I  Introduction
1 Syllabus
 1.1 Discrete Mathematics I
 1.2 Goals
 1.3 Instructor: Jason Riedy
 1.4 Text
 1.5 Grading
 1.6 On homework
 1.7 Submitting homework
2 Syllabus schedule
II  Notes for chapters 1, 2, and 3
3 Notes for 18 August
 3.1 Syllabus and class mechanics
 3.2 Introductions
 3.3 Inductive and deductive reasoning
 3.4 Inductive
 3.5 Deductive
4 Notes for 20 August
 4.1 Review: Inductive and deductive reasoning
 4.2 Inductive reasoning on sequences
 4.3 A tool for sequences: successive differences
 4.4 Successive differences are not useful for everything.
 4.5 An application where successive differences work, amazingly.
 4.6 Next time: Problem solving techniques.
 4.7 Homework
5 Notes for 22 August
 5.1 The problem solving section is important enough for a full class
 5.2 Review successive differences: a tool for inductive reasoning on sequences
 5.3 Moving from a table to a formula
 5.4 Starting point
 5.5 The plan for deriving a formula
 5.6 The derivation
  5.6.1 Rephrasing the problem
  5.6.2 Expressing the base sequence
  5.6.3 Substituting into {Δ}^{(2)} into the expression for {Δ}^{(1)}
  5.6.4 Breaking down the complicated expression
  5.6.5 Pulling the pieces together
  5.6.6 Checking the result
 5.7 Homework
6 Solutions for first week’s assignments
 6.1 Notes on received homeworks
 6.2 Exercises for Section 1.1
  6.2.1 Even problems, 2-12
 6.3 Explain the “trick” of Section 1.1’s example
 6.4 Exercises for Section 1.2
  6.4.1 Problems 2, 9, and 10
  6.4.2 Problems 14 and 16
  6.4.3 Problems 29 and 30
  6.4.4 Problems 32, 39, and 51
  6.4.5 Problem 49
  6.4.6 Problems 51 and 54
7 Notes for 25 August
 7.1 Problem solving principles
  7.1.1 Pólya’s principles
  7.1.2 Understand the problem
  7.1.3 Divise a plan
  7.1.4 Carry out the plan
  7.1.5 Examine your solution
 7.2 Making a lists and tables
  7.2.1 Example of a table
 7.3 Searching by guessing
  7.3.1 Example for guessing and checking
 7.4 Understanding dependencies, or ”working backward”
  7.4.1 Example for following dependencies
 7.5 Next time: more techniques
 7.6 Homework
8 Notes for 27 August
 8.1 Review: Pólya’s problem-solving principles
 8.2 Effective trial and error by bisection
  8.2.1 Understanding the problem
  8.2.2 Forming plans
  8.2.3 Carrying out the new plan
  8.2.4 Looking back
 8.3 Simpler sub-problems for finding patterns
 8.4 Other sources for tactics and examples
 8.5 Next time: Reading graphs and charts
 8.6 Homework
9 Notes for 29 August
 9.1 Review: Pólya’s problem-solving principles
 9.2 Notes on the homework
 9.3 Reading graphs: delayed until Monday (or later)
 9.4 Homework
10 Solutions for second week’s assignments
 10.1 Exercises for Section 1.3
  10.1.1 Problem 6: Understanding
  10.1.2 Problem 12: Guessing and checking
  10.1.3 Problem 31: Listing
  10.1.4 Problem 35: Listing
  10.1.5 Problem 28: Following dependencies
  10.1.6 Problem 57: Following dependencies
  10.1.7 Problem 40: Bisection and guessing a range
  10.1.8 Problem 52: Think about bisection
  10.1.9 Problem 56
  10.1.10 Problem 61: Look for a pattern
 10.2 Making change
 10.3 Writing out problems
  10.3.1 Section 1.2, problem 9
  10.3.2 Section 1.2, problem 49
  10.3.3 Section 1.3, problem 40
 10.4 Computing with numbers
  10.4.1 Extra digits from 1∕7
  10.4.2 Binary or decimal?
11 Notes for reading graphs
 11.1 Reading graphs
 11.2 Creating a graphical depiction of data
 11.3 Graph galleries and resources
12 Homework for reading graphs
 12.1 Homework
13 Notes for the third week: set theory
 13.1 Language of set theory
 13.2 Basic definitions
 13.3 Translating sets into (and from) English
 13.4 Relations
