Math 347 (Rezk, Section X1H 12:00 MWF).

Math 347 (Rezk, 12:00 MWF, Section X1H, 152 Henry).

Office hours

See my homepage.

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 17. MT pp. 2-15. (Sets and functions)
Friday, January 19. MT pp. 15-18. (The real numbers.)
Monday, January 22. (Order properties of the real numbers.)
Wednesday, January 24. MT pp. 27-35. (Quantifiers.)
Friday, January 26. (Compound statements.)
Monday, January 29. MT pp. 35-44. (Methods of proof.)
Wednesday, January 31. MT pp. 50- 57. (Principle of Induction.)
Friday, February 2. (ctd.)
Monday, February 5. (no class)
Wednesday, February 7. MT pp. 58-62. (Applications of Induction.)
Friday, February 9. (ctd.)
Monday, February 12. MT pp. 63-66. (Strong Induction.)
Wednesday, February 14. (no class)
Friday, February 16. (ctd.)
Monday, February 19. MT pp. 66-71. (Examples of Induction.)
Wednesday, February 21. (Discussion of problems.)
Friday, February 23. MT pp. 80-83. (Bijections.)
Monday, February 26. First Midterm.
Wednesday, February 28. (no class)
Friday, March 2. [D'Angelo.] MT pp. 83-92. (Injections and surjections, Schroeder-Bernstein.)
Monday, March 5. [Ando]
Wednesday, March 7. [Ando]
Friday, March 9. [Ando] MT pp. 104-110. (Binomial Coefficients)
Monday, March 12. [D'Angelo] MT pp. 123-129. (Divisibility, gcd, Euclidean algorithm)
Wednesday, March 14. [Ando]
Friday, March 16. [Ando]
Monday, March 26. Review.
Wednesday, March 28. MT pp. 131-134. (Polynomials)
Friday, March 30. MT pp. 139-145. (Equivalence relations, congruence.)
Monday, April 2. MT pp. 145-147. (Chinese remainder theorem; Wilson's theorem)
Wednesday, April 4. MT pp. 147-149. (Fermat's little theorem)
Friday, April 6. MT pp. 160-162. (Irrational numbers)
Monday, April 9. MT pp. 157-160, 162-164. (Parameterization of unit circle, Pythagorean triples.)
Wednesday, April 11. MT pp. 255-258. (Completeness Axiom.)
Friday, April 13. MT pp. 258-263. (Limits)
Monday, April 16. Second midterm.
Wednesday, April 18. (Monotone Convergence theorem.)
Friday, April 20. (Monotone Convergence theorem, continued.)
Monday, April 23. MT pp. 271-275. (Properties of Convergent sequences.)
Wednesday, April 25. MT pp. 275-279. (Cauchy Sequences.)
Friday, April 27. (Cauchy Convergence Criterion.)
Monday, April 30. MT pp. 279-284. (Series.)
Wednesday, May 2. (Review.)

Tests

Midterm 1. Monday, February 26. Here is a practice exam, with solutions. Here are solutions for the exam itself.
Midterm 2. Monday, April 16. Here is a practice exam, with solutions. Here are solutions for the exam itself.
Final. Tuesday, May 8, at 7-10pm. Here is a study guide. Here is a practice exam with solutions.
Special office hours: Monday, May 7, at 3:00-5:00, and Tuesday, May 8, 2:30-5:00.

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 Friday, January 19.
PS 1. Due Monday, January 29. Solutions. MT 1.13, 1.29, 1.47, 2.4. And these:
1. Using only the order axioms for a field, prove that 0<x implies that 0 < x^-1.
2. Using only the order axioms for a field, prove that 0< x< y implies 0 < y^-1 < x^-1. (Note: some problems in MT have hints at the back of the book. For part (a) of 1.47, you may use the fact (which we haven't actually proved yet), that integers are either even or odd. In part (b) of 1.47, I don't want a proof, just a description of the answer. For the two problems about ordered fields, you can use any fact which follows from the field axioms withou explicitly refering to it. However, you must be explicit any time you use the ordered field axioms P1, P2, P3, or something which depends on them.)
WA 2. Due Wednesday, January 31.
WA 3. Due Wednesday, February 7.
PS 2. Due Friday, February 9. MT 2.2, 2.10, 2.52, 2.53, 3.23, 3.27. Solutions.
WA 4. Due Friday, February 14.
PS 3. Due Friday, February 23. MT 3.15, 3.16, 3.24, 3.26, 3.38, 3.43, 3.56, 3.62 Solutions.
PS 4. Due Friday, March 16. MT 4.22, 4.29, 4.34. MT 5.5, 5.9, 5.14, 5.31, 5.39. Solutions.
PS 5. Due Friday, March 30. MT 6.22, 6.28, 6.39, 6.56, 6.58. Solutions.
PS 6. Due Monday, April 9. MT 7.8, 7.18, 7.19, 7.21, 7.22, 7.35, 7.42. (For problem 7.21, replace "modular arithmetic" with "induction and properties of divisible".) (Note change in due date.) Solutions.
PS 7. Due Friday, April 13. MT 8.8, 8.23, 8.26, 8.30. Solutions.
PS 8. Due Monday, April 23. MT 13.8, 13.23, 13.25, 13.26, 13.28, 13.29, 13.30. Solutions.
PS 9. Due Wedensday, May 2. MT 14.4, 14.10, 14.13, 14.14, 14.19, 14.20, 14.29, 14.44. Solutions.

Contact info.

email:
office: Illini Hall 242
office hours: Check here.

Last modified 8 May 2007 by Charles Rezk.

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