The interactive pages listed below supplement a textbook for Discrete Mathematics, written by myself and Winston Crawley, and published by John Wiley & Sons, Inc. Complete information about the book can be found at the Wiley website or on

Early versions of the interactives for this site exist for browsers that support Adobe Flash Player at (email me if you'd like a link to this page). The development of these computer-based material for teaching and learning mathematical reasoning and proof were initially funded through a National Science Foundation educational materials development grant (NSF DUE 0230755). I have run several workshops over the years on the use of this material for teaching Discrete Mathematics and introduction to proof.

HTML5/JavaScript Applets

Chapter 1

Chapter 2. A Primer of Mathematical Writing

2.2. Proofs about numbers

Counterexamples Scrambled proofs

2.3. Mathematical induction (sequences)

Building inductive reasoning:

Sequence #1 Sequence #2 Sequence #3 Sequence #4

Practicing the induction step:

Sequence #1 Sequence #2 Sequence #3 Sequence #4

2.3. Mathematical induction (summations)

Building inductive reasoning:

Summation #1 Summation #2 Summation #3 Summation #4

Practicing the induction step:

Summation #1 Summation #2 Summation #3 Summation #4

Other applets:

Scrambled proofs

Chapter 3. Sets and Boolean Algebra

3.2. More operations on sets


3.5. Proving set properties

Truth tables for logical expressions

Chapter 4. Functions and relations

4.4. Properties of relations

Counterexamples Scrambled proofs

Chapter 5. Combinatorics

5.3. Combinations and the Binomial Theorem

Practice, answers can use C(n,k) notation

Chapter 6. Probability

6.2. Sum and product rules for probability


Chapter 7. Graphs and Trees

7.2. Proofs about graphs and trees

Fill-in-the-blanks proofs

Contact Doug Ensley

Douglas Ensley, Ph.D.
Professor of Mathematics
Shippensburg University
Shippensburg, PA 17257
Phone: 717.477.1406