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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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, analysing 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 analysing 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
  • 1. Sets
  • 2. Logic
  • 3. Direct Proof and Proof by Contrapositive
  • 4. More on Direct Proof and Proof by Contrapositive
  • 5. Existence and Proof by Contradiction
  • 6. Mathematical Induction
  • 7. Reviewing Proof Techniques
  • 8. Prove or Disprove
  • 9. Equivalence Relations
  • 10. Functions
  • 11. Cardinalities of Sets
  • 12. Proofs in Number Theory
  • 13. Proofs in Combinatorics
  • 14. Proofs in Calculus
  • 15. Proofs in Group Theory

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