love , and good principals. 4. Inheritance- Juan del Salto works very hard in order to provide an education for his son and leave him well off for the future. 5.)The complexity of silence- This theme means that you cannot always tell the truth because. Puerto Rico 1439 Words | 4 Pages. What is considered art has been a controversial question for research papers many years in history and today. There are various forms and leick dissertation, types of research on disability, . College Essays! art . Because art is papers very complex and diverse, it is viewed and conceptualized in many different ways. Nancy G. Titanic Movie! Heller states even though a type of artwork is research hard to understand, it’s considered art , and artwork that people don’t understand shouldn’t be disregarded from other types of essay movie, art . Papers! She feels as though people shouldn’t be intimidated by intelligence, artwork that’s hard to understand. Art , Cubism , Present 1296 Words | 4 Pages.
work was also included in the Best American Short Stories collections for 1946, 1948 and papers, 1952. Perhaps Bradbury's most unusual honor came from the Apollo . Phd Thesis Emotional! astronaut who named Dandelion Crater after Bradbury's novel, Dandelion Wine. Research! Bradbury's lifetime love of cinema fuelled his involvement in many Hollywood productions, including The Beast from essay titanic movie 20,000 Fathoms (a version of his story, The Fog Horn), Something Wicked This Way Comes (based on his novel,) and research papers, director John Huston's version of Moby Dick. Dandelion Wine , Fahrenheit 451 , Leigh Brackett 1683 Words | 6 Pages. ?The Magic Flute Review Kristyn Davis Dr. Eubanks November 28, 2011 Liberal Arts “ Art is one way whereby man seeks to . Movie! understand the world.”. This is a quote from Oscar Brockett’s book, The Essential Theater. Over the research, weekend the Ouachita Baptist University: School of Fine Arts , division of thesis binding green, music put on an opera entitled The Magic Flute. Originally composed by papers, Mozart, the students in ncssm application, the production did an excellent job of bringing his composition to life. Going into the opera, my expectations.
Art , Music , Opera 794 Words | 4 Pages. medium one chooses to use to express oneself determine whether or not it is truly art ? While digital artists’ artistic ability is often . Research On Disability! questioned and the credit is given to the computer being used, the art itself springs from the mind of the digital artist. I can say this with personal fervor: Digital art is truly in college essays addiction, essence a form of art that merely takes advantage of the innovations of modern technology. Digital Art isn’t computer-generated. While it might involve using tools offered by specialized. Art , Computer , Computer graphics 1392 Words | 4 Pages. ? Art Essay Draft The nude has changed dramatically throughout time in terms of its role in papers on disability, the art world. It has been used to . Upcoming Competitions In India! portray a person’s power and their weakness, the way they see themselves and the way others see them. The majority of nude artworks are of the female nude, as highlighted by John Berger, ‘men look at women, women look back at themselves being looked at.’ Vanessa Beecroft, a contemporary artist deems to challenge the way society views the nude in both high art and everyday. Aesthetics , Art , Female 986 Words | 3 Pages.
Alexis Cota September 14, 2013 LOVE IS LOVE People live in a world where, nowadays, anyone will be judged for any little . thing they do. It may be the way people look, act, smell, walk, talk, dress, and papers on disability, even by intelligence, liking the same sex as them. Papers On Disability! Nothing in application, the world will ever please society. Research Papers! People are supposed to be free to sabine leick dissertation love anyone they want. Yet, society makes it so hard for anyone to papers try, and be with the same sex. Either it will turn out to be their closest friends, or family who will end up. Bisexuality , Gay , Homosexuality 1033 Words | 3 Pages. The Art of Loving is a slim volume of only titanic a little over a hundred pages yet it packs one hell of a punch. Research Papers On Disability! Written some fifty years ago, here . is a more damning indictment of modern society than anything the existential crowd of Bertrand Russell, Albert Camus or Jean Paul Sartre could cook up. The Art of ncssm application, Loving is research papers on disability a very concise and application, pithy read, it is written in research papers on disability, the terse lucid style of gospel, each word in binding gloucester, each line serving a critical function.
This is not a writer's style nor is a critic's but that. Erich Fromm , Frankfurt School , God 1588 Words | 4 Pages. Naomi McFarland Out of Class Essay #2 Final Copy Suffering through Art Art speaks and shows us the reality of research, people by . Phd Thesis! expressing human behavior, thoughts, ideas and emotions through a piece of research, work. As Google Definition’s says, “ Art is the works produced by such skill and imagination.” Art has the ability to express the painful truths that exist in oxford gloucester, the world and its reality. No matter how painful it might be to have a legitimate knowledge about the research on disability, truth, I believe people need to see. Art , Earth , Emotion 1857 Words | 5 Pages. The Marketing of Art Part 1: Target Market and Competition When determining a target market a marketer must first research their product and . the consumers who purchase the product, then decide what type of consumer would the marketer prefer to attract to the product they are marketing (Guille, n.d.). The product that was chosen for this class was Art . To determine our particular target market we must get to know our product.
Britannica Encyclopedia defines art as, “the use of skill and imagination. Advertising , Art , Arts 1219 Words | 4 Pages. Upon reading Erich Fromm's The Art of phd thesis intelligence, Loving, I gained a better understanding of what love really is. Research! Fromm's book puts . love into perspective. He begins with several facts with regards to the attitude in sabine leick dissertation, which people treat love . They are the problems of how to on disability be loved, the object to love as well as the confusion between the initial experience of falling in love and the permanent state of being in love , which had a great impact on me, as far as thinking about what love is. Strangers meet, they. Father , Feeling , Interpersonal relationship 1185 Words | 3 Pages. ? Art is life, it is beauty, it is emotion, it is you, it is me, it is college essays addiction everything. Papers On Disability! Art defines all that we are, and all that we . could become. Art is of the past and movie, of the future, of the influences of our daily lives, of our pasts combined with who we are today. Art is an indescribable joy, an expansion of the mind, body and soul.
We are art , every last individual of the human race. Research! Art comes in sabine, the form of research, music, dance, theater, painting, drawing, blowing, throwing, and even in the math equations. Aesthetics , Ancient Egypt , Art 2290 Words | 4 Pages.
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Algebraic Number Theory - Essay - Mathematics. Algebraic Number Theory. Version 3.03 May 29, 2011. An algebraic number field is a finite extension of Q; an algebraic number is an element of an algebraic number field. Algebraic number theory studies the arithmetic of algebraic number fields — the ring of integers in the number field, the ideals and units in the ring of integers, the extent to which unique factorization holds, and so on. An abelian extension of a field is a Galois extension of the field with abelian Galois group. Class field theory describes the papers on disability 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. Emotional Intelligence. v2.10 (August 31, 1998). Fixed many minor errors; added exercises and research papers on disability, 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. . . . . . . . Essay Competitions. . . . . . . . . . . . . . . . . . . . . Research On Disability. . . . Application Essay. . . . . . . . . 5 Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . Research. . . . . Application Essay. . . . . . . 5 Acknowledgements . . . . . . Research. . . . . . Sabine. . Papers. . . Ncssm. . . . . Research. . . . . . . . . . . . . . . . 5 Introduction . . . . . . . . . . . . Ncssm. . . . . Research. . . . . Thesis Oxford Green. . Research. . . . . . . . . . . . . . . . . 1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. 1 Preliminaries from Commutative Algebra 7 Basic definitions . . . Upcoming Essay Competitions. . . . . . . . . . . . . . . . . . . . . . . Research Papers On Disability. . . Application Essay. . . . . . . . . 7 Ideals in products of rings . . . . . . . . . . . . . . . . . . . . . . . Papers On Disability. . . . . . . . 8 Noetherian rings . . . . . . . . . . . . . . . . . . . . . . . . College Essays Addiction. . . . . . . . . . . . 8 Noetherian modules . . . . . . . . . Papers. . . . . . . . . . Sabine. . . . . . . . . . . . . . . Research Papers On Disability. . 10 Local rings . . . . . . . . . . . . . . . . . . Upcoming Essay In India. . . . Papers. . . . . . . . . . . . . . . . . 10 Rings of fractions . . . . . . . . . . Thesis Binding Green. . . . . . . . . . . . . . . . . . . Research Papers On Disability. . . . . . . 11 The Chinese remainder theorem . . . . . . . . . Phd Thesis Emotional Intelligence. . . . . . . . . . . . Research On Disability. . . . . . . 12 Review of binding oxford gloucester green tensor products . . . . . . . . . . . . . . . . . . Research. . . Upcoming Competitions. . . . . . . . . . . 14 Exercise . . Research. . . Essay. . Research Papers On Disability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ncssm Application. . . . 18. 2 Rings of Integers 19 First proof that the integral elements form a ring . . . . . . . Research On Disability. . . . . . . Phd Thesis. . . . . . Papers. 19 Dedekind’s proof that the integral elements form a ring . . . . . . . . Upcoming. . . . . . . 20 Integral elements . . . . . . . . . Papers On Disability. . . . . . Binding Oxford Gloucester. . . . . . Research Papers. . . . . . . . Leick Dissertation. . . . . . . . . 22 Review of bases of A-modules . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Review of norms and traces . . . Research. . . . . . . . . . Ncssm. . Research. . . . . . . . . . . . . . . . Ncssm. . Research On Disability. 25 Review of bilinear forms . . . . . . . Upcoming Essay Competitions In India. . . . . . . . . . . On Disability. . . . . . . . . . Thesis Binding. . . . . 26 Discriminants . . . . . . . . . . . . . . . . . . . . . . . . . . Research On Disability. . . . . . . . . . . 27 Rings of integers are finitely generated . . . . . . . . . . . . . . . . . . . . . . . 29 Finding the ncssm application essay ring of integers . . . . . . . . . . . . Research On Disability. . . . . . . . . . . . . . . . . . 31 Algorithms for finding the thesis binding gloucester green ring of integers . . . . . . . . Research. . . Thesis. . . . . . Research Papers On Disability. . . Ncssm. . . . . 34 Exercises . . . . . . . . Research. . . . . . . . . . . . . . . . . . . . . . . . . . . Upcoming Essay In India. . . . . 38. 3 Dedekind Domains; Factorization 40 Discrete valuation rings . . . . . . . . . . . . . . . Research On Disability. . . . . . . . . . . . . . . Essay Movie. . . 40 Dedekind domains . . . . . . . . . . . . . . . . . . . . . . . Research On Disability. . Movie. . . . . . . . . . 42 Unique factorization of ideals . . . . . . . . . . . . . . . . . . . . . Papers. . . Thesis Binding Gloucester Green. . . . . . 43 The ideal class group . On Disability. . . . Phd Thesis Emotional Intelligence. . . . . . . . . . Research Papers On Disability. . . . . . . . . . . . . College Addiction. . . Research On Disability. . . Essay Competitions In India. . . Papers On Disability. . 46 Discrete valuations . . . . . . . . . . . . . . . . . . . . . College Essays. . . . . . . . . Papers On Disability. . . . . Emotional. 49 Integral closures of Dedekind domains . . . . . . . . . . . . . . . . . . . . . . . 51 Modules over Dedekind domains (sketch). . . . . . . On Disability. . . . . . . . . . . . Emotional Intelligence. . . . . 52.
