Higher Education

A Transition to Advanced Mathematics, 8th Edition

  • Doug Smith University of North Carolina at Wilmington
  • Maurice Eggen Trinity University
  • Richard St. Andre Central Michigan University
  • ISBN-10: 1285463269  |  ISBN-13: 9781285463261
  • 448 Pages
  • Previous Editions: 2011, 2006, 2001
  • © 2015 | Published
  • College Bookstore Wholesale Price = $233.50
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A TRANSITION TO ADVANCED MATHEMATICS helps students to 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 students to think and express themselves 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 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.

Features and Benefits

  • The authors follow a logical development of topics, and write in a readable style that is consistent and concise. As each new mathematical concept is introduced the emphasis remains on improving students' ability to write proofs.
  • Worked examples and exercises throughout the text, ranging from the routine to the challenging, reinforce the concepts.
  • Proofs to Grade exercises test students' ability to distinguish correct reasoning from logical or conceptual errors.
  • A flexible organization allows instructors to expand coverage or emphasis on certain topics and include a number of optional topics without any disruption to the flow or completeness of the core material.-

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
Answers to selected exercises.

What's New

  • A new mini-section in Chapter 1 on mathematical writing style that describes good practices and some of the special characteristics that distinguish the way mathematics is communicated. Besides advice on what to include in a proof and what to leave out, this short section offer tips on the use of symbols and other details that help in writing clear, readable proofs.
  • An expanded section on strategies for constructing proofs follows the introductory sections on methods of proof and the discussion on writing style. This section summarizes basic proof methods and includes more than sixty exercises involving proofs.
  • A new section, Section 3.4, on modular arithmetic, and a new Section 4.7 on limits of functions and continuity of real functions.
  • Revised Sections, 2.6 on combinatorial counting and Section 4.6 on sequences provide the most current content.


All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

Complete Solutions Manual on Instructor Companion Website for A Transition to Advanced Mathematics, 8th  (ISBN-10: 1305107020 | ISBN-13: 9781305107021)

Meet the Author

Author Bio

Doug Smith

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

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

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.