Learning Modern Algebra
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Learning Modern Algebra
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Author : Albert Cuoco
language : en
Publisher: Mathematical Association of America (MAA)
Release Date : 2013-01-01
Learning Modern Algebra written by Albert Cuoco and has been published by Mathematical Association of America (MAA) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with MATHEMATICS categories.
"Learning Modern Algebra is designed for college students who want to teach mathematics in high school, but it can serve as a text for standard abstract algebra courses as well. [...] The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem."--Publisher description.
Learning Modern Algebra
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Author : Albert Cuoco
language : en
Publisher: MAA
Release Date : 2013
Learning Modern Algebra written by Albert Cuoco and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
Much of modern algebra arose from attempts to prove Fermat's Last Theorem, which in turn has its roots in Diophantus' classification of Pythagorean triples. This book, designed for prospective and practising mathematics teachers, makes explicit connections between the ideas of abstract algebra and the mathematics taught at high-school level. Algebraic concepts are presented in historical order, and the book also demonstrates how other important themes in algebra arose from questions related to teaching. The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalisations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the work of Galois and Abel. Results are motivated with specific examples, and applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions.
Modern Algebra
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Author : John R. Durbin
language : en
Publisher: John Wiley & Sons
Release Date : 2008-12-31
Modern Algebra written by John R. Durbin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-31 with Mathematics categories.
The new sixth edition of Modern Algebra has two main goals: to introduce the most important kinds of algebraic structures, and to help students improve their ability to understand and work with abstract ideas. The first six chapters present the core of the subject; the remainder are designed to be as flexible as possible. The text covers groups before rings, which is a matter of personal preference for instructors. Modern Algebra, 6e is appropriate for any one-semester junior/senior level course in Modern Algebra, Abstract Algebra, Algebraic Structures, or Groups, Rings and Fields. The course is mostly comprised of mathematics majors, but engineering and computer science majors may also take it as well.
Advanced Modern Algebra
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Author : Joseph J. Rotman
language : en
Publisher: American Mathematical Society
Release Date : 2025-06-25
Advanced Modern Algebra written by Joseph J. Rotman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-25 with Mathematics categories.
This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Gröbner bases.
Elements Of Modern Algebra
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Author : Linda Gilbert
language : en
Publisher: Cengage Learning
Release Date : 2008-10-20
Elements Of Modern Algebra written by Linda Gilbert and has been published by Cengage Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-20 with Mathematics categories.
ELEMENTS OF MODERN ALGEBRA is intended for an introductory course in abstract algebra taken by Math and Math for Secondary Education majors. Helping to make the study of abstract algebra more accessible, this text gradually introduces and develops concepts through helpful features that provide guidance on the techniques of proof construction and logic analysis. The text develops mathematical maturity for students by presenting the material in a theorem-proof format, with definitions and major results easily located through a user-friendly format. The treatment is rigorous and self-contained, in keeping with the objectives of training the student in the techniques of algebra and of providing a bridge to higher-level mathematical courses. The text has a flexible organization, with section dependencies clearly mapped out and optional topics that instructors can cover or skip based on their course needs. Additionally, problem sets are carefully arranged in order of difficulty to cater assignments to varying student ability levels. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Connecting Abstract Algebra To Secondary Mathematics For Secondary Mathematics Teachers
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Author : Nicholas H. Wasserman
language : en
Publisher: Springer
Release Date : 2018-12-12
Connecting Abstract Algebra To Secondary Mathematics For Secondary Mathematics Teachers written by Nicholas H. Wasserman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Education categories.
Secondary mathematics teachers are frequently required to take a large number of mathematics courses – including advanced mathematics courses such as abstract algebra – as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that such advanced mathematics is unrelated to their future professional work in the classroom. This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics.
Essentials Of Abstract Algebra
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Author : Sachin Nambeesan
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Essentials Of Abstract Algebra written by Sachin Nambeesan and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Essentials of Abstract Algebra" offers a deep exploration into the fundamental structures of algebraic systems. Authored by esteemed mathematicians, this comprehensive guide covers groups, rings, fields, and vector spaces, unraveling their intricate properties and interconnections. We introduce groups, exploring their diverse types, from finite to infinite and abelian to non-abelian, with concrete examples and rigorous proofs. Moving beyond groups, we delve into rings, explaining concepts like ideals, homomorphisms, and quotient rings. The text highlights the relevance of ring theory in number theory, algebraic geometry, and coding theory. We also navigate fields, discussing field extensions, Galois theory, and algebraic closures, and exploring connections between fields and polynomial equations. Additionally, we venture into vector spaces, examining subspaces, bases, dimension, and linear transformations. Throughout the book, we emphasize a rigorous mathematical foundation and intuitive understanding. Concrete examples, diagrams, and exercises enrich the learning experience, making abstract algebra accessible to students, mathematicians, and researchers. "Essentials of Abstract Algebra" is a timeless resource for mastering the beauty and power of algebraic structures.
Classical Modern Algebra
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Author : Seth Warner
language : en
Publisher: Prentice Hall
Release Date : 1971
Classical Modern Algebra written by Seth Warner and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Introduction To Modern Algebra
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Author : Zoltan Paul Dienes
language : en
Publisher:
Release Date : 1966
Introduction To Modern Algebra written by Zoltan Paul Dienes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Algebra categories.
Abstract Algebra
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Author : William Paulsen
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Abstract Algebra written by William Paulsen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
The new edition of Abstract Algebra: An Interactive Approach presents a hands-on and traditional approach to learning groups, rings, and fields. It then goes further to offer optional technology use to create opportunities for interactive learning and computer use. This new edition offers a more traditional approach offering additional topics to the primary syllabus placed after primary topics are covered. This creates a more natural flow to the order of the subjects presented. This edition is transformed by historical notes and better explanations of why topics are covered. This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area. Each chapter includes, corresponding Sage notebooks, traditional exercises, and several interactive computer problems that utilize Sage and Mathematica® to explore groups, rings, fields and additional topics. This text does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. The author also incorporates problem sequences that allow students to delve into interesting topics, including Fermat’s two square theorem.