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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
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