 13.5 Translating relations into (and from) English
 13.6 Consequences of the set relation definitions
 13.7 Visualizing two or three sets: Venn diagrams
 13.8 Operations
  13.8.1 Similarities to arithmetic
 13.9 Translating operations into English
 13.10 Special operations
  13.10.1 Universes and complements
  13.10.2 Tuples and cross products
 13.11 Cardinality and the power set
14 Homework for the third week: set theory
 14.1 Homework
15 Solutions for third week’s assignments
 15.1 Section 1.4, problem 54
 15.2 Section 2.1
  15.2.1 Problems 1-8
  15.2.2 Problems 11 and 17
  15.2.3 Problems 30 and 32
  15.2.4 Problems 62, 63, and 66
  15.2.5 Problems 68, 71, 74, and 78
  15.2.6 Problem 92
 15.3 Section 2.2
  15.3.1 Problems 8, 10, 12, 14
  15.3.2 Even problems 24-34
 15.4 Section 2.3
  15.4.1 Problems 1-6
  15.4.2 Problems 10, 17, 18, 23, 24
  15.4.3 Problem 31
  15.4.4 Problem 33
  15.4.5 Problems 61, 62
  15.4.6 Problems 72, 73
  15.4.7 Problems 117, 118, 121-124
III  Notes for chapters 4, 5, and 6
16 Notes for the fourth week: symbolic logic
 16.1 Language of logic
 16.2 Symbolic logic
 16.3 Logical operators and truth tables
 16.4 Properties of logical operators
 16.5 Truth tables and logical expressions
  16.5.1 De Morgan’s laws
  16.5.2 Logical expressions from truth tables
 16.6 Conditionals
  16.6.1 English and the operator →
  16.6.2 Defining p → q
  16.6.3 Converse, inverse, and contrapositive
  16.6.4 If and only if, or ↔
 16.7 Quantifiers
  16.7.1 Negating quantifiers
  16.7.2 Nesting quantifiers
  16.7.3 Combining nesting with negation
 16.8 Logical deduction: Delayed until after the test
17 Homework for the fourth week: symbolic logic
 17.1 Homework
18 Solutions for fourth week’s assignments
 18.1 Section 3.1
  18.1.1 Problems 1-5
  18.1.2 Problems 40, 42, 44
  18.1.3 Problems 49-54
 18.2 Section 3.2
  18.2.1 Problems 15-18
  18.2.2 Problems 37-40
  18.2.3 Problems 53-55
  18.2.4 Problems 61, 62
 18.3 Section 3.3
  18.3.1 Problems 1-5
  18.3.2 Problems 13, 15, 20
  18.3.3 Problems 35-38
  18.3.4 Problems 58, 60
  18.3.5 Problems 67, 68
  18.3.6 Problems 74, 75
 18.4 Section 3.4
  18.4.1 Problems 1, 3, 6
  18.4.2 Problem 51, 57, 58
 18.5 Section 3.1 again
  18.5.1 Problems 55, 56
  18.5.2 Problems 60-64
  18.5.3 Problem 75
  18.5.4 Problem 76
 18.6 Negating statements
 18.7 Function from truth table
19 Notes for the fifth week: review
 19.1 Review
 19.2 Inductive and deductive reasoning
 19.3 Problem solving
  19.3.1 Understand the problem
  19.3.2 Devise a plan
  19.3.3 Carry out the plan
  19.3.4 Look back at your solution
 19.4 Sequences
 19.5 Set theory
 19.6 Symbolic logic
  19.6.1 From truth tables to functions
  19.6.2 De Morgan’s laws and forms of conditionals
  19.6.3 Quantifiers
  19.6.4 Nesting and negating quantifiers
20 First exam and solutions
21 Notes for the sixth week: numbers and computing
 21.1 Positional Numbers
 21.2 Converting Between Bases
  21.2.1 Converting to Decimal
  21.2.2 Converting from Decimal
 21.3 Operating on Numbers
  21.3.1 Multiplication
  21.3.2 Addition
  21.3.3 Subtraction
  21.3.4 Division and Square Root: Later
 21.4 Computing with Circuits
  21.4.1 Representing Signed Binary Integers
  21.4.2 Adding in Binary with Logic
  21.4.3 Building from Adders
  21.4.4 Decimal Arithmetic from Binary Adders
22 Homework for the sixth week: numbers and computing
 22.1 Homework
23 Solutions for sixth week’s assignments
 23.1 Section 4.1, problems 35 and 36
 23.2 Section 4.2
 23.3 Section 4.3
 23.4 Positional form
 23.5 Operations
24 Notes for the seventh week: primes, factorization, and modular arithmetic
 24.1 Divisibility
 24.2 Primes
