Chapters and sections refer to our textbook, *Mathematical Reasoning: Writing and Proof* by Ted Sundstrom.

- 1st Week, Aug. 21-25. Chapter 1 Introduction to writing proofs in Mathematics
- 1.1 Statements and Conditional Statements
- 1.2 Constructing Direct Proofs

- 2nd Week, Aug. 28 - Sept. 1. Chapter 2 Logical Reasoning
- 2.1 Statements and Logical Operations
- 2.2 Logically Equivalent Statements.
- Supplementary example: creating a formula with a given truth table.
- 2.3 Open Sentences and Sets

- 3rd Week, Sept. 4-8. Chapter 2 (cont.).
**Labor Day holiday, Monday Sept. 4**- 2.4 Quantifiers and Negations. (No quiz today).

- 4th Week, Sept. 11-15. Chapter 3 Constructing and Writing Proofs in Mathematics
- 2.4 Quantifiers and Negations (cont.)
- Homework: Write up exercise 2.4 #13 and turn it in Monday.

- 5th Week, Sept. 18-22. Chapter 3 (cont.)
- 3.1 Direct Proofs
- 3.2 More Methods of Proof
- Homework: Section 3.1 #6, 10, 16 and section 3.2 #11, 12, 14, 19. Due Monday.

- 6th Week, Sept. 25-29. Chapter 3 (cont.)
- Test postponed until next week.
- 3.3 Proof by Contradiction
- Homework 3.3 #7, 9 (prove or give counterexample), 10, 13.

- 7th Week, Oct. 2-6. Chapter 4 Mathematical Induction
- 4.1 The Principle of Mathematical Induction
- Homework 4.1 #3bc,10,18abc. Also this: Let f and g be differentiable functions. The product rule for derivatives says \((fg)'=f'g+fg'\). Work out formulas for the second, third, and fourth derivatives \((fg)''\), \((fg)'''\), \((fg)''''\) of a product. Based on these results, guess a formula for the \(n\)-th derivative \( (fg)^{(n)}\) of the product \(fg\). Then prove your formula, using mathematical induction.
- Read on your own 3.4 Using Cases in Proofs
- Skip 3.5 The Division Algorithm and Congruence
- Read on your own 3.6 Review of Proof Methods
- Test postponed until next week.

- 8th Week, Oct. 9-13. Chapter 4 (cont.)
- 4.2 Other Forms of Mathematical Induction
- 4.3 Induction and Recursion
**Test Wednesday Oct. 11**(postponed from last week) Covers chapters 1-3 (not induction). Solutions

- 9th Week, Oct. 16-20. Chapter 5 Set Theory
- Homework: Do sec 4.2 #1c, 3 7, 14, 17. Due next Monday.
- Read sections 5.1-5.3 in the text. Sections 5.1 and 5.2 are mainly just definitions of words: subset, union, intersection, etc. We'll go over this quickly on Monday, then we'll start in section 5.3.

- 10th Week, Oct. 23-27. Chapter 5 (cont.)
- Notes: Typical formats for induction proofs.
- 5.1 Sets and Operations on Sets (briefly)
- 5.2 Proving Set Relationships (briefly)
- 5.3 Properties of Set Operations (we'll be here on Monday.)
- Homework 5.1 #14, 5.2 #2b, 13, 5.3 #3, 6b, 11abc, 12a

- 11th Week, Oct. 30 - Nov. 3. Chapter 5 (cont.), Chapter 6 Functions
- 5.4 Cartesian Products
- 5.5 Indexed Families of Sets
- Homework 5.4 # 1a,d,e, 2a,c,g, 5, 6
- More homework 5.5 #5b, 8b, 13abc

- 12th Week, Nov. 6-10. Chapter 6 (cont.)
**Test Monday Nov. 6**Solutions- 6.1 Introduction to Functions
- 6.2 More about Functions
- 6.3 Injections, Surjections, and Bijections
**Veterans' Day Holiday Friday Nov. 10**

- 13th Week, Nov. 13-17. Chapter 6 (cont.)
- 6.4 Composition of Functions
- 6.5 Inverse Functions
- 6.6 Functions Acting on Sets
- Homework 6.3 #1, 4d, 13, 15, 16, 6.4 #9, 10, 6.5 # 6c, 6.6 #5, 6, 10, 14. Due Wednesday Nov. 22, or Monday Dec. 4 if it's not done by Wednesday.

- 14th Week, Nov. 20-24. Chapter 7 Equivalence Relations
- 7.1 Relations
- 7.2 Equivalence Relations
**Thanksgiving Holiday Thursday, Friday Nov. 23-24**

- 15th Week, Nov. 27 - Dec. 1.
- 7.3 Equivalence Classes
- Homework 7.2 #5, 14, 7.3 #3,4,5,11. Due Monday Dec. 4. (If you can't get it in by Monday then slip it under my office door later on.)

- 16th Week, Monday Dec. 4 only.
- Review

**Final Exam Wednesday Dec. 13 8:30-10:30am**Solutions