Flash
Applications

These
applets
accompany the textbook, Discrete Mathematics: Mathematical
Reasoning and Proof with Puzzles, Patterns and Games, by Doug Ensley and Winston Crawley, published by
John Wiley
and Sons. The development of some material on this site was funded
by NSF DUE0230755.
All
of the material linked from this page requires the Flash
player, a free plugin from Adobe
that is available for many operating systems and browsers. 

Instructors interested in customizing
some of these applets without doing any Flash program should download this tutorial. Instructors
interested in designing their own applets using Flash should check out
the MathDL Flash Forum (www.mathflashforum.org).

The
resources below are referenced to the items in the textbook to which
the activity is related.
Chapter
1. Puzzles, Patterns, and Mathematical Thinking
Section
1.1. First examples
Josephus
problem (Example 2, Exercise 3)
Draw this! (Example
3, Exercise 11)
Grid game (Practice
Problem 5, Exercise 12)
Section
1.2. Number puzzles and sequences
Sequence self test (Example 5, Exercises 4 and 7)
Graphical sequence self
test (Example 5, Exercises 4 and 7)
Recursive sequences (Example 5, Exercises 8 and 9)
Notation for sums (Example 11, Exercises
19 and 20)
Josephus
problem
again (Example 12, Exercise
25)
Section
1.3. Truthtellers, liars and propositional logic
Truth tables (Practice Problems 4 and 8; Exercises 11, 12, 1622)
Logically equivalent
statements (Practice Problems 4 and 8; Exercises
11, 12, 1622)
Section
1.4. Predicates
Predicates and domains (Practice Problem 1; Exercises 3 and 4)
Negation of predicates (Example
3; Practice Problem 2; Exercise 5)
Quantified statements (Practice Problems 2, 3 and 4; Exercises 6 and 7)
Section
1.5. Implications
More truth
tables (Exercises 4 and 5)
And even more truth tables and
even some with
subexpressions
Applications
of truth tables (Exercises 2 and 7)
Negation of predicates
with implications (Exercises 10 and 11)
Chapter
2. A Primer of Mathematical Writing
Section
2.1. Mathematical writing
Counterexamples (Practice Problem 4, Exercises 2 and 3)
Fill in the blanks (Exercise 5)
ProofReader (Tracing proofs, Example 6, Exercise 6)
Scrambled proofs (Exercises
4, 5, and 11)
Section
2.2. Proofs about numbers
Counterexamples (Exercise 4)
ProofReader (Practice
Problem 4, Exercises 5, 7, 14, and 23)
Scrambled proofs (Practice Problem 1, Exercises 7, 14, and 23)
Section
2.3. Mathematical induction
Proving closed forms for recursive
sequences. (Practice Problems 1 and 5, Exercises 3
and 4)
Proving closed formulas for sums.
(Practice Problems 2 and
4, Exercises 8 and 9)
Scrambled induction proofs (More practice reading proofs)
Section
2.4. More on induction
Divisibility proofs (Example 6, Exercises 3, 4, 5)
Fill in the blanks (Example 6, Exercises 3, 4, 5)
Section
2.5. Proof by contradiction and the Pigeonhole Principle
Scrambled proofs (Example 1, Exercises 4 and 7)
Fill in the blanks (Exercises 1 and 2)
Pigeonhole principle in action (Example 7, Practice Problem 4, Exercises 32, 33, and 34)
Section
2.6. Representations of Numbers
Flash
Magic Trick (External
Link)
Converting
Between Bases (Examples 710, Exercises 18)
Hexadecimal Colors (Exercise 19)
Chapter
3. Sets and Boolean Algebra
Section
3.1. Set definitions and operations
Set notation (Practice
Problem 3, Exercises 4 and 11)
Set operations (Practice
Problem 4, Exercise 1)
Counterexamples (Practice
Problem 7, Exercises 13, 17, and 32)
Twoset Venn diagrams (Warmup)
