Linear Algebra As An Introduction To Abstract Mathematics

Author : Isaiah Lankham
Publisher : World Scientific Publishing Company
ISBN 13 : 9814723797
Total Pages : 208 pages
Book Rating : 4.94/5 ( download)

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Download or read book Linear Algebra as an Introduction to Abstract Mathematics written by Isaiah Lankham and published by World Scientific Publishing Company. This book was released on 2015-11-30 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Robert J. Valenza
Publisher : Springer Science & Business Media
ISBN 13 : 1461209013
Total Pages : 253 pages
Book Rating : 4.10/5 ( download)

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Download or read book Linear Algebra written by Robert J. Valenza and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Robert J. Bond
Publisher : Waveland Press
ISBN 13 : 1478608056
Total Pages : 344 pages
Book Rating : 4.59/5 ( download)

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Download or read book An Introduction to Abstract Mathematics written by Robert J. Bond and published by Waveland Press. This book was released on 2007-08-24 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Robert J. Valenza
Publisher : Springer
ISBN 13 : 0387940995
Total Pages : 237 pages
Book Rating : 4.91/5 ( download)

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Download or read book Linear Algebra written by Robert J. Valenza and published by Springer. This book was released on 1999-02-01 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jonathan D. H. Smith
Publisher : CRC Press
ISBN 13 : 1498731813
Total Pages : 324 pages
Book Rating : 4.12/5 ( download)

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Download or read book Introduction to Abstract Algebra written by Jonathan D. H. Smith and published by CRC Press. This book was released on 2015-10-23 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Leonid Mirsky
Publisher :
ISBN 13 :
Total Pages : 460 pages
Book Rating : 4.05/5 ( download)

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Download or read book An Introduction to Linear Algebra written by Leonid Mirsky and published by . This book was released on 1963 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alan Tucker
Publisher : MacMillan Publishing Company
ISBN 13 :
Total Pages : 570 pages
Book Rating : 4.04/5 ( download)

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Download or read book A Unified Introduction to Linear Algebra written by Alan Tucker and published by MacMillan Publishing Company. This book was released on 1988 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Hiram Paley
Publisher : Holt McDougal
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.87/5 ( download)

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Download or read book Elements of Abstract and Linear Algebra written by Hiram Paley and published by Holt McDougal. This book was released on 1971 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jonathan D. H. Smith
Publisher : CRC Press
ISBN 13 : 9781420063721
Total Pages : 344 pages
Book Rating : 4.23/5 ( download)

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Download or read book Introduction to Abstract Algebra written by Jonathan D. H. Smith and published by CRC Press. This book was released on 2016-04-19 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.

Author : Ralph W. Oberste-Vorth
Publisher : American Mathematical Soc.
ISBN 13 : 0883857790
Total Pages : 232 pages
Book Rating : 4.93/5 ( download)

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Download or read book Bridge to Abstract Mathematics written by Ralph W. Oberste-Vorth and published by American Mathematical Soc.. This book was released on 2012 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Throughout the text, some pieces (usually proofs) are left as exercises. Part V gives hints to help students find good approaches to the exercises. Part I introduces the language of mathematics and the methods of proof. The mathematical content of Parts II through IV were chosen so as not to seriously overlap the standard mathematics major. In Part II, students study sets, functions, equivalence and order relations, and cardinality. Part III concerns algebra. The goal is to prove that the real numbers form the unique, up to isomorphism, ordered field with the least upper bound. In the process, we construct the real numbers starting with the natural numbers. Students will be prepared for an abstract linear algebra or modern algebra course. Part IV studies analysis. Continuity and differentiation are considered in the context of time scales (nonempty, closed subsets of the real numbers). Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented.