How To Think About Abstract Algebra
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A Book Of Abstract Algebra
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Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2010-01-14
A Book Of Abstract Algebra written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
How To Think About Abstract Algebra
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Author : Lara Alcock
language : en
Publisher: Oxford University Press
Release Date : 2021-02-04
How To Think About Abstract Algebra written by Lara Alcock and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-04 with Science categories.
How to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory. Abstract Algebra is central in most undergraduate mathematics degrees, and it captures regularities that appear across diverse mathematical structures - many people find it beautiful for this reason. But its abstraction can make its central ideas hard to grasp, and even the best students might find that they can follow some of the reasoning without really understanding what it is all about. This book aims to solve that problem. It is not like other Abstract Algebra texts and is not a textbook containing standard content. Rather, it is designed to be read before starting an Abstract Algebra course, or as a companion text once a course has begun. It builds up key information on five topics: binary operations, groups, quotient groups, isomorphisms and homomorphisms, and rings. It provides numerous examples, tables and diagrams, and its explanations are informed by research in mathematics education. The book also provides study advice focused on the skills that students need in order to learn successfully in their own Abstract Algebra courses. It explains how to interact productively with axioms, definitions, theorems and proofs, and how research in psychology should inform our beliefs about effective learning.
How To Think About Analysis
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Author : Lara Alcock
language : en
Publisher: OUP Oxford
Release Date : 2014-09-25
How To Think About Analysis written by Lara Alcock and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-25 with Mathematics categories.
Analysis (sometimes called Real Analysis or Advanced Calculus) is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the student's existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.
Algebra Chapter 0
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Author : Paolo Aluffi
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Algebra Chapter 0 written by Paolo Aluffi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Abstract Algebra
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Author : Thomas Judson
language : en
Publisher: Orthogonal Publishing L3c
Release Date : 2023-08-11
Abstract Algebra written by Thomas Judson and has been published by Orthogonal Publishing L3c this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-11 with categories.
Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
Abel S Theorem In Problems And Solutions
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Author : V.B. Alekseev
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-31
Abel S Theorem In Problems And Solutions written by V.B. Alekseev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-31 with Mathematics categories.
Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.
Visual Group Theory
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Author : Nathan Carter
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-08
Visual Group Theory written by Nathan Carter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-08 with Education categories.
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Fundamental Concepts Of Abstract Algebra
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Author : Gertrude Ehrlich
language : en
Publisher: Courier Corporation
Release Date : 2013-05-13
Fundamental Concepts Of Abstract Algebra written by Gertrude Ehrlich and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-13 with Mathematics categories.
This undergraduate text presents extensive coverage of set theory, groups, rings, modules, vector spaces, and fields. It offers numerous examples, definitions, theorems, proofs, and practice exercises. 1991 edition.
Mathematics Rebooted
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Author : Lara Alcock
language : en
Publisher: Oxford University Press
Release Date : 2017
Mathematics Rebooted written by Lara Alcock and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Education categories.
Would you like to understand more about mathematics? Perhaps at school you liked it for a while but were put off because you missed a key idea and kept getting stuck. Whatever the case, this book is for you.
An Invitation To Abstract Algebra
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Author : Steven J. Rosenberg
language : en
Publisher:
Release Date : 2024-08-26
An Invitation To Abstract Algebra written by Steven J. Rosenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-26 with Mathematics categories.
Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks. This book is offered as a manual to a new way of thinking. The author aims to instill the desire to understand the material, to encourage more discovery, and to appreciate the subject for its own sake.