An Introduction to Abstract Mathematics

An Introduction to Abstract Mathematics

Author: Robert J. Bond

Publisher: Waveland Press

ISBN: 9781478608059

Category: Mathematics

Page: 323

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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.
An Introduction to Abstract Mathematics
Language: en
Pages: 323
Authors: Robert J. Bond, William J. Keane
Categories: Mathematics
Type: BOOK - Published: 2007-08-24 - Publisher: Waveland Press

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
Linear Algebra as an Introduction to Abstract Mathematics
Language: en
Pages: 208
Authors: Isaiah Lankham, Bruno Nachtergaele, Anne Schilling
Categories: Mathematics
Type: BOOK - Published: 2015-11-30 - Publisher: World Scientific Publishing Company

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
Introduction to Abstract Mathematics
Language: en
Pages: 382
Authors: John F. Lucas
Categories: Mathematics
Type: BOOK - Published: 1990 - Publisher: Rowman & Littlefield

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.
Sets, Functions, and Logic
Language: en
Pages: 160
Authors: Keith Devlin
Categories: Mathematics
Type: BOOK - Published: 2018-10-03 - Publisher: CRC Press

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
Sets, Groups, and Mappings: An Introduction to Abstract Mathematics
Language: en
Pages: 304
Authors: Andrew D. Hwang
Categories: Algebra
Type: BOOK - Published: 2019-09-26 - Publisher: American Mathematical Soc.

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