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?

Old versions of the book