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.
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.
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Douglas Smith
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.
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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.
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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.
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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.
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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.
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A new section, Section 3.4, on modular arithmetic, and a new Section 4.7 on limits of functions and continuity of real functions.
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Revised Sections, 2.6 on combinatorial counting and Section 4.6 on sequences provide the most current content.
-
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.
-
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.-
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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.
Complete Solutions Manual on Instructor Companion Website for A Transition to Advanced Mathematics, 8th
9781305107021
Solutions Builder for Smith/ Eggen/St. Andre’s A Transition to Advanced Mathematics, 8th
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