A Transition To Advanced Mathematics

By (author) Smith, Douglas; By (author) Eggen Maurice; By (author) St. Andre, Richard
Short description/annotation:
Helps students to bridge the gap between calculus and advanced math courses. This 8th edition provides 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.
Description:
A TRANSITION TO ADVANCED MATHEMATICS helps you bridge the gap between calculus and advanced math courses. The most successful text of its kind, the 8th edition continues to provide a firm foundation in major concepts needed for continued study and guides you to think and express yourself mathematically—to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors present introductions to modern algebra and analysis and place continuous emphasis throughout on improving your 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. You will come away with a solid intuition for the types of mathematical reasoning you’ll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems. You will be exposed to a large number of examples and exercises that allow you to practice developing the skills needed to help them write and think like a mathematician.
Table of contents:
1. Logic and Proofs. 2. Sets and Induction. 3. Relations and Partitions. 4. Functions. 5. Cardinality. 6. Concepts of Algebra. 7. Concepts of Analysis Appendix. Answers to selected exercises. Index.
Biographical note:
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.