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
About the Author
The authors are the leaders in this course area. They decided to write this text based upon a successful transition course that Richard St. Andre developed at Central Michigan University in the early 1980s. This was the first text on the market for a transition to advanced mathematics course and it has remained at the top as the leading text in the market. 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.
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