Linear Algebra As An Introduction To Abstract Mathematics
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Linear Algebra As An Introduction To Abstract Mathematics
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Author : Isaiah Lankham
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-11-30
Linear Algebra As An Introduction To Abstract Mathematics written by Isaiah Lankham and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-30 with Mathematics categories.
This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.
Linear Algebra
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Author : Robert J. Valenza
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Algebra written by Robert J. Valenza 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 2012-12-06 with Mathematics categories.
Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.
Linear Algebra As An Introduction To Abstract Mathematics
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Author : Bruno Nachtergaele
language : en
Publisher:
Release Date : 2015
Linear Algebra As An Introduction To Abstract Mathematics written by Bruno Nachtergaele and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Electronic books categories.
Linear Algebra
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Author : Robert J. Valenza
language : en
Publisher: Springer
Release Date : 1999-02-01
Linear Algebra written by Robert J. Valenza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-01 with Mathematics categories.
Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.
An Introduction To Abstract Mathematics
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Author : Robert J. Bond
language : en
Publisher: Waveland Press
Release Date : 2007-08-24
An Introduction To Abstract Mathematics written by Robert J. Bond and has been published by Waveland Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-24 with Mathematics categories.
Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments.
Introduction To Abstract Mathematics
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Author : Theodore A. Bick
language : en
Publisher:
Release Date : 1971
Introduction To Abstract Mathematics written by Theodore A. Bick and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Sets Groups And Mappings An Introduction To Abstract Mathematics
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Author : Andrew D. Hwang
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-26
Sets Groups And Mappings An Introduction To Abstract Mathematics written by Andrew D. Hwang 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 2019-09-26 with Algebra categories.
This book introduces students to the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students of math education, computer science or physics who are looking for an easy-going entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry. In its presentation, the book takes special care to forge linguistic and conceptual links between formal precision and underlying intuition, tending toward the concrete, but continually aiming to extend students' comfort with abstraction, experimentation, and non-trivial computation. The main part of the book can be used as the basis for a transition-to-proofs course that balances theory with examples, logical care with intuitive plausibility, and has sufficient informality to be accessible to students with disparate backgrounds. For students and instructors who wish to go further, the book also explores the Sylow theorems, classification of finitely-generated Abelian groups, and discrete groups of Euclidean plane transformations.
Introduction To Abstract Algebra
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Author : W. Keith Nicholson
language : en
Publisher: John Wiley & Sons
Release Date : 2012-03-20
Introduction To Abstract Algebra written by W. Keith Nicholson 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 2012-03-20 with Mathematics categories.
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.
An Introduction To Abstract Algebra
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Author : John W. Lawrence
language : en
Publisher: Cambridge University Press
Release Date : 2021-04-15
An Introduction To Abstract Algebra written by John W. Lawrence and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-15 with Mathematics categories.
A lucid guide to abstract algebra, this comprehensive textbook provides in depth coverage for upper undergraduate students.
Vectors Pure And Applied
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Author : T. W. Körner
language : en
Publisher: Cambridge University Press
Release Date : 2013
Vectors Pure And Applied written by T. W. Körner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
Explains both the how and the why of linear algebra to get students thinking like mathematicians.