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

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