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A Transition to Advanced Mathematics

A Transition to Advanced Mathematics
Author: Douglas Smith - Maurice Eggen - Richard St. Andre
ISBN 13: 9780495562023
ISBN 10: 495562025
Edition: 7
Publisher: Brooks Cole
Publication Date: 2010-06-01
Format: Hardcover
Pages: 416
List Price: $304.95

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


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)