Mathematical Proofs: A Transition to Advanced Mathematics, 4th edition

Published by Pearson (October 27, 2017) © 2018

  • Gary Chartrand Western Michigan University
  • Albert D. Polimeni SUNY, College at Fredonia
  • Ping Zhang Western Michigan University
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Products list

Details

  • A print text

This product is expected to ship within 3-6 business days for US and 5-10 business days for Canadian customers.

For courses in Transition to Advanced Mathematics or Introduction to Proof.


Meticulously crafted, student-friendly text that helps build mathematical maturity

Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. Written in a student-friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such as number theory, combinatorics, and calculus. The exercises receive consistent praise from users for their thoughtfulness and creativity.  They help students progress from understanding and analyzing proofs and techniques to producing well-constructed proofs independently. This book is also an excellent reference for students to use in future courses when writing or reading proofs.


0. Communicating Mathematics

0.1 Learning Mathematics

0.2 What Others Have Said About Writing

0.3 Mathematical Writing

0.4 Using Symbols

0.5 Writing Mathematical Expressions

0.6 Common Words and Phrases in Mathematics

0.7 Some Closing Comments About Writing

1. Sets

1.1. Describing a Set

1.2. Subsets

1.3. Set Operations

1.4. Indexed Collections of Sets

1.5. Partitions of Sets

1.6. Cartesian Products of Sets

Chapter 1 Supplemental Exercises

2. Logic

2.1. Statements

2.2. The Negation of a Statement

2.3. The Disjunction and Conjunction of Statements

2.4. The Implication

2.5. More On Implications

2.6. The Biconditional

2.7. Tautologies and Contradictions

2.8. Logical Equivalence

2.9. Some Fundamental Properties of Logical Equivalence


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