Factorization in extensions . . . . . . . . . Research Papers On Disability. . . . . . . . . Thesis Green. . . . . . . . . . . . . 52 The primes that ramify . . . . . On Disability. . Binding. . . . . . . . . . . . . . . . . . Research On Disability. . . . . Essay Competitions In India. . . . . 54 Finding factorizations . . On Disability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Examples of factorizations . . Ncssm Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . Research Papers. . 57 Eisenstein extensions . . . . . . . . . . . . . . . . . . Leick. . . . . . . . . . . . . . . 60 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61. 4 The Finiteness of the Class Number 63 Norms of ideals . . . . . . . . . . . Research Papers. . . . . . . . . Sabine Leick Dissertation. . . . . . . . Papers On Disability. . . Ncssm Application Essay. . . . . . . . 63 Statement of the main theorem and its consequences . . . . . . . . . . . . . Papers On Disability. . . . 65 Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Some calculus . . . . . . . . . . . . . . . . . . . . . Ncssm Essay. . . . . . Papers On Disability. . . Intelligence. . . . . Research Papers. . . . . 73 Finiteness of the class number . . . . . . . . . . . . . . . . . Essay Movie. . . . . . . . . . . 75 Binary quadratic forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Research. . 76 Exercises . . . . Emotional Intelligence. . . . . . . . Research On Disability. . . . . Application Essay. . . . . . . . . . . . . . . . . . . . . Research On Disability. . . . 78. 5 The Unit Theorem 80 Statement of the theorem . . . . . . . . . . . . . . . . College. . . . . . . . Research. . . . . Sabine Dissertation. . . . 80 Proof that UK is finitely generated . . . . . . . . . . . . . . . . . . On Disability. . . . . . . . 82 Computation of the rank . . . . . . . . . . . . . . . . . . . . . . Essays Addiction. . . . . . . . . 83 S -units . . . . . . . . . . . Research Papers On Disability. . . . Essay. . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Example: CM fields . . . . . . Papers On Disability. . . . . . . . . . . . . Phd Thesis Intelligence. . Research Papers On Disability. . . . College Addiction. . . . . . . . . . . . 86 Example: real quadratic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Example: cubic fields with negative discriminant . . . . . . . . . . . . . . . . . 87 Finding .K/ . . . . . . . . . . . . . . On Disability. . . . . . . . . . . . . . . . . . . . . . . 89 Finding a system of fundamental units . . . . . . . Competitions. . Research Papers. . . . . . . . . . . . . . . . 89 Regulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . College. . . . . . Papers. . . 89 Exercises . . . . . . . . Leick Dissertation. . . . . . . . . . Research Papers. . . . . . . . . . . . . . . . . Movie. . . . Papers On Disability. . . 90. 6 Cyclotomic Extensions; Fermat’s Last Theorem. Upcoming Essay Competitions. 91 The basic results . . . . . . . Papers On Disability. . . . . . . Upcoming Essay In India. . . . . . . . . . . . . . . . . . . . . On Disability. . . 91 Class numbers of cyclotomic fields . . . . . . . . . . . . . . . . . . . . . . . . Essay Movie. . 97 Units in cyclotomic fields . . Papers On Disability. . . . . . . . Emotional. . . . Research. . . Movie. . . . . . . . . . . . . . . . . 97 The first case of Fermat’s last theorem for regular primes . . . . . . . . . . . . . 98 Exercises . . . . . Research Papers On Disability. . Thesis Oxford Gloucester Green. . . . . . . . . . . . . . . Research Papers. . . . . Ncssm Application. . . . Research Papers On Disability. . . . . . . . . . . . 100. 7 Valuations; Local Fields 101 Valuations . . Intelligence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . On Disability. . Dissertation. . Research Papers. . . . 101 Nonarchimedean valuations . . . . . . . . . Phd Thesis Emotional. . . . . . . . . . . . . . . . . . . . . 102 Equivalent valuations . . . . . . . . . . . . . . . . . . . . . . . . On Disability. . . Thesis Binding Green. . . . Papers. . . . 103 Properties of discrete valuations . . Thesis Binding. . . On Disability. . . . . . . . . . College. . . . . . . . . . . . . . On Disability. 105 Complete list of valuations for the rational numbers . Emotional Intelligence. . . Research Papers. . . . . . . . Essay Titanic. . . Research Papers On Disability. . . . . 105 The primes of a number field . . . . . . . . . . Upcoming In India. . . . . . . . . . Papers. . . . . Essay Titanic. . . . . . 107 The weak approximation theorem . . . . . . . . . . . . . . . . . . . . . . . . . 109 Completions . . . . . . . . . . . . . . . Research On Disability. . . . . . . . . . . . . . . . . . . . . . . 110 Completions in the nonarchimedean case . . . . . . . . . . . . . . . . . . . . . . 111 Newton’s lemma . . Upcoming Essay Competitions. . . . . Papers. . . . . . . . . . . . . . . Upcoming In India. . . . . . . . . . . . . . . 115 Extensions of nonarchimedean valuations . . . . . . . . On Disability. . . . Thesis Oxford. . . . . . . . . . . Papers On Disability. 118.
Newton’s polygon . . . . . . . . . . Application Essay. . . . . . . . . . . . . . Research Papers. . . . . . . . . . . Leick Dissertation. . 120 Locally compact fields . . . . . . . . . . . . Research. . . . . . . Essay. . . . . . . . . . . . . . 122 Unramified extensions of a local field . . . Research Papers On Disability. . . . . . . Leick. . . . Research Papers On Disability. . . . . . . . . Phd Thesis Emotional Intelligence. . . . 123 Totally ramified extensions of K . Research On Disability. . . Essay. . Research Papers On Disability. . . . . . . . . . . . . Phd Thesis. . . . . . . . . . Research Papers. . Emotional. 125 Ramification groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Research. 126 Krasner’s lemma and applications . . . . . . Dissertation. . . . . . . . . . . . . . . . . . . . 127 Exercises . . Papers On Disability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Upcoming Essay In India. 129. 8 Global Fields 131 Extending valuations . . . . . . . . . . . . . . . . . . . . . On Disability. . . . . . . . . . . . 131 The product formula . . . Essay Titanic Movie. . . . . . . . . . . . . . . . . . Research On Disability. . . . . . . . . . . . . 133 Decomposition groups . . . . . . . . . . . . . . . . . . . Upcoming Essay Competitions In India. . . Research Papers On Disability. . . . . . . . Sabine Leick. . . . 135 The Frobenius element . . . . . . . . . . . . . . . . . . . Research. . . . . . . . . . . . . 137 Examples . . . . . . . . . . . . . . . . Essay Competitions. . . . . . . . . Research Papers On Disability. . . . . . . . . . . . . . . 139 Computing Galois groups (the hard way) . . . . . . . . . . . . . . . . . . . . . . 140 Computing Galois groups (the easy way) . . . . . . . . . College. . . . . . Research. . . . . . . . . 141 Applications of the Chebotarev density theorem . . . . . . . . . . . . . . . . . Essay. . 146 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . On Disability. . . . . . . . . . . . . 147. A Solutions to the Exercises 149. B Two-hour examination 155. We use the standard (Bourbaki) notations: ND f0;1;2; : : :g; ZD ring of integers; RD field of thesis oxford 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 papers on disability, S when S is finite). Let I and A be sets; a family of elements of ncssm essay A indexed by I , denoted .ai /i2I , is a function i 7! ai WI ! A. X Y X is a subset of Y (not necessarily proper); X. def D Y X is defined to papers, be Y , or equals Y by definition; X Y X is isomorphic to titanic movie, Y ; X ' Y X and Y are canonically isomorphic (or there is a given or unique isomorphism); ,! denotes an injective map; denotes a surjective map. It is standard to use Gothic (fraktur) letters for research papers, 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 sabine, multilinear algebra. Research Papers. An undergraduate number theory course will also be helpful. In addition to the references listed at the end and in footnotes, I shall refer to the following of my course notes (available at www.jmilne.org/math/): FT Fields and Galois Theory, v4.22, 2011. GT Group Theory, v3.11, 2011. Upcoming Competitions. CFT Class Field Theory, v4.01, 2011. I thank the following for providing corrections and comments for earlier versions of research papers on disability these notes: Vincenzo Acciaro; Michael Adler; Giedrius Alkauskas; Francesc Castella?; Kwangho Choiy; Dustin Clausen; Keith Conrad; Paul Federbush; Hau-wen Huang; Roger Lipsett; Loy Jiabao, Jasper; Lee M. Goswick; Samir Hasan; Lars Kindler; Franz Lemmermeyer; Siddharth Mathur; Bijan Mohebi; Scott Mullane; Wai Yan Pong; Nicola?s Sirolli; Thomas Stoll; Vishne Uzi; and others. PARI is an open source computer algebra system freely available from http://pari.math.u- bordeaux.fr/. FERMAT (1601–1665). Stated his last “theorem”, and proved it for mD 4. He also posed the problem of finding integer solutions to the equation, X2?AY 2 D 1; A 2 Z; (1) which is essentially the problem1 of finding the units in Z? p A?.
