Mathematical Proofs: A Transition to Advanced Mathematics (3rd Edition) (Featured Titles for Transition to Advanced Mathematics)
by: Gary Chartrand – Albert D. Polimeni – Ping Zhang
ISBN-10: 0321797094
ISBN-13: 9780321797094
Edition 版本: 3
Released: 2012-09-27
Pages: 424
Book Description
Mathematical Proofs: A Transition to Advanced Mathematics,Third Edition,prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom,this text introduces students to proof techniques,analyzing proofs,and writing proofs of their own. Written in a clear,conversational style,this book provides a solid introduction to such topics as relations,functions,and cardinalities of sets,as well as the theoretical aspects of fields such as number theory,abstract algebra,and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.
Contents
0 Communicating Mathematics
1Sets
2 Logic
3 Direct Proof and Proof by Contrapositive
4 More on Direct Proof and Proof by Contrapositive
5 Existence and Proof by Contradiction
6Mathematical Induction
7 Prove or Disprove
8 Equivalence Relations
9 Functions
10 Cardinalities of Sets
11Proofs in Number Theory
12 Proofs in Calculus
13 Proofs in Group Theory
14 Proofs in Ring Theory (Online)
15 Proofs in Linear Algebra (Online)
16Proofs in Topology (Online)
Answers and Hints to Odd-Numbered Section
Exercises
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