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 amazon.com.

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

### 1.2. Number puzzles and sequences

Sequence self test (Example 5, Exercises 4 and 7) Reading sigma notation (Example 11, Exercises 19 and 20)

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

## Chapter 2. A Primer of Mathematical Writing

### 2.1. Mathematical writing

Counterexamples Fill-in-the-blank proofs Scrambled proofs

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

Scrambled proofs

### 2.4. More on induction

Fill-in-the-blanks proofs

#### Divisibility proofs

Divisibility proof #1 Divisibility proof #2 Divisibility proof #3 Divisibility proof #4

Starting a proof by contradiction Fill-in-the-blank proofs Scrambled proofs

### 2.6. Representation of numbers

Conversion to/from base ten Direct converstion between bases 2, 8, 16

## Chapter 3. Sets and Boolean Algebra

Counterexamples

### 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

### 5.4. Binary sequences

Practice, allows P(n,r) and C(n,r) notation

## Chapter 6. Probability

Practice

### 6.5. Expected value in games

Simulate tennis game tied at deuce Simulate Hank and Ted game

## Chapter 7. Graphs and Trees

### 7.2. Proofs about graphs and trees

Fill-in-the-blanks proofs

### 7.3. Isomorphishm and planarity

First example for isomorphism Planarity: Example 1 Planarity: Example 2 Is K_{3,3} planar?

## Contact Doug Ensley

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

deensley@ship.edu