The English mathemati- cians found an algorithm for solving the problem, but neglected to prove that the algorithm always works. EULER (1707–1783). He introduced analysis into the study of the prime numbers, and he discovered an early version of the quadratic reciprocity law. LAGRANGE (1736–1813). He found the 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 upcoming classification of binary quadratic forms over Z, which is closely related to the problem of finding the class numbers of quadratic fields.
DIRICHLET (1805–1859). He introduced L-series, and used them to prove an analytic for- mula for the class number and a density theorem for the primes in an arithmetic progression. Papers. 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 upcoming essay competitions in india 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 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 integers in a number field, by proving that ideals factor uniquely into products of prime ideals in such rings, and by showing that, modulo principal ideals, they fall into finitely many classes. Defined the zeta function of a number field. WEBER (1842–1913). Made important progress in class field theory and the Kronecker Jugendtraum. HENSEL (1861–1941).
He gave the first definition of the field of p-adic numbers (as the set of infinite sums. n, an research papers on disability, 2 f0;1; : : : ;p?1g). HILBERT (1862–1943). He wrote a very influential book on algebraic number theory in 1897, which gave the first systematic account of the theory. Some of his famous problems were on number theory, and have also been influential. TAKAGI (1875–1960). He proved the fundamental theorems of abelian class field theory, as conjectured by Weber and Hilbert. NOETHER (1882–1935). Together with Artin, she laid the foundations of modern algebra in which axioms and conceptual arguments are emphasized, and she contributed to the classification of central simple algebras over number fields. HECKE (1887–1947).
Introduced HeckeL-series generalizing both Dirichlet’sL-series and Dedekind’s zeta functions. ARTIN (1898–1962). He found the “Artin reciprocity law”, which is the main theorem of oxford 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 number fields. BRAUER (1901–1977). Defined the Brauer group, and research, contributed to the classification of central simple algebras over number fields. WEIL (1906–1998). Defined the Weil group, which enabled him to give a common gener- alization of Artin L-series and Hecke L-series. CHEVALLEY (1909–84). The main statements of class field theory are purely algebraic, but all the earlier proofs used analysis; Chevalley gave a purely algebraic proof. With his introduction of ide?les he was able to give a natural formulation of class field theory for infinite abelian extensions. Leick. IWASAWA (1917–1998). He introduced an 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 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 research papers, 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 ncssm cyclotomic fields].
Kummer 1844 (as translated by Andre? Weil) The fundamental theorem of arithmetic says that every nonzero integerm can be writ- ten in papers on disability, 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. 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 hold, in number fields. Ncssm Application. 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 order to research papers, 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 phd thesis intelligence, Q, and ? is an algebraic integer if it satisfies such an equation with coefficients a1; : : : ;an in Z. We shall see that the algebraic integers form a subring OK of K. The criterion as stated is difficult to apply. We shall show (2.11) that ? is an algebraic integer if and only if its minimum polynomial over Q has coefficients in Z. Consider for papers on disability, example the field K D Q? p d?, where d is a square-free integer. The. College Addiction. minimum polynomial of ? D aCb p d , b ¤ 0, a;b 2Q, is. Papers. .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 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 a unique factorization domain if every nonzero element of A can be expressed as a product of irreducible elements in essentially one way. Is the ring of integers OK a unique factorization domain?
No, not in general! We shall see that each element of OK can be written as a product of irreducible elements (this is true for all Noetherian rings), and so it is the uniqueness that fails. For example, in Z? p ?5? we have. 6D 2 3D .1C p ?5/.1?. To see that 2, 3, 1C p ?5, 1?. p ?5 are irreducible, and no two are associates, we use the. p ?5 7! a2C5b2: This is multiplicative, and it is easy to see that, for ? 2OK , Nm.?/D 1 ” ? N? D 1 ” ? is a unit. (*) If 1C p ?5D ??, then Nm.??/D Nm.1C. Oxford. 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. Papers. 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 phd thesis intelligence, enlarge the set of “prime numbers” so that, for example, in Z? p ?5? there is a unique factorization, 6D .p1 p2/.p3 p4/D .p1 p3/.p2 p4/; underlying the above factorization; here the pi are “ideal prime factors”.
How do we define “ideal factors”? Clearly, an ideal factor should be characterized. by 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 research papers, 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 dissertation, ideal, and that if. aD .a1; . ;am/ and bD .b1; . ;bn/ then a bD .a1b1; . ;aibj ; . ;ambn/: With these definitions, one recovers unique factorization: if a ¤ 0, then there is an essentially unique factorization: .a/D p1 pn with each pi a prime ideal. In the above example, .6/D .2;1C p ?5/.2;1?.
In fact, I claim. .2;1C p ?5/.2;1?. .3;1C p ?5/.3;1?. .2;1? p ?5/.3;1?. For example, .2;1C p ?5/.2;1?. p ?5;6/. Since every gen- erator is divisible by 2, we see that. .2;1C p ?5/.2;1?. Conversely, 2D 6?4 2 .4;2C2. and so .2;1C p ?5/.2;1?. p ?5/ D .2/, as claimed. I further claim that the four ideals. .2;1C p ?5/, .2;1?. Research Papers On Disability. 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. Essays. Z? p ?5?=.3;1?. which is an integral domain. How far is papers, this from what we want, namely, unique factorization of elements? In other. words, how many “ideal” elements have we had to add to our “real” elements to get unique factorization. In a certain sense, only a finite number: we shall see that there exists a finite set S of ideals such that every ideal is of the form a .a/ for some a 2 S and 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. Phd Thesis Emotional Intelligence. 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 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 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 research papers, that no such factorization exists into polynomials with integer coefficients of degree 2. This led people to look at more general factorizations. In a famous incident, the French mathematician Lame? gave a talk at the Paris Academy in 1847 in which he claimed to prove Fermat’s last theorem using the following ideas. Let p 2 be a prime, and suppose x, y, z are nonzero integers such that.
Write xp D zp?yp D. Y .z? iy/; 0 i p?1; D e2i=p: He then showed how to obtain a smaller solution to the equation, and hence a contradiction. Liouville immediately questioned a step in Lame?’s proof in which he assumed that, in order to show that each factor .z ? iy/ is a pth power, it suffices to show that the factors are relatively prime in pairs and their product is a pth power. In fact, Lame? couldn’t justify his step (Z?? is not always a principal ideal domain), and Fermat’s last theorem was not proved for almost 150 years. However, shortly after Lame?’s embarrassing lecture, Kummer used his results on competitions in india 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 research on disability degree is very small. By using algebraic number theory one can write down an algorithm to do it for any degree. For applications of essay algebraic number theory to elliptic curves, see, for example, Milne 2006. Some comments on the literature. COMPUTATIONAL NUMBER THEORY.
Cohen 1993 and Pohst and Zassenhaus 1989 provide algorithms for most of the construc- tions we make in this course. The first assumes the reader knows number theory, whereas the second develops the whole subject algorithmically. Cohen’s book is the more useful as a supplement to this course, but wasn’t available when these notes were first written. While the books are concerned with more-or-less practical algorithms for fields of small degree and small discriminant, Lenstra (1992) concentrates on research on disability 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 application, excellent idea of how algebraic number theory developed. Edwards 1977 is research, a history of algebraic number theory, con- centrating on the efforts to prove Fermat’s last theorem. The notes in Narkiewicz 1990 document the origins of most significant results in algebraic number theory. Lemmermeyer 2009, which explains the origins of “ideal numbers”, and other writings by the same author, e.g., Lemmermeyer 2000, 2007. 0-1 Let d be a square-free integer. Complete the verification that the ring of integers in Q? p d? is as described. 0-2 Complete the verification that, in Z? p ?5?, .6/D .2;1C p ?5/.2;1?. is a factorization of .6/ into a product of prime ideals. CHAPTER 1 Preliminaries from Commutative.
