An Introduction To Abstract Mathematics

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An Introduction to Abstract Mathematics

Robert J. Bond,William J. Keane
An Introduction to Abstract Mathematics Book PDF

Author : Robert J. Bond,William J. Keane
Publisher : Waveland Press
Page : 344 pages
File Size : 41,5 Mb
Release : 2007-08-24
Category : Mathematics
ISBN : 9781478608059

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An Introduction to Abstract Mathematics by Robert J. Bond,William J. Keane Pdf

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.

Linear Algebra as an Introduction to Abstract Mathematics

Isaiah Lankham,Bruno Nachtergaele,Anne Schilling
Linear Algebra as an Introduction to Abstract Mathematics Book PDF

Author : Isaiah Lankham,Bruno Nachtergaele,Anne Schilling
Publisher : World Scientific Publishing Company
Page : 208 pages
File Size : 55,8 Mb
Release : 2015-11-30
Category : Mathematics
ISBN : 9789814723794

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Linear Algebra as an Introduction to Abstract Mathematics by Isaiah Lankham,Bruno Nachtergaele,Anne Schilling Pdf

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.

Introduction to Abstract Mathematics

John F. Lucas
Introduction to Abstract Mathematics Book PDF

Author : John F. Lucas
Publisher : Rowman & Littlefield
Page : 400 pages
File Size : 55,9 Mb
Release : 1990
Category : Mathematics
ISBN : 091267573X

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Introduction to Abstract Mathematics by John F. Lucas Pdf

This is a book about mathematics and mathematical thinking. It is intended for the serious learner who is interested in studying some deductive strategies in the context of a variety of elementary mathematical situations. No background beyond single-variable calculus is presumed.

Introduction to Proof in Abstract Mathematics

Andrew Wohlgemuth
Introduction to Proof in Abstract Mathematics Book PDF

Author : Andrew Wohlgemuth
Publisher : Courier Corporation
Page : 385 pages
File Size : 48,5 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9780486141688

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Introduction to Proof in Abstract Mathematics by Andrew Wohlgemuth Pdf

The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.

Introduction to Abstract Mathematics

T. A. Bick
Introduction to Abstract Mathematics Book PDF

Author : T. A. Bick
Publisher : Elsevier
Page : 232 pages
File Size : 48,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483276595

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Introduction to Abstract Mathematics by T. A. Bick Pdf

Introduction to Abstract Mathematics focuses on the principles, approaches, and operations involved in abstract mathematics, including metric spaces, sets, axiom systems, and open sentences. The book first offers information on logic and set theory, natural numbers, and integers and rational numbers. Discussions focus on rational numbers and ordered fields, ordering, arithmetic, axiom systems and methods of proof, functions of kindred matters, ordered pairs and relations, sets, and statements and open sentences. The text then examines real and complex numbers, metric spaces, and limits. Topics include generalized limits, continuous functions, openness, closedness, and neighborhood systems, definition and basic properties, and construction of R. The publication is a vital reference for mathematicians and students interested in abstract mathematics.

Linear Algebra

Robert J. Valenza
Linear Algebra Book PDF

Author : Robert J. Valenza
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209010

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Linear Algebra by Robert J. Valenza Pdf

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.

Bridge to Abstract Mathematics

Ralph W. Oberste-Vorth,Bonita A. Lawrence
Bridge to Abstract Mathematics Book PDF

Author : Ralph W. Oberste-Vorth,Bonita A. Lawrence
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 55,8 Mb
Release : 2012
Category : Education
ISBN : 9780883857793

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Bridge to Abstract Mathematics by Ralph W. Oberste-Vorth,Bonita A. Lawrence Pdf

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.

Introduction to Abstract Algebra

Jonathan D. H. Smith
Introduction to Abstract Algebra Book PDF

Author : Jonathan D. H. Smith
Publisher : CRC Press
Page : 324 pages
File Size : 49,5 Mb
Release : 2015-10-23
Category : Mathematics
ISBN : 9781498731812

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Introduction to Abstract Algebra by Jonathan D. H. Smith Pdf

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 Abstract Analysis

Marvin E. Goldstein,Burt M. Rosenbaum
Introduction to Abstract Analysis Book PDF

Author : Marvin E. Goldstein,Burt M. Rosenbaum
Publisher : Courier Corporation
Page : 256 pages
File Size : 41,9 Mb
Release : 2014-10-27
Category : Mathematics
ISBN : 9780486799919

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Introduction to Abstract Analysis by Marvin E. Goldstein,Burt M. Rosenbaum Pdf

Concise text prepares readers to pursue abstract analysis in the literature of pure mathematics. Detailed, easy-to-follow proofs and examples illustrate topics including real numbers, vector and metric spaces, infinite series, and other concepts. 1969 edition.

An Invitation to Abstract Mathematics

Béla Bajnok
An Invitation to Abstract Mathematics Book PDF

Author : Béla Bajnok
Publisher : Springer Nature
Page : 443 pages
File Size : 53,9 Mb
Release : 2020-10-27
Category : Mathematics
ISBN : 9783030561741

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An Invitation to Abstract Mathematics by Béla Bajnok Pdf

This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH

Introduction to Abstract Algebra

Jonathan D. H. Smith
Introduction to Abstract Algebra Book PDF

Author : Jonathan D. H. Smith
Publisher : CRC Press
Page : 344 pages
File Size : 46,8 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 1420063723

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Introduction to Abstract Algebra by Jonathan D. H. Smith Pdf

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.

A Book of Abstract Algebra

Charles C Pinter
A Book of Abstract Algebra Book PDF

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 48,9 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9780486474175

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A Book of Abstract Algebra by Charles C Pinter Pdf

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.

Proofs and Fundamentals

Ethan D. Bloch
Proofs and Fundamentals Book PDF

Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 51,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461221302

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Proofs and Fundamentals by Ethan D. Bloch Pdf

The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

Linear Algebra

Robert J. Valenza
Linear Algebra Book PDF

Author : Robert J. Valenza
Publisher : Springer
Page : 237 pages
File Size : 44,8 Mb
Release : 1999-02-01
Category : Mathematics
ISBN : 9780387940991

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Linear Algebra by Robert J. Valenza Pdf

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.

Sets, Functions, and Logic

Keith Devlin
Sets Functions and Logic Book PDF

Author : Keith Devlin
Publisher : CRC Press
Page : 160 pages
File Size : 50,6 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781482286021

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Sets, Functions, and Logic by Keith Devlin Pdf

Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students. Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead. Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read...and enjoy...and learn from. About the Author Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,. Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.