Flash Applications
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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 DUE-0230755.
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, 16-22)
Logically equivalent statements (Practice Problems 4 and 8; Exercises 11, 12, 16-22)
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 7-10, Exercises 1-8)
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)
Two-set Venn diagrams (Warm-up)
Three-set 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
Two-set arrow diagrams for functions (Exercises 3 and 6)
Two-set arrow diagrams for relations (Practice Problem 4, Exercises 8 and 9)
One-set 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)
One-to-one correspondence (Practice Problem 4, Exercise 18)
Section 5.2. Basic rules of counting
Practice problems (Exercises 5, 6-8, 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 1-3, 16-20)
Chapter 6. Probability
Section 6.1. Introduction
Birthday problem (Practice Problem 3, Exercises 14-17)
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 1-6)
Series simulator (Practice Problem 2, Exercises 20 and 22)
Section 6.4. Expected value in games
Series simulator (Practice Problem 4, Exercises 16-20)
Section 6.5. Recursive games
Tennis problem (Exercises 9-12, 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 12-18, 24-29)
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 13-17)
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 21-24)