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 : Bruno Nachtergaele
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-11-30

Linear Algebra As An Introduction To Abstract Mathematics written by Bruno Nachtergaele 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:
Release Date : 1993

Linear Algebra written by Robert J. Valenza and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 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

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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.

An Introduction To Abstract Mathematics

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Author : Robert J. Bond
language : en
Publisher: Cengage Learning
Release Date : 1999

An Introduction To Abstract Mathematics written by Robert J. Bond and has been published by Cengage Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

The goal of this book is to show students how mathematicians think and to glimpse some of the fascinating things they think about. Bond and Keane develop students' ability to do abstract mathematics by teaching the form of mathematics in the context of real and elementary mathematics. Students learn the fundamentals of mathematical logic; how to read and understand definitions, theorems, and proofs; and how to assimilate abstract ideas and communicate them in written form. Students will learn to write mathematical proofs coherently and correctly.

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.

Introduction To Abstract Algebra

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Author : Jonathan D. H. Smith
language : en
Publisher: CRC Press
Release Date : 2015-10-23

Introduction To Abstract Algebra written by Jonathan D. H. Smith and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-23 with Mathematics categories.

Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups.This new edition of a widely adopted textbook covers

Introduction To Applied Linear Algebra

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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07

Introduction To Applied Linear Algebra written by Stephen Boyd 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 2018-06-07 with Business & Economics categories.

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Introduction To Abstract Algebra

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Author : Benjamin Fine
language : en
Publisher: JHU Press
Release Date : 2014-07-01

Introduction To Abstract Algebra written by Benjamin Fine and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-01 with Mathematics categories.

A new approach to abstract algebra that eases student anxieties by building on fundamentals. Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic

Logic Sets And Numbers

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Author : Frank Blume
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-07-19

Logic Sets And Numbers written by Frank Blume and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-19 with categories.

Logic, Sets, and Numbers is a brief introduction to abstract mathematics that is meant to familiarize the reader with the formal and conceptual rigor that higher-level undergraduate and graduate textbooks commonly employ. Beginning with formal logic and a fairly extensive discussion of concise formulations of mathematical statements, the text moves on to cover general patterns of proofs, elementary set theory, mathematical induction, cardinality, as well as, in the final chapter, the creation of the various number systems from the integers up to the complex numbers. On the whole, the book's intent is not only to reveal the nature of mathematical abstraction, but also its inherent beauty and purity.