Math 347 (Rezk, Section G1 3:00 MWF).

Math 347 (Rezk, 3:00 MWF, Section G1, 149 Henry).

Office hours

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Syllabus

Here is the syllabus.

Errata for textbook

Our text is Mathematical Thinking (MT) by D'Angelo and West. This page has a list of errors in the text.

Reading

Wednesday, January 21. MT pp. 2-15. (Sets and functions)
Friday, January 23. (Sets and functions, continued.)
Monday, January 26. (continued.)
Wednesday, January 28. MT pp. 15-18. (The real numbers.)
Friday, January 30. (Real numbers, continued.)
Monday, February 2. MT pp. 27-35. (Quantifiers.)
Wednesday, February 4. MT pp. 35-44. (Logical connectives.)
Friday, February 6. (Methods of proof.)
Monday, February 9. MT pp. 50- 57. (Principle of Induction.)
Wedenesday, February 11. MT pp. 58-62. (Applications of Induction.)
Friday, February 13. MT pp. 63-66. (Strong Induction.)
Monday, February 16. MT pp. 66-71. (Examples of Induction.)
Wednesday, February 18. MT pp. 80-83. (Bijections.)
Friday, February 20. MT pp. 83-85. (Injections and surjections.)
Monday, February 23. MT pp. 76-80. (Representation of natural numbers.)
Wednesday, February 25. (Representation of natural numbers, continued.)
Friday, February 27. MT pp. 85-92. (Composition of functions. Cardinality.)
Monday, March 2. (Cardinality, continued.)
Wednesday, March 4. First midterm.
Friday, March 6. MT pp. 101-104. (Arrangements and selections.)
Monday, March 9. Go over midterm.
Wednesday, March 11. MT pp. 104-110. (Binomial Coefficients)
Friday, March 13. (Binomial coefficients, continued.)
Monday, March 16. (Binomial coefficients, continued.)
Wednesday, March 18. (Binomial coefficients, continued.)
Friday, March 20. (Binomial coefficients, continued.)
Monday, March 30. MT pp. 111-115. (Permutations.)
Wednesday, April 1. (Permutations, continued.)
Friday, April 3. MT pp. 123-126. (Divisibility.)
Monday, April 6. (Divisibility, continued.)
Wednesday, April 8. Second midterm
Friday, April 10. (GCD.)
Monday, April 13. (GCD, continued. Euclidean algorithm.)
Wednesday, April 15. (Euclidean algorithm, continued.)
Friday, April 17. MT pp. 139-145. (Equivalence relations, congruence.)
Monday, April 20. (Congruence, continued.)
Wednesday, April 22. MT pp. 147-149. (Fermat's little theorem)
Friday, April 24. (Fermat's little theorem, continued.)
Monday, April 27. MT pp. 255-258. (Completeness Axiom.)
Wednesday, April 29. MT pp. 258-263. (Limits)
Friday, May 1. (Limits, continued.)
Monday, May 4. (Monotone convergence theorem.)

Tests

The first midterm has been rescheduled to Wednesday, March 4. It will cover the material from chapters 1-4.

The second midterm was on Wednesday, April 8. It mainly covered material from chapter 5.

The final is on Friday, May 15, 1:30-4:30 in the usual classroom. Here are two practice finals for you to study.

First practice final. Here are solutions.
Second practice final. Here are solutions.

Homework

Note: When a problem asks to "prove" or "show" something, I expect to see a formal proof from you (unless I say otherwise.) WA=Writing Assignment, PS=Problem Set.

WA 1. Due Monday, January 26.
PS 1. Due Friday, January 30. MT 1.13, 1.15, 1.41, 1.45, 1.47, 2.4. Formal proofs are required for 1.13 and 1.47(a)); verbal or visual explanations are acceptible for the others. (Note: I replaced problem 1.29 with 1.41.) Here are solutions.
PS 2. Due Friday, February 6. Here are solutions.
1. Using only the Ordered Field axioms, show that x≤ y and u ≤ v imply x+u ≤ y+v.
2. Using only the Ordered Field axioms, show that 0<x implies 0<x^-1. (In this problem and the last, you are free to use any facts about fields (i.e., algebraic properties of addition, subtraction, multiplication, division) without comment. However, the only facts about order relations you can use are the ordered field axioms (Definition 1.40.))
3. MT 1.29, 2.3, 2.9, 2.10, 2.11.
WA 2. MT 3.15. Due Wednesday, February 11.
PS 3. MT 1.50, 2.21, 2.26, 2.33, 2.37. Due Friday, February 13. Here are solutions.
PS 4. MT 3.23, 3.26, 3.32, 3.47. Due Monday, February 23. Here are solutions.
WA 3. Due Wednesday, February 25.
PS 5. MT 4.20, 4.22, 4.25, 4.29, 4.37. (For 4.25, give a proof or counterexample in each case.) Due Monday, March 2. Here are solutions.
PS 6. MT 4.47, 5.9, 5.14, 5.24, 5.31, 5.32. Due Monday, March 16 (note change in due date.) Here are solutions.
PS 7. MT 5.28, 5.36, 5.39. Due Friday, March 20. Here are solutions.
PS 8. MT 5.49, 5.57, 5.60. Due Friday, April 3. Here are solutions.
PS 9. MT 6.4, 6.17, 6.22, 6.26. Due Friday, April 10. Here are solutions.
PS 10. MT 6.5, 6.23, 6.28, 6.39. Due Friday, April 17. Here are solutions.
PS 11. MT 7.11, 7.13, 7.18, 7.19, 7.25. Due Friday, April 24. Here are solutions.
PS 12. MT 7.31, 7.42, 13.8, 13.21, 13.23. Due Friday, May 1. Here are solutions.
PS 13. MT 13.26, 13.28, 13.29. Due Wednesday, May 6. Here are solutions.

Contact info.

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office hours: Check here.

Last modified 11 May 2009 by Charles Rezk.

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