This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

Book of Proof

Science & Math

Richard Hammack

Mathematics

Virginia Commonwealth Universi

The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: A semester of calculus. Students with three semesters of calculus can skip a few sections. Applications: Each chapter has three or four discussions of additional topics and applications. These are suitable for independent study or for small group work. What makes it different? The approach is developmental. Although the presentation is focused on covering the requisite material by proving things, it does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.

Linear Algebra

Jim Hefferon

This text is intended for a one- or two-semester undergraduate course in abstract algebra and covers the traditional theoretical aspects of groups, rings, and fields. Many applications are included, including coding theory and cryptography. The nature of the exercises ranges over several categories; computational, conceptual, and theoretical problems are included.

Abstract Algebra: Theory and Applications

Thomas W Judson

This book is designed for a one-semester course in set theory at the advanced undergraduate or beginning graduate level. Three features are the full integration into the text of the study of models of set theory, the use of illustrative examples both in the text and in the exercises, and the integration of consistency results and large cardinals into the text early on. This book is aimed at two audiences: students who are interested in studying set theory for its own sake, and students in other areas who may be curious about applications of set theory to their field. In particular, great care is taken to develop the intuitions that lie behind modern, as well as classical, set theory, and to connect set theory with the rest of mathematics.

Introduction to Modern Set Theory

Judith Roitman

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Books by Virginia Commonwealth Universi

See the best price to sell, buy or rent books by the Virginia Commonwealth Universi publisher. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Book of Proof

Linear Algebra

Abstract Algebra: Theory and Applications

Introduction to Modern Set Theory

Abstract Algebra: Theory and Applications