Math 348 (Rezk, 9:00 MTWR, Section B1, 443 Altgeld).

Office hours

Syllabus

Errata for textbook

Reading

• Monday, January 14. Introduction. MT pp. 6-12. (Sets.)
• Tuesday, January 15. LaTeX. MT pp. 12-15. (Functions.)
• Wednesday, January 16. Proofreading. MT pp. 15-18. (The real numbers.)
• Thursday, January 17. MT pp. 15-18. (Fields; Ordered fields.)

• Tuesday, January 22. MT pp. 15-18. (Ordered fields.)
• Wednesday, January 23. MT pp. 4-6. (Elementary inequalities.)
• Thursday, January 24. MT pp. 27-31. (Quantifiers.)

• Monday, January 28. MT pp. 31-35. (Compound Statements.)
• Tuesday, January 29. MT pp. 35-44. (Methods of Proof.)
• Wednesday, January 30. MT pp. 51-57. (Principle of induction.)
• Thursday, January 31. MT pp. 51-57. (Principle of induction.)

• Monday, February 4. MT pp. 57- 62. (Applications of induction.)
• Tuesday, February 5. MT pp. 63-66. (Strong induction.)
• Wednesday, February 6. MT pp. 66-71. (Strong induction, continued.)
• Thursday, February 7. (More induction.)

• Monday, February 11. MT pp. 76-79. (Representation of natural numbers.)
• Tuesday, February 12. MT pp. 79-85. (Bijections, injections, surjections.)
• Wednesday, Feburary 13. MT. pp. 85-92. (Composition of functions; cardinality.)
• Thursday, February 14. (Cardinality continued.)

• Monday, February 18. MT pp. 91-92. (Schroeder-Bernstein Theorem.)
• Tuesday, February 19. MT pp. 101-104. (Arrangements and selections.)
• Wednesday, February 20. MT pp. 104-110. (Binomial Coefficents.)
• Thursday, February 21. (Binomial coefficients, continued.)

• Monday, Feburary 25. (Selection with repetition.)
• Tuesday, February 26. MT pp. 111-115. (Permutations.)
• Wednesday, February 27. First midterm.
• Thursday, February 28. (Permutations, continued.)

• Monday, March 3. MT pp. 123-129. (Divisibility.)
• Tuesday, March 4. MT pp. 131-134. (Divisibility for polynomials.)
• Wednesday, March 5. (Divisibility for polynomials, continued.)
• Thursday, March 6. (Divisibility for polynomials, and ideals, continued.)

• Monday, March 10. (Ideals, continued.)
• Tuesday, March 11. MT pp. 140-141. (Relations and equivalence relations.)
• Wednesday, March 12. MT pp. (Equivalence relations.)
• Thursday, March 13. MT pp. 142-145. (Congruence.)

• Monday, March 24. (Congruence, continued.)
• Tuesday, March 25. MT pp. 145-147. (Chinese Remainder Theorem.)
• Wednesday, March 26. MT pp. 147-149. (Fermat's Little Theorem.)
• Thursday, March 27. (Fermat's Little Theorem, continued.)

• Monday, March 30. MT pp. 256-258. (Completeness Axiom.)
• Tuesday, April 1. MT pp. 259-261. (Limits.)
• Wednesday, April 2. MT pp. 261-263. (Monotone Convergence.)
• Thursday, April 3. MT pp. 263-267. (Decimal expansion and uncountability.)

• Monday, April 7. (Decimal expansion, continued.)
• Tuesday, April 8. MT pp. 271-275. (Properties of convergent sequences.)
• Wednesday, April 9. MT pp. 276-279. (Cauchy sequences.)
• Thursday, April 10. (Cauchy sequences, continued.)

Tests

• Midterm 1. Wednesday, February 27. Here is a practice test (pdf), with solutions (pdf).
• Midterm 2. Thursday, April 17. Here is a practice test (pdf), with solutions (pdf). (Revised 4/14.)
• Final.

Homework

• WA 1 (pdf, tex). Draft due Wednesday, January 16. Final copy due Tuesday, January 22 (as .tex file).
• PS 1. Due Tuesday, January 22. MT 1.13, 1.45, 1.47, 1.50. (Note that this has changed.) Here are solutions (pdf, tex).
• WA 2. (pdf, tex). (Important typos fixed.) Draft due Thursday, January 24, in class. Final copy due Tuesday, January 29 (as .tex file).
• PS 2. Due Monday, January 28. 1.29, 2.4, 2.11, 2.24, 2.26. Here are solutions (pdf, tex).
• WA 3. If your last name starts with
  • D, E, G, H, J, or K, do problem 3.15.
  • M, P, or Ros, do problem 3.16.
  • Rot, S, or T, do problem 3.17.
  Draft due Thursday, January 31. .tex file due Tuesday, Feb 5.
• PS 3. Due Monday, February 4. 2.52, 2.53, 3.7, 3.23, 3.28. Here are solutions (pdf, tex).
• WA 4. Bring draft to class Thursday, February 7. If your last name starts with
  D, G, K, or R, do problem 3.65.
  • E, P, or S, do problem 3.62.
  • H, M, or T, do problem 3.63.
  • (These are all strong induction problems.)
• PS 4. Due Tuesday, February 12. 3.24, 3.38, 3.43, 3.47, 3.56. Here are solutions (pdf, tex).
• WA 5. Problem 4.21. Draft due in class Thursday, February 14.
• PS 5. Due Tuesday, February 19. 4.13, 4.20, 4.22, 4.25, 4.34. Here are solutions (pdf, tex).
• PS 6. Due Tuesday, February 26. 5.5, 5.9, 5.12, 5.14, 5.31, 5.39. Here are solutions (pdf, tex).
• PS 7. Due Tuesday, March 4. 5.57, 5.58, 6.22. Here are solutions (pdf, tex).
• PS 8. Due Tuesday, March 10. 6.17, 6.28, 6.43, 6.65. Note change in due date. Also note that 6.43 is stated incorrectly in at least some versions of the book: the incorrect version does not correctly compute the GCD. Use this revised version.
• WA 6. Draft due Thursday, March 13. Final version due Thursday, March 27. Instructions (revised; revised again 3/26) (pdf, tex).
• PS 9. Due Tuesday, April 1. 7.8, 7.15, 7.18, 7.32, 7.42. Here are solutions (pdf, tex).
• PS 10. Due Tuesday, April 8. 13.8, 13.21, 13.23, 13.25, 13.26. Here are solutions (pdf, tex).
• PS 11. Due Wednesday, April 16. 14.3, 14.4, 14.19, 14.23. Here are solutions (pdf, tex).
• PS 12. Due Tuesday, April 29. 14.15, 14.30, 15.3, 15.12. Here are solutions (pdf)

LaTeX.

All writing assignments are to be completed using LaTeX. Information on downloading and using LaTeX is given here.

Contact info.

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

Last modified 30 April 2008 by Charles Rezk.

Department of Mathematics College of Liberal Arts and Sciences University of Illinois at Urbana-Champaign 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576