This is Version 1.3b (2017), a variant of 1.3 (2013) with some modest changes for use by recent versions of the U. Illinois course. It will eventually turn into a real version 1.4. You can download the whole book as a single pdf file, or select from the individual files below.

Also see our collection of study problems with annotated solutions.

Instructors may find the instructor manual helpful.

• Table of Contents
• Preface
• Chapter 1: Math Review (revised)
• Chapter 2: Logic
• Chapter 3: Proofs
• Chapter 4: Number Theory
• Chapter 5: Sets
• Chapter 6: Relations
• Chapter 7: Functions and onto
• Chapter 8: Functions and one-to-one
• Chapter 9: Graphs
• Chapter 10: 2-way Bounding
• Chapter 11: Induction
• Chapter 12: Recursive Definition
• Chapter 13: Trees
• Chapter 14: Big-O (revised)
• Chapter 15: Algorithms (revised)
• Chapter 16: NP
• Chapter 17: Proof by Contradiction
• Chapter 18: Collections of Sets
• Chapter 19: State Diagrams
• Chapter 20: Countability
• Chapter 21: Planar Graphs
• Appendix A: Jargon
• Appendix B: Acknowledgements and Supplementary Readings
• Appendix C: Where Did It Go?

errata file

Old versions of the book

• version 1.0
• version 1.2
• version 1.3