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

5.7 Homework

6 Solutions for first week’s assignments

6.1 Notes on received homeworks

6.2 Exercises for Section 1.1

6.3 Explain the “trick” of Section 1.1’s example

6.4 Exercises for Section 1.2

7 Notes for 25 August

7.1 Problem solving principles

7.2 Making a lists and tables

7.3 Searching by guessing

7.4 Understanding dependencies, or ”working backward”

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

8.3 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

10.2 Making change

10.3 Writing out problems

10.4 Computing with numbers

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

13.9 Translating operations into English

13.10 Special operations

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

15.3 Section 2.2

15.4 Section 2.3

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

5.7 Homework

6 Solutions for first week’s assignments

6.1 Notes on received homeworks

6.2 Exercises for Section 1.1

6.3 Explain the “trick” of Section 1.1’s example

6.4 Exercises for Section 1.2

7 Notes for 25 August

7.1 Problem solving principles

7.2 Making a lists and tables

7.3 Searching by guessing

7.4 Understanding dependencies, or ”working backward”

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

8.3 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

10.2 Making change

10.3 Writing out problems

10.4 Computing with numbers

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

13.9 Translating operations into English

13.10 Special operations

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

15.3 Section 2.2

15.4 Section 2.3