Many results that were first proved for rings of integers in number fields are true for more general commutative rings, and it is sabine leick, 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 the identity element. A ring B together with a homomorphism of rings A! B will be referred to on disability, as an A-algebra. We use this terminology mainly when A is a subring of B . In this case, for elements ?1; . ;?m of B , A??1; . ;?m? denotes the smallest subring of B containing A and the ?i . It consists of all polynomials in the ?i with coefficients in A, i.e., elements of the form X. ai1. im? i1 1 . ? im m ; ai1. im 2 A: We also refer to A??1; . ;?m? as the A-subalgebra of B generated by the ?i , and when B D A??1; . ;?m? we say that the ?i generate B as an A-algebra. For elements a1;a2; : : : of A, we let .a1;a2; : : :/ denote the smallest ideal containing the ai . It consists of finite sums. P ciai , ci 2 A, and it is called the ideal generated by. a1;a2; : : :. 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 A — in fact, it is the essay smallest ideal containing both a and b. If aD .a1; . ;am/ and bD .b1; . ;bn/, then aCbD .a1; . Research On Disability. ;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. 1See also the notes A Primer of Commutative Algebra available on my website. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. College Essays. 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 research on disability, integral domain. A nonzero element of A is said to be prime if ./ is a prime ideal; equivalently, if jab) ja or jb. An ideal m in essay, A is maximal if it is maximal among the proper ideals of A, i.e., if m¤A and papers on disability, there does not exist an ideal a ¤ A containing m but distinct from it. An ideal a is maximal if and only if A=a is a field. Every proper ideal a of A is contained in a maximal ideal — if A is titanic, 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 on disability rings AB . If a and b are ideals in A and B respectively, then ab is an ideal in ncssm application essay, 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 research on disability, A1 Am are of the form a1 am with ai an ideal in Ai ; moreover, a1 am is essays, prime if and only if there is a j such that aj is a prime ideal in Aj and ai DAi for i ¤ j: A ring A is Noetherian if every ideal in A is finitely generated. Research. 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 ncssm essay, 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 will contain all the ai , and so an D anC1 D D a. (b) (c): Let a1 2 S . If a1 is not a maximal element of S , then there exists an a2 2 S such that a1 a2. If a2 is not maximal, then there exists an a3 etc.. From (b) we know that this process will lead to a maximal element after only finitely many steps. Research Papers On Disability. (c) (a): Let a be an ideal in A, and let S be the set of finitely generated ideals contained in a. Then S is nonempty because it contains the zero ideal, and so it contains a maximal element, say, a0 D .a1; : : : ;ar/.
If a0 ¤ a, then there exists an element a 2 ar a0, and sabine leick dissertation, .a1; : : : ;ar ;a/ will be a finitely generated ideal in a properly containing a0. This contradicts the definition of a0. 2. A famous theorem of Hilbert states that k?X1; . ;Xn? is Noetherian. In practice, al- most all the rings that arise naturally in algebraic number theory or algebraic geometry are Noetherian, but not all rings are Noetherian. For example, the ring k?X1; : : : ;Xn; : : :? of polynomials in an infinite sequence of symbols is not Noetherian because the 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 research on disability, 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 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 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 essay titanic movie all algebraic integers in the algebraic closure of 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. Papers On Disability. p ? will also be. an algebraic integer and ? D p ? p ?. Sabine Leick. 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 research papers on disability 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 . Essay Titanic Movie. If N and M=N are both Noetherian, then so also is M . PROOF. I claim that if M 0 M 00 are submodules of M such that M 0N DM 00N and M 0 and M 00 have the same image in M=N , then M 0 DM 00. To see this, let x 2M 00; the second condition implies that there exists a y 2M 0 with the same image as x inM=N , i.e., such that x?y 2N . Then x?y 2M 00N M 0, and so x 2M 0. Now consider an ascending chain of submodules of M . If M=N is Noetherian, the image of the chain in M=N becomes constant, and research papers on disability, 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 generated by a single element, then M A=a for some ideal a in A, and the statement is obvious. We argue by induction on the minimum number n of generators ofM . SinceM contains a submoduleN generated by n?1 elements such that the quotient M=N is generated by a single element, the statement follows from (1.7). 2. A ring A is said to local if it has exactly one maximal ideal m. Movie. 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 research, a submodule of M such that N CaM DM , then N DM: Rings of titanic movie 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. Papers On Disability. e1 D a1e1C Canen, ai 2 a: Then .1?a1/e1 D a2e2C Canen: As 1? a1 is not in m, it is a unit, and so fe2; . ; eng generates M , which contradicts our choice of fe1; : : : ; eng. (b) It suffices to show that a.M=N/DM=N for 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 college essays fractions of Z, and k.X/ is the field of fractions of k?X?: Let A be an integral domain with field of papers 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 essays, obviously a subring of K: EXAMPLE 1.10 (a) Let t be a nonzero element of A; then. St def D f1,t ,t2. Research. g. is a multiplicative subset of A, and we (sometimes) write At for S?1t A. For example, if d is essays, 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 papers on disability, a prime ideal, then SpDArp is a multiplicative set (if neither a nor b belongs to p, then ab does not belong to p/. We write Ap for S?1p A. For example, Z.p/ D fm=n 2Q j n is titanic movie, not divisible by pg:
2This notation conflicts with a later notation in research on disability, which Zp denotes the ring of p-adic integers. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. PROPOSITION 1.11 Consider an integral domainA and application essay, 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 papers S?1A, write ac for titanic movie, aA. Then: ace D a for all ideals a of S?1A aec D a if a is a prime ideal of on disability 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 emotional reverse inclusion, let b 2 a. We can write it b D a=s with a 2 A, s 2 S . Then aD s .a=s/ 2 aA, and so a=s D .s .a=s//=s 2 .aA/e: Let p be a prime ideal disjoint from S . Clearly .S?1p/A p. Papers On Disability. For the reverse inclu- sion, let a=s 2 .S?1p/A, a 2 p, s 2 S . Consider the equation a. s s D a 2 p. Both a=s. and s are in A, and so at least one of a=s or s is in p (because it is prime); but s … p (by assumption), and so a=s 2 p: 2. 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 set of upcoming in india prime ideals in A such that pS D? to on disability, the set of prime ideals in S?1A; the inverse map is p 7! pA. Emotional Intelligence. PROOF. It is easy to see that. p a prime ideal disjoint from S) pe is a prime ideal in S?1A, p a prime ideal in S?1A) pA is a prime ideal in A disjoint from S; and (1.11) shows that the two maps are inverse.
2. EXAMPLE 1.13 (a) If p is a prime ideal in A, then Ap is a local ring (because p contains every prime ideal disjoint from Sp). (b) We list the prime ideals in some rings: Note that in general, for papers, t a nonzero element of an essay titanic, 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. We want to translate this in terms of ideals. Integersm and n are relatively prime if and only if .m;n/D Z, i.e., if and only if .m/C .n/D Z. This suggests defining ideals a and b in a ring A to be relatively prime if aCbD A. If m1; . ;mk are integers, then T .mi / D .m/ where m is the least common multiple. Research Papers On Disability. of the mi . Thus T .mi / . Essays Addiction. Q mi /, which equals. Q .mi /. If the mi are relatively prime in. pairs, then mD Q mi , and research papers, 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 following statement. THEOREM 1.14 Let a1; . ;an be ideals in a ring A, relatively prime in pairs. Then for any elements x1; . ;xn of A, the congruences. have a simultaneous solution x 2 A; moreover, if x is one solution, then the other solutions are the elements of the form xC a with a 2. Q ai . In other words, the. natural maps give an exact sequence.
PROOF. Suppose first that n D 2. As a1C a2 D A, there are elements ai 2 ai such that a1Ca2 D 1. The element x D a1x2Ca2x1 has the required property. For each i we can find elements ai 2 a1 and bi 2 ai such that. 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 oxford gloucester green A such that. y1 1 mod a1; y1 0 mod Y. These conditions imply. y1 1 mod a1; y1 0 mod aj , all j 1: Similarly, there exist elements y2; . ;yn such that. yi 1 mod ai ; yi 0 mod aj for j ¤ i: The element x D P xiyi now satisfies the requirements. 1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. It remains to prove that T. ai . We have already noted that T. ai . First suppose that nD 2, and let a1Ca2 D 1, as before. For c 2 a1a2, we have. c D a1cCa2c 2 a1 a2. which proves that a1 a2 D a1a2.
We complete the proof by induction. This allows us to research on disability, assume that. T i2 ai . We showed above that a1 and. Leick. Q i2 ai are relatively. Papers. 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 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. Sabine Leick. 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. On Disability. A pair .Q;f / consisting of an A-module Q and an A-bilinear map f WM N !Q is called the tensor product of M and N if any other A- bilinear map f 0WM N ! P factors uniquely into f 0 D ? ?f with ?WQ!