 24.3 Factorization
 24.4 Modular Arithmetic
 24.5 Divisibility Rules
25 Homework for the seventh week: primes, factorization, and modular arithmetic
 25.1 Homework
26 Solutions for seventh week’s assignments
 26.1 Section 5.1 (prime numbers)
  26.1.1 Problem 80
 26.2 Section 5.1 (factorization)
 26.3 Section 5.4 (modular arithmetic)
  26.3.1 Problems 9-13
  26.3.2 Other problems
 26.4 Section 5.1 (divisibility rules)
  26.4.1 Take a familiar incomplete integer\mathop{\mathop{…}}
27 Notes for the eighth week: GCD, LCM, ax + by = c
 27.1 Modular arithmetic
 27.2 Divisibility rules
 27.3 Greatest common divisor
 27.4 Least common multiple
 27.5 Euclidean GCD algorithm
 27.6 Linear Diophantine equations : Likely delayed
28 Homework for the eighth week: GCD, LCM, ax + by = c
 28.1 Homework
29 Solutions for eighth week’s assignments
 29.1 Exercises 5.3
 29.2 Computing GCDs
 29.3 Computing LCMs
30 Notes for the ninth week: ax + by = c and fractions
 30.1 Linear Diophantine equations
  30.1.1 In general\mathop{\mathop{…}}
  30.1.2 The other example
 30.2 Into real numbers
  30.2.1 Operator precedence
 30.3 Rational numbers
 30.4 Review of rational arithmetic
  30.4.1 Multiplication and division
  30.4.2 Addition and subtraction
  30.4.3 Comparing fractions
 30.5 Complex fractions
31 Homework for the ninth week: ax + by = c and fractions
 31.1 Homework
32 Solutions for ninth week’s assignments
 32.1 Linear Diophantine equations
 32.2 Exercises 6.3
33 Notes for the tenth week: Irrationals and decimals
 33.1 Real numbers
 33.2 Exponents and roots
  33.2.1 Positive exponents
  33.2.2 Zero exponent
  33.2.3 Negative exponents
  33.2.4 Rational exponents and roots
  33.2.5 Irrational numbers
 33.3 Decimal expansions and percentages
  33.3.1 Representing rationals with decimals
  33.3.2 The repeating decimal expansion may not be unique!
  33.3.3 Rationals have terminating or repeating expansions
  33.3.4 Therefore, irrationals have non-repeating expansions.
  33.3.5 Percentages as rationals and decimals
 33.4 Fixed and floating-point arithmetic
  33.4.1 Rounding rules
  33.4.2 Floating-point representation
  33.4.3 Binary fractional parts
34 Homework for the tenth week: Irrationals and decimals
 34.1 Homework
35 Solutions for tenth week’s assignments
 35.1 Exercises 6.4
 35.2 Exercises 6.3
 35.3 Exercises 6.5
 35.4 Rounding and floating-point
  35.4.1 Rounding
  35.4.2 Errors in computations
  35.4.3 Extra digits
36 Second exam and solutions
IV  Notes for chapters 7 and 8
37 Notes for the twelfth week
 37.1 Covered So Far
 37.2 What Will Be Covered
 37.3 An Algebraic Example
 37.4 The Example’s Graphical Side
 37.5 Definitions
 37.6 Algebraic Rules for Transformations Between Equivalent Equations
 37.7 Transformation Examples
 37.8 Manipulating Formulæ by Transformations
38 Homework for the twelfth week
 38.1 Homework
39 Solutions for twelfth week’s assignments
 39.1 Exercises for 7.1
 39.2 Exercises for 7.2
40 Homework for the thirteenth week
 40.1 Homework
41 Solutions for the thirteenth week’s assignments
 41.1 Exercises for 8.2
 41.2 Exercises for 8.3
 41.3 Exercises for 8.7
 41.4 Exercises for 8.8
42 Homework for the fourteenth week
 42.1 Homework
43 Solutions for the fourteenth week’s assignments
 43.1 Exercises for 7.3
 43.2 Exercises for 7.4
 43.3 Exercises for 7.5
 43.4 Exercises for 7.7
 43.5 Exercises for 8.1
 43.6 Exercises for 8.3
 43.7 Exercises for 8.6
 43.8 Exercises for 8.7
 43.9 Exercises for 8.8
44 Third exam, due 1 December
45 Third exam solutions
46 Final exam
V  Resources
47 Math Lab
48 On-line
 48.1 General mathematics education resources
 48.2 Useful software and applications