Book of Proof

Written by: Richard Hammack (Virginia Commonwealth University)

The Book of Proof was written to help students transition from the computational aspects of mathematics to the more theoretical ones with the goal “to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories.”

This abstract math textbook was written by Associate Professor Richard Hammack, member of the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. Hammack, at the time of writing his text, had taught proof courses for 14 years at Virginia Commonwealth and Randolph-Macon College. This textbook is currently being used by a number of colleges and universities in the United States, Finland, Moldova, Turkey, Canada, Sweden, Indonesia, Brunei, Thailand, The Netherlands, and The Gambia; including University of the Gambia, William Patterson University, University of Arizona, Pennsylvania State University, Johns Hopkins University and a number of others. Course titles have included: discrete math, fundamentals of mathematics, introduction to proof techniques, number theory, introduction to the theory of computation, pure mathematics, discrete structures, introduction to proofs, and transition to advanced mathematics.

Chapter sections are offered as individual PDFs or students can purchase a printed copy.

Chapters in the Book of Proof Online Abstract Math Textbook

  1. Fundamentals
    • Sets
    • Logic
    • Counting
  2. How to Prove Conditional Statements
    • Direct Proof
    • Contrapositive Proof
    • Proof by Contradiction
  3. More on Proof
    • Proving Non-Conditional Statements
    • Proofs Involving Sets
    • Disproof
    • Mathematical Induction
  4. Relations, Functions and Cardinality
    • Relations
    • Functions
    • Cardinality

The text also includes a set of solutions for odd-numbered exercises.


View this Free Online Material at the source:
Book of Proof

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