P A-linear. The tensor product exists, and is unique (up to a unique isomorphism making the obvious diagram commute). We denote it by M ?AN , and binding gloucester, 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 research papers on disability, A-bilinear, and 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. Let ?WM !M 0 and ?WN !N 0 be A-linear maps. Then. Phd Thesis. .m;n/ 7! ?.m/??.n/WM N !M 0?AN 0. is A-bilinear, and therefore factors uniquely through M N !M ?AN . Research On Disability. 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 B is r s (so a linear map ks! kr ), then A?B is the mr ns matrix (linear map kns! kmr ) with. 0B@ a11B a1nB. Sabine Leick. : : : . am1B amnB. 1CA : LEMMA 1.17 If ?WM !M 0 and ?WN !N 0 are surjective, then so also is. ???WM ?AN !M 0 ?AN. PROOF. 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. Research Papers On Disability. 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. 4Kronecker products of matrices pre-date tensor products by about 70 years.
1. PRELIMINARIES FROM COMMUTATIVE ALGEBRA. The image of a?AM in college addiction, 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 on disability, note that .Z. m ! Z/?Z .Z=mZ/ equals Z=mZ. which is the intelligence zero map. PROOF (OF THEOREM 1.15) Return to the situation of the theorem. When we tensor the isomorphism. with M , we get an isomorphism. 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 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. Research. .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 essays addiction 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. Research Papers On Disability. According to the primitive element theorem (FT 5.1), K D k??? for some ? 2K. Let f .X/ be the minimum polynomial of ?. By definition this means that the map g.X/ 7! g.?/ determines an isomorphism.
Hence K?k? ' .k?X?=.f .X///?k? '??X?=.f .X// by (3) and (4). Because K is separable over k, f .X/ has distinct roots. Therefore f .X/ factors in ??X? into monic irreducible polynomials. that are relatively prime in pairs. We can apply the Chinese Remainder Theorem to deduce that. Finally, ??X?=.fi .X// is a finite separable field extension of ? of degree degfi . Thus we have proved the oxford following result: THEOREM 1.18 Let K be a finite separable field extension of k, and let ? be an arbitrary field extension. Papers On Disability. 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 ? in binding, ?i is a primitive element for?i=?, and if f .X/ and fi .X/ are the minimum polynomials for ? and papers on disability, ?i respectively, then. Emotional Intelligence. 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 papers conjugates of ? in C. The composite of ? 7! 1??WK!
C?QK with projection onto the i th factor is. We note that it is essential to assume in intelligence, (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 papers on disability fields. NOTES Ideals were introduced and studied by Dedekind for rings of algebraic integers, and later by others in polynomial rings. It was not until the 1920s that the theory was placed in its most natural setting, that of arbitrary commutative rings (by Emil Artin and Emmy Noether). Embed this document on your website. If you don't receive any email, please check your Junk Mail box.
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essay heroism Paradise is under the shadow of swords. Ruby wine is papers, drunk by knaves, Sugar spends to sabine fatten slaves, Rose and vine-leaf deck buffoons; Thunderclouds are Jove's festoons, Drooping oft in wreaths of dread Lightning-knotted round his head; The hero is not fed on sweets, Daily his own heart he eats; Chambers of the great are jails, And head-winds right for royal sails. In the elder English dramaetcher, there is a constant recognition of gentility, as if a noble behaviour were as easily marked in the society of their age, as color is in our American population. Research On Disability. When any Rodrigo, Pedro, or Valerio enters, though he be a stranger, the duke or governor exclaims, This is a gentleman,-- and proffers civilities without end; but all the rest are slag and refuse. In harmony with this delight in personal advantages, there is in movie their plays a certain heroic cast of character and dialogue,--as in Bonduca, Sophocles, the Mad Lover, the Double Marriage,--wherein the research papers on disability, speaker is so earnest and cordial, and on such deep grounds of character, that the dialogue, on the slightest additional incident in the plot, rises naturally into titanic movie poetry. Among many texts, take the following. The Roman Martius has conquered Athens,--all but the invincible spirits of Sophocles, the duke of Athens, and Dorigen, his wife. The beauty of the latter inflames Martius, and papers he seeks to save her husband; but Sophocles will not ask his life, although assured that a word will save him, and the execution of upcoming competitions, both proceeds. Valerius . Bid thy wife farewell. Soph . No, I will take no leave.
My Dorigen, Yonder, above, 'bout Ariadne's crown, My spirit shall hover for thee. Prithee, haste. Dor . Stay, Sophocles,--with this tie up my sight; Let not soft nature so transformed be, And lose her gentler sexed humanity, To make me see my lord bleed. So, 't is well; Never one object underneath the sun. Will I behold before my Sophocles:
Farewell; now teach the Romans how to die. Mar . Dost know what 't is to research on disability die? Soph . Thou dost not, Martius, And, therefore, not what 't is to live; to die Is to begin to live. It is to end. An old, stale, weary work, and to commence. A newer and a better. 'T is to application leave. Deceitful knaves for the society. Of gods and goodness. Thou thyself must part.
At last from all thy garlands, pleasures, triumphs, And prove thy fortitude what then 't will do. Val . But art not grieved nor vexed to leave thy life thus? Soph . Why should I grieve or vex for being sent. To them I ever loved best? Now I'll kneel, But with my back toward thee; 't is the last duty. This trunk can do the gods. Mar . Strike, strike, Valerius, Or Martius' heart will leap out at his mouth: This is a man, a woman!
Kiss thy lord, And live with all the freedom you were wont. O love! thou doubly hast afflicted me. With virtue and with beauty. Treacherous heart, My hand shall cast thee quick into my urn, Ere thou transgress this knot of piety. Val . Research Papers On Disability. What ails my brother?
Soph . Martius, O Martius, Thou now hast found a way to emotional intelligence conquer me. Dor . O star of Rome! what gratitude can speak. Fit words to follow such a deed as this? Mar. This admirable duke, Valerius, With his disdain of fortune and of death,
Captived himself, has captivated me, And though my arm hath ta'en his body here, His soul hath subjugated Martius' soul. By Romulus, he is on disability, all soul, I think; He hath no flesh, and spirit cannot be gyved; Then we have vanquished nothing; he is free,
And Martius walks now in captivity. I do not readily remember any poem, play, sermon, novel, or oration, that our press vents in the last few years, which goes to the same tune. We have a great many flutes and flageolets, but not often the sound of any fife. Yet, Wordsworth's Laodamia, and the ode of Dion, and essays addiction some sonnets, have a certain noble music; and research on disability Scott will sometimes draw a stroke like the protrait of Lord Evandale, given by Balfour of Burley. Thomas Carlyle, with his natural taste for what is manly and daring in character, has suffered no heroic trait in his favorites to sabine leick drop from his biographical and historical pictures. Earlier, Robert Burns has given us a song or two.
In the Harleian Miscellanies, there is an account of the battle of Lutzen, which deserves to be read. And Simon Ockley's History of the on disability, Saracens recounts the prodigies of individual valor with admiration, all the more evident on essay movie, the part of the narrator, that he seems to think that his place in Christian Oxford requires of papers on disability, him some proper protestations of abhorrence. But, if we explore the literature of Heroism, we shall quickly come to Plutarch, who is thesis, its Doctor and historian. To him we owe the Brasidas, the Dion, the Epaminondas, the Scipio of old, and I must think we are more deeply indebted to him than to all the ancient writers. Each of research papers, his Lives is a refutation to the despondency and cowardice of upcoming in india, our religious and political theorists. Research On Disability. A wild courage, a Stoicism not of the schools, but of the phd thesis emotional intelligence, blood, shines in every anecdote, and has given that book its immense fame. We need books of this tart cathartic virtue, more than books of political science, or of private economy. Life is a festival only to the wise. Seen from the nook and chimney-side of prudence, it wears a ragged and research dangerous front.
The violations of the laws of nature by our predecessors and our contemporaries are punished in us also. The disease and deformity around us certify the infraction of natural, intellectual, and moral laws, and often violation on violation to breed such compound misery. A lock-jaw that bends a man's head back to thesis gloucester his heels, hydrophobia, that makes him bark at his wife and babes, insanity, that makes him eat grass; war, plague, cholera, famine, indicate a certain ferocity in nature, which, as it had its inlet by human crime, must have its outlet by human suffering. Papers. Unhappily, no man exists who has not in his own person become, to some amount, a stockholder in the sin, and so made himself liable to a share in the expiation. Our culture, therefore, must not omit the arming of the thesis binding oxford, man.
Let him hear in season, that he is born into papers the state of war, and that the commonwealth and his own well-being require that he should not go dancing in the weeds of peace, but warned, self-collected, and neither defying nor dreading the thunder, let him take both reputation and life in his hand, and, with perfect urbanity, dare the gibbet and the mob by the absolute truth of his speech, and the rectitude of his behaviour. Towards all this external evil, the man within the breast assumes a warlike attitude, and ncssm application essay affirms his ability to cope single-handed with the research on disability, infinite army of enemies. Binding Oxford Gloucester Green. To this military attitude of the soul we give the name of Heroism. Its rudest form is the contempt for safety and on disability ease, which makes the attractiveness of war. It is a self-trust which slights the phd thesis emotional, restraints of prudence, in the plenitude of its energy and power to papers on disability repair the harms it may suffer. The hero is a mind of such balance that no disturbances can shake his will, but pleasantly, and, as it were, merrily, he advances to his own music, alike in frightful alarms and in the tipsy mirth of universal dissoluteness. There is somewhat not philosophical in heroism; there is somewhat not holy in it; it seems not to know that other souls are of one texture with it; it has pride; it is the extreme of emotional intelligence, individual nature. Nevertheless, we must profoundly revere it. There is research on disability, somewhat in emotional intelligence great actions, which does not allow us to go behind them. Heroism feels and never reasons, and on disability therefore is always right; and although a different breeding, different religion, and greater intellectual activity would have modified or even reversed the intelligence, particular action, yet for the hero that thing he does is the papers, highest deed, and is not open to the censure of philosophers or divines.
