Flash
Applications
These activities accompany
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 Macromedia
that is available for many operating systems and browsers.
The resources below
are referenced to the items in the textbook to which the activity is related,
but they may also be used independently in conjunction with any discrete
math text.
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)
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)
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)
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
Markov
chain matrix calculator (Exercises
1218, 2429)
Chapter
7. Graphs and Trees
Section 7.1. Graph
theory
Eulerian
Graphs (Practice Problem 6, Exercise 9)
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)
