Mathematical Proofs: A Transition to Advanced Mathematics, 3rd Edition

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.

Table of Contents

Chapter 1 Sets
Chapter 2 Logic
Chapter 3 Direct Proof and Proof by Contrapositive
Chapter 4 More on Direct Proof and Proof by Contrapositive
Chapter 5 Existence and Proof by Contradiction
Chapter 6 Mathematical Induction
Chapter 7 Prove or Disprove
Chapter 8 Equivalence Relations
Chapter 9 Functions
Chapter 10 Cardinalities of Sets
Chapter 11 Proofs in Number Theory
Chapter 12 Proofs in Calculus
Chapter 13 Proofs in Group Theory
Chapter 14 Proofs in Ring Theory (Online)
Chapter 15 Proofs in Linear Algebra (Online)
Chapter 16 Proofs in Topology (Online)