It is the avowal of the unschooled man, that he finds a quality in him that is negligent of expense, of health, of life, of danger, of hatred, of reproach, and knows that his will is higher and more excellent than all actual and all possible antagonists. Heroism works in contradiction to the voice of mankind, and in contradiction, for a time, to the voice of the great and ncssm good. On Disability. Heroism is an leick obedience to a secret impulse of an on disability individual's character. Now to sabine no other man can its wisdom appear as it does to him, for every man must be supposed to see a little farther on his own proper path than any one else. Therefore, just and papers wise men take umbrage at his act, until after some little time be past: then they see it to be in unison with their acts.
All prudent men see that the action is clean contrary to ncssm application a sensual prosperity; for every heroic act measures itself by its contempt of papers on disability, some external good. But it finds its own success at ncssm application, last, and then the prudent also extol. Self-trust is the essence of heroism. It is the state of the soul at war, and its ultimate objects are the last defiance of falsehood and wrong, and the power to research bear all that can be inflicted by evil agents. It speaks the thesis binding oxford green, truth, and it is just, generous, hospitable, temperate, scornful of petty calculations, and scornful of being scorned.
It persists; it is of an undaunted boldness, and of a fortitude not to be wearied out. Research Papers On Disability. Its jest is the littleness of common life. That false prudence which dotes on health and wealth is the butt and merriment of heroism. Heroism, like Plotinus, is almost ashamed of its body. What shall it say, then, to the sugar-plums and cats'-cradles, to phd thesis emotional the toilet, compliments, quarrels, cards, and custard, which rack the wit of all society. What joys has kind nature provided for research us dear creatures! There seems to be no interval between greatness and meanness. When the application, spirit is not master of the world, then it is its dupe.
Yet the little man takes the great hoax so innocently, works in it so headlong and believing, is born red, and dies gray, arranging his toilet, attending on his own health, laying traps for sweet food and strong wine, setting his heart on a horse or a rifle, made happy with a little gossip or a little praise, that the great soul cannot choose but laugh at such earnest nonsense. Indeed, these humble considerations make me out of love with greatness. What a disgrace is it to on disability me to take note how many pairs of silk stockings thou hast, namely, these and those that were the peach-colored ones; or to bear the movie, inventory of thy shirts, as one for papers superfluity, and one other for use! Citizens, thinking after the laws of titanic, arithmetic, consider the papers, inconvenience of receiving strangers at their fireside, reckon narrowly the loss of time and the unusual display: the soul of a better quality thrusts back the unseasonable economy into the vaults of life, and says, I will obey the God, and the sacrifice and thesis oxford green the fire he will provide. Ibn Haukal, the Arabian geographer, describes a heroic extreme in the hospitality of Sogd, in Bukharia. When I was in Sogd, I saw a great building, like a palace, the gates of which were open and fixed back to the wall with large nails. I asked the reason, and was told that the house had not been shut, night or day, for a hundred years. Strangers may present themselves at research papers, any hour, and in whatever number; the master has amply provided for the reception of the college essays addiction, men and their animals, and is never happier than when they tarry for some time.
Nothing of the kind have I seen in any other country. The magnanimous know very well that they who give time, or money, or shelter, to the stranger--so it be done for love, and not for ostentation--do, as it were, put God under obligation to papers on disability them, so perfect are the compensations of the universe. In some way the time they seem to lose is essay titanic, redeemed, and research papers the pains they seem to take remunerate themselves. These men fan the flame of human love, and thesis oxford gloucester raise the standard of papers on disability, civil virtue among mankind. But hospitality must be for service, and ncssm application not for research on disability show, or it pulls down the host. Essay Competitions In India. The brave soul rates itself too high to value itself by the splendor of its table and draperies.
It gives what it hath, and all it hath, but its own majesty can lend a better grace to bannocks and fair water than belong to research on disability city feasts. The temperance of the phd thesis emotional, hero proceeds from the same wish to do no dishonor to the worthiness he has. But he loves it for its elegancy, not for its austerity. It seems not worth his while to be solemn, and denounce with bitterness flesh-eating or wine-drinking, the use of papers, tobacco, or opium, or tea, or silk, or gold. A great man scarcely knows how he dines, how he dresses; but without railing or precision, his living is natural and poetic. John Eliot, the binding, Indian Apostle, drank water, and said of wine,--It is research papers on disability, a noble, generous liquor, and oxford gloucester green we should be humbly thankful for it, but, as I remember, water was made before it. Better still is the temperance of King David, who poured out on the ground unto the Lord the water which three of papers on disability, his warriors had brought him to drink, at the peril of their lives. It is told of Brutus, that when he fell on his sword, after the titanic movie, battle of research, Philippi, he quoted a line of Euripides,--O virtue! I have followed thee through life, and I find thee at last but a shade.
I doubt not the phd thesis, hero is research papers on disability, slandered by this report. The heroic soul does not sell its justice and its nobleness. It does not ask to dine nicely, and to sleep warm. The essence of greatness is the perception that virtue is enough. Poverty is its ornament.
It does not need plenty, and can very well abide its loss. But that which takes my fancy most, in the heroic class, is the good-humor and hilarity they exhibit. It is a height to which common duty can very well attain, to suffer and to dare with solemnity. But these rare souls set opinion, success, and life, at so cheap a rate, that they will not soothe their enemies by petitions, or the show of sorrow, but wear their own habitual greatness. Scipio, charged with peculation, refuses to do himself so great a disgrace as to thesis oxford gloucester green wait for justification, though he had the scroll of his accounts in his hands, but tears it to pieces before the tribunes. Socrates's condemnation of himself to research be maintained in all honor in the Prytaneum, during his life, and binding oxford gloucester Sir Thomas More's playfulness at the scaffold, are of the same strain. In Beaumont and Fletcher's Sea Voyage, Juletta tells the stout captain and his company,-- Jul. Why, slaves, 't is in our power to hang ye. Master . Very likely, 'T is in our powers, then, to be hanged, and scorn ye.
These replies are sound and whole. Research On Disability. Sport is the bloom and glow of a perfect health. Phd Thesis Emotional. The great will not condescend to take any thing seriously; all must be as gay as the research, song of a canary, though it were the building of cities, or the eradication of old and foolish churches and nations, which have cumbered the earth long thousands of years. Simple hearts put all the history and customs of thesis green, this world behind them, and on disability play their own game in innocent defiance of the Blue-Laws of the upcoming in india, world; and such would appear, could we see the human race assembled in vision, like little children frolicking together; though, to the eyes of mankind at large, they wear a stately and solemn garb of works and influences. The interest these fine stories have for papers us, the power of essay, a romance over the boy who grasps the forbidden book under his bench at school, our delight in the hero, is the main fact to our purpose. All these great and transcendent properties are ours. If we dilate in beholding the Greek energy, the papers on disability, Roman pride, it is that we are already domesticating the same sentiment. Let us find room for this great guest in our small houses. The first step of worthiness will be to disabuse us of our superstitious associations with places and times, with number and college essays addiction size. Why should these words, Athenian, Roman, Asia, and England, so tingle in research on disability the ear? Where the heart is, there the muses, there the gods sojourn, and not in any geography of sabine leick, fame.
Massachusetts, Connecticut River, and papers Boston Bay, you think paltry places, and the ear loves names of foreign and classic topography. But here we are; and, if we will tarry a little, we may come to learn that here is best. See to dissertation it, only, that thyself is here;--and art and nature, hope and fate, friends, angels, and the Supreme Being, shall not be absent from the chamber where thou sittest. Epaminondas, brave and affectionate, does not seem to us to need Olympus to die upon, nor the Syrian sunshine. He lies very well where he is. Research Papers On Disability. The Jerseys were handsome ground enough for Washington to tread, and London streets for the feet of Milton. Competitions In India. A great man makes his climate genial in the imagination of men, and its air the beloved element of all delicate spirits. That country is the fairest, which is papers on disability, inhabited by the noblest minds. The pictures which fill the imagination in reading the actions of Pericles, Xenophon, Columbus, Bayard, Sidney, Hampden, teach us how needlessly mean our life is, that we, by the depth of our living, should deck it with more than regal or national splendor, and act on principles that should interest man and nature in the length of our days. We have seen or heard of many extraordinary young men, who never ripened, or whose performance in actual life was not extraordinary.
When we see their air and mien, when we hear them speak of society, of books, of religion, we admire their superiority, they seem to throw contempt on our entire polity and social state; theirs is the essay titanic movie, tone of a youthful giant, who is sent to work revolutions. But they enter an active profession, and the forming Colossus shrinks to the common size of man. Papers On Disability. The magic they used was the ideal tendencies, which always make the Actual ridiculous; but the tough world had its revenge the moment they put their horses of the emotional intelligence, sun to plough in its furrow. They found no example and no companion, and their heart fainted. What then? The lesson they gave in their first aspirations is yet true; and a better valor and a purer truth shall one day organize their belief. Or why should a woman liken herself to on disability any historical woman, and emotional intelligence think, because Sappho, or Sevigne, or De Stael, or the cloistered souls who have had genius and cultivation, do not satisfy the imagination and the serene Themis, none can,--certainly not she. Why not? She has a new and unattempted problem to solve, perchance that of the on disability, happiest nature that ever bloomed. Let the maiden, with erect soul, walk serenely on her way, accept the hint of each new experience, search in turn all the objects that solicit her eye, that she may learn the power and the charm of her new-born being, which is the kindling of a new dawn in the recesses of space.
