[request_ebook] A Transition to Advanced Mathematics

Synopsis

Many undergraduates find themselves stuck in the transition between beginning calculus to a more rigorous level of mathematics by their inability to do proofs. This text bridges the gap by explaining the basics of the concepts they will need in their next steps, helps them think and express themselves mathematically, and prepares students specifically for higher algebra and analysis. It covers logic and proofs (including quanitifiers), set theory (including operations and induction), relations (Cartesian products, equivalence, partitions, ordering relations and graphs), functions, cardinality, and concepts of algebra (structures, groups, subgroups, operation preserving maps, rings and fields) and analysis (including ordered field properties of the real numbers, the Henine-Bodel theorem, and the Bolzano- Weierstrass theorem). The authors provide answers to selected exercises. Annotation ©2005 Book News, Inc., Portland, OR

Booknews

This text was developed from lecture notes for a course at Central Michigan U. that was designed to bridge the gap between calculus and advanced courses for students who say: "I understand mathematics, but I just can't do proofs." Provides an overview of the major ideas needed for continued work, guides students to think and express themselves mathematically, and presents an introduction to modern algebra and analysis, including the foundational topics of logic, sets, relations, and functions. To help make the introduction to elementary proof techniques more manageable, new to this edition are separate sections on direct proofs and proofs by contrapositive and contradiction. There are also new and revised explanations, examples, and exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Biography

Douglas Smith is Professor of Mathematics at the University of North Carolina at Wilmington. Dr. Smith's fields of interest include Combinatorics / Design Theory (Team Tournaments, Latin Squares, and applications), Mathematical Logic, Set Theory, and Collegiate Mathematics Education.

Maurice Eggen is Professor of Computer Science at Trinity University. Dr. Eggen's research areas include Parallel and Distributed Processing, Numerical Methods, Algorithm Design, and Functional Programming.

Richard St. Andre is Associate Dean of the College of Science and Technology at Central Michigan University. Dr. St. Andre's teaching interests are quite diverse with a particular interest in lower division service courses in both mathematics and computer science.