Part II
Notes for chapters 1 and 2

3 Notes for 18 August
 3.1 Syllabus and class mechanics
 3.2 Introductions
 3.3 First ”homework”
 3.4 Problem solving
4 Notes for 20 August
 4.1 Review
 4.2 Today’s goal: Problem solving principles
 4.3 Pólya’s principles
 4.4 Two closely related tactics, guessing and making a list
 4.5 Next time: More problem solving ideas.
 4.6 Homework
5 Notes for 22 August
 5.1 Review
 5.2 New tactic: Drawing a diagram
 5.3 Homework
6 Solutions for first week’s assignments
 6.1 Problem Set 1.1
 6.2 Example like 1.3 with no solution
 6.3 Problem Set 1.2
 6.4 Consider solving Example 1.3 with a table
 6.5 More in Problem Set 1.2
7 Notes for 25 August
 7.1 Review
 7.2 Draw a diagram, follow dependencies
 7.3 Look for a pattern
 7.4 Patterns and representative special cases
 7.5 Homework
8 Notes for 27 August
 8.1 Review
 8.2 Ruling out possibilities
 8.3 The pigeonhole principle
 8.4 Mathematical reasoning
 8.5 Next time: structures and kinds of proofs
 8.6 Homework
9 29 August: Review of previous notes
10 Solutions for second week’s assignments
 10.1 Patterns: The 87th digit past the decimal in 1/7?
 10.2 Patterns: Units digit of \mathbf{{3}^{100}}
 10.3 Problem set 1.3
 10.4 Problem set 1.4
 10.5 Inductive or deductive?
11 Notes for 1 September
 11.1 Review
 11.2 Proof
 11.3 Direct proof
 11.4 Proof by contrapositives
 11.5 Homework
12 Notes for 3 September
 12.1 Proof review
 12.2 Inductive proof
 12.3 Starting with set theory
 12.4 Language of set theory
 12.5 Basic definitions
 12.6 Translating sets into (and from) English
 12.7 Next time: Relations between and operations on sets
 12.8 Homework
13 Notes for 8 September
 13.1 Review
 13.2 Relations and Venn diagrams
 13.3 Translating relations into (and from) English
 13.4 Consequences of the set relation definitions
 13.5 Operations
 13.6 Homework
14 Solutions for third week’s assignments
 14.1 Induction: Sum of first n integers
 14.2 Problem set 2.1 (p83)
15 Notes for 10 September
 15.1 Review
 15.2 From sets to whole numbers
 15.3 Homework
16 Notes for 12 September
 16.1 Review
 16.2 Addition of whole numbers
 16.3 Subtraction of whole numbers
 16.4 Multiplication of whole numbers
 16.5 Monday: Division and exponentials
 16.6 Homework
17 Solutions for fourth week’s assignments
 17.1 Problem set 2.2
 17.2 Problem set 2.3
 17.3 Write 2 + 3 using disjoint sets.
 17.4 Illustrate 2 + 3 using Peano arithmetic.
 17.5 Problem set 2.4
 17.6 Illustrate 2 ⋅ 3 using Peano arithmetic. You do not need to expand addition.
 17.7 Illustrate (1 ⋅ 2) ⋅ 3 = 1 ⋅ (2 ⋅ 3) using a volume of size six.
18 Notes for the fifth week: review
 18.1 Review
 18.2 Problem solving
 18.3 Set theory
 18.4 Operations and whole numbers
19 First exam and solutions