The fair girl, who repels interference by a decided and proud choice of essay titanic movie, influences, so careless of pleasing, so wilful and lofty, inspires every beholder with somewhat of her own nobleness. The silent heart encourages her; O friend, never strike sail to a fear! Come into port greatly, or sail with God the seas. On Disability. Not in vain you live, for binding every passing eye is papers, cheered and refined by in india the vision. The characteristic of heroism is its persistency. All men have wandering impulses, fits, and starts of generosity. But when you have chosen your part, abide by it, and do not weakly try to reconcile yourself with the world. The heroic cannot be the common, nor the common the on disability, heroic.
Yet we have the weakness to expect the sympathy of gloucester green, people in those actions whose excellence is papers, that they outrun sympathy, and sabine leick appeal to research a tardy justice. If you would serve your brother, because it is fit for you to serve him, do not take back your words when you find that prudent people do not commend you. Adhere to your own act, and congratulate yourself if you have done something strange and extravagant, and upcoming essay competitions broken the monotony of a decorous age. It was a high counsel that I once heard given to a young person,--Always do what you are afraid to on disability do. A simple, manly character need never make an apology, but should regard its past action with the calmness of essay competitions in india, Phocion, when he admitted that the event of the battle was happy, yet did not regret his dissuasion from the battle. There is no weakness or exposure for which we cannot find consolation in the thought,--this is a part of my constitution, part of my relation and office to my fellow-creature. Has nature covenanted with me that I should never appear to disadvantage, never make a ridiculous figure? Let us be generous of our dignity, as well as of our money. Greatness once and for ever has done with opinion.
We tell our charities, not because we wish to papers be praised for them, not because we think they have great merit, but for our justification. Essay Titanic Movie. It is a capital blunder; as you discover, when another man recites his charities. To speak the truth, even with some austerity, to live with some rigor of temperance, or some extremes of generosity, seems to be an asceticism which common good-nature would appoint to those who are at ease and in plenty, in sign that they feel a brotherhood with the research papers, great multitude of suffering men. And not only need we breathe and exercise the soul by assuming the penalties of abstinence, of ncssm essay, debt, of solitude, of unpopularity, but it behooves the wise man to look with a bold eye into those rarer dangers which sometimes invade men, and to familiarize himself with disgusting forms of disease, with sounds of execration, and the vision of violent death. Times of heroism are generally times of terror, but the day never shines in which this element may not work. The circumstances of man, we say, are historically somewhat better in this country, and at this hour, than perhaps ever before. More freedom exists for culture. It will not now run against an axe at the first step out of the papers, beaten track of sabine, opinion. Research On Disability. But whoso is heroic will always find crises to try his edge.
Human virtue demands her champions and martyrs, and the trial of persecution always proceeds. It is but the other day that the brave Lovejoy gave his breast to phd thesis the bullets of papers on disability, a mob, for binding oxford gloucester green the rights of free speech and opinion, and died when it was better not to live. I see not any road of research papers on disability, perfect peace which a man can walk, but after the counsel of his own bosom. Let him quit too much association, let him go home much, and stablish himself in those courses he approves. The unremitting retention of simple and high sentiments in obscure duties is hardening the character to that temper which will work with honor, if need be, in the tumult, or on the scaffold. Whatever outrages have happened to men may befall a man again; and very easily in a republic, if there appear any signs of essay titanic movie, a decay of religion. Coarse slander, fire, tar and papers feathers, and the gibbet, the essays, youth may freely bring home to his mind, and with what sweetness of temper he can, and inquire how fast he can fix his sense of research on disability, duty, braving such penalties, whenever it may please the next newspaper and a sufficient number of his neighbours to pronounce his opinions incendiary.
It may calm the apprehension of calamity in dissertation the most susceptible heart to see how quick a bound nature has set to the utmost infliction of malice. We rapidly approach a brink over which no enemy can follow us. On Disability. Let them rave: Thou art quiet in thy grave. [Tennyson] In the gloom of our ignorance of what shall be, in application essay the hour when we are deaf to the higher voices, who does not envy those who have seen safely to an end their manful endeavour? Who that sees the research papers, meanness of our politics, but inly congratulates Washington that he is long already wrapped in upcoming competitions his shroud, and for ever safe; that he was laid sweet in his grave, the hope of humanity not yet subjugated in him? Who does not sometimes envy the good and on disability brave, who are no more to suffer from the tumults of the natural world, and await with curious complacency the leick, speedy term of his own conversation with finite nature? And yet the love that will be annihilated sooner than treacherous has already made death impossible, and affirms itself no mortal, but a native of the deeps of absolute and on disability inextinguishable being. Nelson, Carl.
The Rhetoric of Emerson's Hindu 'Heroism'. Upcoming Essay Competitions In India. ESQ 69 (1972), 258-64. Stein, William B. Emerson's 'History':The Rhetoric of Cosmic Consciousness. ESQ 69 (1972), 199-206. Elbert, Monika. From Merlin to Faust: Emerson's Democratization of the 'Heroic Mind'. In Spivak, Charlotte, ed. Merlin versus Faust: Contending Archetypes in Western Culture , pp. 113-37..
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Compare and papers, contrast 2 forms of addiction Essay Sample. Use, as the term infers is any use of a drug. Essays! The majority of people use a form of drug in one way or another, ranging from the use of prescribed medication over the counter, to alcohol, tobacco, caffeine or illicit drugs such as cannabis, or amphetamines. Papers! In reference to use, abuse and titanic, addiction two models will be addressed as a way to explain this epidemic. Exploring the disease model, from the 1930’s post-Prohibition it was a common perception that alcoholism was a moral failure. Medical and professional standards of the time treated it as a condition that was expected to research, be incurable and lethal.
Moreover use, abuse and addiction will be explored through a psychological perspective where a psychodynamic modality will be discussed as a way to explain substance abuse. The Australian Drug Foundation (2010) notes, there is no safe level of drug use. The use of any drug always carries some risk even medications can produce unwanted side effects, thus it is important to be careful when there is a level of any drug use. Abuse, the Diagnostic and Statistical Manual of Mental Disorders fourth edition (DSM-IV, 2000) outlines substance abuse as a ‘maladaptive pattern of use leading to clinically significant impairment or distress.’ Dependence and addiction, the definitions of these two terms are somewhat debatable. There is also some debate over the use of these terms to describe how people use drugs. This is sabine leick because the language used can affect perspectives on treatments, outcomes, motives and behaviors of those who use them. Papers On Disability! For an example; some people do not like the term addiction as it implies that the person is powerless over their use of the drug, however others argue that this powerlessness is the essay titanic movie foundation of diagnosis and treatment.
Furthermore, others argue that substance use and dependency are not psychiatric disorders, as the DSM IV classification suggests. The DSM IV limits it classification of substance related disorders to dependence, it does not include a classification for research papers on disability, addiction. “In 1964 the World health organization recommended using the ncssm essay term ‘dependence’ in place of on disability terms ‘addiction’ and ‘alcoholism’ (World Health Organization Technical Report series: No. 273, 1964). Essays Addiction! In 1981, ‘dependence’ as a socio-psycho-biological syndrome manifested by research papers, a behavioral pattern in which the use of a given psychoactive drug (or class of drugs) is given a sharply higher priority over other behaviors which once had significantly greater value (for example drug use comes to sabine leick, have a grater relative value).” (Edwards et al., 1980, p.240). The two terms dependence and addiction are very closely intertwined as it is research on disability argued that the tolerance and withdrawal associated with dependence are what exactly defines addictions. However, the DSM IV classification more so describes what is known as a physical dependence, and does not take account of psychological dependence. Moreover, psychological dependence is intelligence when the person believes that they need to use the drug in order to feel emotionally stable or function efficiently.
According to the Centre for Addiction and on disability, Mental Health (2011), addiction is: “A primary, chronic, neurobiological disease with genetic, psychosocial and environmental factors that influence its development and manifestations. It is characterized by behaviors that include one or more of the following: loss of control over drug use, continued use despite harm, compulsive use and craving.” Use, Abuse and addiction and the disease model: In the 1930’s post-Prohibition it was a common perception that alcoholism was a moral failure. Medical and professional standards of the time treated it as a condition that was expected to be incurable and lethal. In the thesis gloucester same year Alcoholics Anonymous was founded by Bill Wilson and research papers, Dr.
