Synopsis

A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful text of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides students to think and express themselves mathematically--to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving students' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems.

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.