Threeset Venn diagrams (Practice Problem 6, Exercises 16 and 17)
Section
3.2. More operations on sets
Counterexamples (Exercises 10 and 11)
Section
3.3. Proving set properties
Fill in the blanks (Practice
Problem 3, Exercises 4 and 5)
Scrambled Proofs (Practice
Problems 4 and 5, Exercises 14 and 16)
Section
3.4: Boolean algebra
Scrambled Proofs (Practice Problem 4, Exercises
3 and 5)
Section
3.5: Logic circuits
Truth tables revisited (Practice
Problems 1 and 3, Exercise 3)
Chapter
4. Functions and relations
Section
4.1. Definitions, diagrams and inverses
Twoset arrow diagrams for
functions (Exercises 3 and 6)
Twoset arrow diagrams
for relations (Practice Problem 4, Exercises 8 and
9)
Oneset arrow diagrams for
relations (Practice Problem 2, Exercises 10 and 12)
Fill in the blanks (Exercise 16)
Section
4.2. The composition operation
Function composition (Practice Problem 2, Exercises 6 and 7)
Oracle of
Bacon at UVA (http://www.cs.virginia.edu/oracle/) (Exercise
22)
Section
4.3. Properties of functions
Fill in the blanks (Practice Problems 2 and 3, Exercises 7 and 8)
Scrambled proofs (Exercises
14  18)
Section
4.4. Properties of relations
Scrambled proofs (Practice
Problems 3, 4 and 5)
Counterexamples (Exercises
2, 3, 4, 9, and 10)
Chapter
5. Combinatorics
Section
5.1. Introduction
Dice Problems (Exercises 5 and 6)
Onetoone correspondence (Practice Problem 4, Exercise 18)
Section
5.2. Basic rules of counting
Practice problems (Exercises 5, 68, 20, 21)
Section
5.3. Combinations and the Binomial Theorem
Practice problems (Practice Problems 3 and
4, Exercises 15, 16, 23, 27, 31, 32)
Section
5.4. Binary sequences
Practice problems (Practice
Problems 2 and 4, Exercises 13, 1620)
Chapter
6. Probability
Section
6.1. Introduction
Birthday problem (Practice
Problem 3, Exercises 1417)
Dice problems (Exercise 3)
Simple dice game (Exercise 19)
Section
6.2. Sum and product rules for probability
Practice problems (Exercises
2, 3, 5, 7, and 8)
Section
6.3. Probability in games
Bernoulli trials (Practice
Problem 1, Exercises 16)
Series simulator (Practice
Problem 2, Exercises
20 and 22)
Section
6.4. Expected value in games
Series simulator (Practice
Problem 4, Exercises
1620)
Section
6.5. Recursive games
Tennis problem (Exercises
912, 15 and 16)
Hank and Ted (Exercises 18 and 19)
Section
6.6. Markov chains
Chutes and Ladders Simulation (External
Link)
Markov chain matrix calculator (Exercises
1218, 2429)
Chapter
7. Graphs and Trees
Section
7.1. Graph theory
Eulerian Graphs (Practice
Problem 6, Exercise 9)
"Eulerizing a graph"
means to add a minimal number of edges to make a new graph that has an
Euler circuit. Each additional edge can be interpreted as a "pencil
lift" in drawing problems or a "repeated edge" in a traveling circuit
problem.
General
graph tools from Christopher Mawatma's "Petersen" Project at http://www.mathcove.net/petersen/
Section
7.2. Proofs about graphs and trees
Fill in the blanks proof (Practice
Problems 1 and 2, Exercises 2, 14, and 18)
Section
7.3: Isomorphism and planarity
Graph Isomorphism (Example 1, Practice Problem 1, Exercise 3)
Planar Graphs (Practice Problem 4,
Exercises 10 and 12)
Section
7.4. Connections to matrices and relations
Practice problems (Exercises 18, 21, and 25)
Section
7.5. Graphs in puzzles and games
Water Puzzle (Exercise
1)
Nim Game (Practice
Problem 5, Exercises 1317)
Grid Game (Exercise 20)
Section
7.7: Hamiltonian graphs and TSP
Hamiltonian Graphs (Exercise
5 and 15)
Sean
Forman's TSP Generator (Resource for comparing
with Exercises 2124)
