A Transition to Advanced Mathematics

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Cengage Learning, Jun 1, 2010 - Mathematics - 416 pages
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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.
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Contents

Logic and Proofs
1
Set Theory
71
Relations and Partitions
135
Functions
184
Cardinality
233
Concepts of Algebra
275
Concepts of Analysis
315
Answers to Selected Exercises
352
Index
393
List of Symbols
399
Copyright

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About the author (2010)

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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