Robert Smith, Alcoholics Anonymous or (AA) holds the stance that the upcoming competitions “primary purpose is to stay sober and help other alcoholics achieve sobriety” (Gross, 2010). With other members the papers founders Wilson and Smith developed the twelve-step program of spiritual character development, basically the principals speak about having an addiction so intense that it leaves you powerless to avoid temptation. Followed by twelve traditions of the twelve-step program, which provided guidelines for relationships between the twelve step groups, members, other groups, the essay titanic global fellowship and the society at large. Papers On Disability! These twelve traditions were put into place in 1946 to help Alcoholics Anonymous stabilize and grow. Traditions placed emphasis that members and groups remain anonymous in public media, intrinsically help other alcoholics, including all who wish to stop drinking who do not affiliate with ‘AA’ or any other organizations. Traditions also recommend that members acting on behalf of the program stay away from dogma, governing hierarchies and involvement in public issues. Sabine Leick Dissertation! Subsequent fellowships such Narcotics Anonymous (NA) adapted and adopted the twelve steps, and traditions to their respective primary purpose although the disease model was introduced as a theory for alcoholism it has evolved into research papers on disability the standard model for treatment of practically all forms of drug addiction (Chapel, 1999). Foremost, the disease model for drug and alcohol addiction is the essay most readily available treatment for research papers on disability, the general public. It gives those who don’t have the means help that they wouldn’t have otherwise. Sabine! From AA/NA meetings that are available for free in nearly every city to the insurance coverage for treatment that is available because addiction is regarded as a disease, the advantages are widespread.
Some say looking at addiction as a disease also allows addicts to deal with the guilt that often accompanies a lifetime of chemically induced missteps. …the loss of control is a disease condition per se which results from a process that superimposes itself upon those abnormal psychological conditions of which excessive drinking is a symptom… (Jelleinek, 1951). People who disagree with the disease model cite an array of disadvantages to research papers on disability, its use. One of the most prevalent disadvantages relates to the statement cited by titanic movie, Peele, in that it defies common sense and is therefore dishonest. Those that subscribe to that concept often believe that the disease model actually renders addicts helpless rather than empowering them to research papers on disability, change (Clark, 2006). Furthermore others who dispute the disease model state that no biological or genetic mechanisms have been identified that account for addictive behaviour. Arguing how could an addiction like smoking be genetic, and why are some types of people more likely to smoke than others. Does believing that an addiction like smoking is genetic help the person quit (are all those smokers who quit not “genetically” addicted) and in relation to alcohol, are people really predestined biologically to become alcoholics and thus to become A.A. members. For example; the rock group Aerosmith; all five members of this group now belong to A.A., just as they previously all drank and college, took drugs together. Thus, how improbable a coincidence it is that five unrelated people with the alcoholic/addictive inheritance should bump into one another and papers on disability, form a band (Peele, 1992). Use, Abuse and addiction from a psychological perspective: Psychodynamic therapy focuses on unconscious processes as they are manifested in the client’s present behavior.
The objectives of leick dissertation psychodynamic therapy are client self-awareness and an understanding of the influence of the papers past on present behavior. In its brief form, a psychodynamic approach allows the client to observe unresolved conflicts and symptoms that arise from past dysfunctional affiliations and manifest themselves in the necessary desire to abuse substances. Short-term psychodynamic therapies can contribute to the armamentarium of treatments for ncssm application, substance abuse disorders. Brief psychodynamic therapies probably have the best chance to be effective when they are integrated into a relatively comprehensive substance abuse treatment program that includes drug-focused interventions such as regular urinalysis, drug counseling, and, for opioid-dependents, methadone maintenance pharmacotherapy. Brief psychodynamic therapies are perhaps more helpful after abstinence is well established.
They may be more beneficial for clients with no greater than moderate severity of research on disability substance abuse. It is also important that the psychodynamic therapist know about the pharmacology of abused drugs, the subculture of substance abuse, and college addiction, 12-Step programs. The theory supporting psychodynamic therapy originated in and is informed by psychoanalytic theory. There are four major schools of psychoanalytic theory, each of which has influenced psychodynamic therapy. Research On Disability! The four schools are: Freudian, Ego Psychology, Object Relations, and Self Psychology. Freudian psychology is based on the theories first conveyed by Sigmund Freud in the early part of this century and is occasionally referred to as the drive or structural model. The substance of Freud’s theory is that sexual and aggressive energies originating in the id (or unconscious) are controlled by binding oxford green, the ego, which is a set of functions that regulates between the id and external reality. Defense mechanisms are constructions of the ego that operate to research, minimize pain and to maintain psychic equilibrium. The superego, formed during latency (between age 5 and puberty), operates to control id drives through guilt (Messer and Warren, 1995). Ego Psychology began from thesis binding gloucester Freudian psychology. Its followers center their work on increasing and sustaining ego function in harmony with the research on disability demands of reality.
Ego Psychology stresses the individual’s capacity for defense, adaptation, and reality testing (Pine, 1990). Supportive-expressive psychotherapy is one brief psychodynamic approach that has been adapted for use with people who have substance abuse conditions. It has been revised for use with opiate addiction in thesis gloucester conjunction with methadone maintenance treatment and for cocaine use disorders (Luborsky, et, al 1997). There have been numerous findings of the use of supportive expressive therapy for substance abuse disorders, resulting in a substantial body of pragmatic data on its effectiveness in treating these problems. Only since the 1980s that psychosocial components of the treatment of substance abuse disorders have become the research papers subject of scientific examination. Leick! Most research on research on disability the effectiveness of thesis binding oxford gloucester psychotherapy for research papers on disability, the treatment of substance abuse disorders has concluded that it can be an effective treatment modality (Woody et al., 1994). Comparisons among specific models of therapy have become the focus of much interest. As previously mentioned, supportive Expressive (SE) psychotherapy has been adapted for use with methadone-maintained opiate dependents and for cocaine dependents.
In SE therapy, the client is assisted to essay, recognize and talk about core relationship patterns and how they correspond to substance abuse. Furthermore, The relationship that develops between therapist and client is a very important factor for effective therapeutic outcomes (Luborsky, 1985). This is true irrespective of the modality of therapy. The psychodynamic model has always regarded the therapist-client relationship as a fundamental and papers, the vehicle through which change occurs. Of all the brief psychotherapies, psychodynamic approaches place the most importance on the therapeutic relationship and deliver the most unambiguous and comprehensive rationalizations of upcoming in india how to use this relationship effectively. To conclude, two models were used to explain use, abuse and addiction, the disease model explored the 1930’s post-Prohibition, as it was a common perception that alcoholism was a moral failure. Medical and professional standards of the time treated it as a condition that was expected to be incurable and lethal. Research Papers On Disability! In the same year Alcoholics Anonymous was founded by ncssm, Bill Wilson and Dr. Robert Smith, Alcoholics Anonymous or (AA) holds the stance that the “primary purpose is to stay sober and research, help other alcoholics achieve sobriety” Twelve-step programs were discussed as this was when alcoholism was more so viewed as a disease rather than a moral failure.
A psychological perspective was also addressed where psychodynamic therapy was the focus. Short-term psychodynamic therapies were seen to contribute to titanic, the armamentarium of treatments for papers, substance abuse disorders. Brief psychodynamic therapies were viewed as having the best chance to be effective when integrated into a relatively comprehensive substance abuse treatment program. Sabine Leick! It was also important that the psychodynamic therapist know about the pharmacology of abused drugs, the subculture of substance abuse, and 12-Step programs. The Australian Drug Foundation – DrugInfo. (2010) Drugs – the facts, Melbourne. Available: http://druginfo.adf.org.au/treatment-options/what-kind-of -help-is-available#pharmacotherapy. Clark, D. 2006. Papers! The disease Model of addiction.
London: www.drinkanddrugs.net/backgroundinformation.breifings/sep2506/background_breifing.pdf. Edwards, G. Arif, A. (1980). Drug problems in the sociocultural context: a basis for policies and essay, programme planning, World Health Organization, Geneva. Papers! http://archives.drugabuse.gov/adac/ADAC10.html. Morse. R., Flavin.
D,. (1992) The definition of application Alcoholism. Research Papers! JAM Med association. Edwards, Griffith (2002) “Alcoholics Anonymous”. Alcohol: the worlds favorite drug. Thomas Dunne Books. Gross.
M., Ph.D (2010) American Journal of thesis binding Public Health. Chappel. J. (1999) Twelve step and mutual help programs for papers, addictive disorders. Psychiatric clinics of college essays addiction North America. Dr. Peele on America’s Fixation on papers the Disease Model of Addiction: (2007) Interview by Andrew Proscyk. Edited by Britt Winston. Copyright Andrew Proscyk. Sabine Leick! http://lifeprocessprogram.com/lp-blog/library/dr-peele-on-americas-fixation-on-the-disease-model-of-addiction/ Stanton Peele, Ph.D., and Archie Brodsky with Mary Arnold (1992), The Truth About Addiction and Recovery. N.Y.: Simon Schuster.
Woody, G.E.; McLellan, A.T.; Luborsky, L.; and O’Brien, C.P. (1995), Psychotherapy in community methadone programs: A validation study. On Disability! American Journal of Psychiatry. Woody, G.E.; McLellan, A.T.; Luborsky, L.; and O’Brien, C.P. (1998), Psychotherapy with opioid-dependent patients. Psychiatric Times. Messer, S. B., Warren, C. Sabine! S. (1995). Models of brief psychodynamic therapy: A comparative approach.
New York: NY: Guilford. Pine, F. (1990). Drive, ego, object, and self. Research! New York: Basic Books. Luborsky, l., Diguer, L, Seligman, D.A., Rosenthal, R. College Essays! Krause, E.D., Johnson, S., Halperin, G., Bishop, M., Berman, J.S., Schweizer, E. (1999). The researcher’s own therapy allegiances: A “wild card” incomparisons of treatment efficacy. Is this the perfect essay for you? Save time and research on disability, order Compare and contrast 2 forms of addiction. essay editing for titanic, only $13.9 per page.
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