MAT 271-01 Calendar. Fall 2017.

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
• 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