# WELCOME

This is the homepage for MA 320: Foundations of Mathematics.

• First-day handout available here

### Preparing for Quizzes

Material for quizzes will usually come from assignments. You are responsible for all assigned material regardless of whether we have gone over it in class.

### Solutions to past quizzes and exams will be here (Click to download.)

• Solutions to Assignment 1 available here
• Solutions to Assignment 2 available here
• Solutions to Quiz 1 available here
• Solutions to Assignment 3 available here
• Solutions to Assignment 4 available here
• Solutions to Exam 1 available here
• Solutions to Quiz 2 available here
• Solutions to Quiz 3 available here
• Solutions to Quiz 4 available here
• Solutions to Exam 1 available here
• Solutions to Quiz 5 available here

### Assignments

Monday, August 20: Section 1.1, 1 -- 9.

Wednesday, August 22: Section 1.2, 13 -- 26.

Friday, August 24: Section 1.3, 29 -- 38, 40. Hand in the following three problems on Monday. (1) Section 1.2, problem 18 b). We did this in class. Here I want you to redo the problem, replacing OR with EOR (exclusive OR). Are the two statements still logically equivalent? Justify your answer; (2) Section 1.2, problem 26; (3) Challenge Question: Express AND in terms of OR and NOT. In other words, write P ∨ Q using only the symbols P, Q, ∧ and ¬ [HINTS: Remember that you can use any symbol more than once. Justify your answer with a truth table.] Write clearly and carefully.

Monday, August 27: Section 1.4, 42 -- 50, 51.

Friday, August 31: Section 1.5, 54 -- 66, 67, 71. Hand in the following two problems next Wednesday. (1) Section 1.3, problem 40. Think and write carefully; (2) Section 1.4, problem 49. First show this using truth tables. Now show it another way, without truth tables, using the logical equivalence of P ⇒ Q and Q ∨ ¬ P.

Wednesday, September 5: No new assignment. Complete any previous assignments in preparation for Friday's quiz.

Friday, September 7: Section 2.1, 1 -- 12, 13, 14. Hand in the following two problems next Wednesday. (1) problem 67 or 71 on page 22; (2) problem 13 or 14 on page 29.

Monday, September 10: Section 2.2, 17 -- 24. Also, problem 26 (model your proof on the one that I gave in class).

Wednesday, September 12: Section 2.3, 32 -- 43. Also 44 -- 53. Problem 53 is an excellent problem!

Friday, September 14: Section 2.4, 54 -- 63, 64, 65, 66, 68, 69. Hand in the following two problems next Wednesday. Remember to write careful explanations. Use complete sentences, not phrases. (1) problem 52 or 53 on page 39; (2) problem 65 on page 42.

Monday, September 17: Section 2.5, 71 -- 84.

Monday, September 24, Section 4.1, 1 -- 9.

Wednesday, September 26, Section 4.2, 18 -- 27 (two-day assignment).

Friday, September 31, Complete previous day's assignment.

Monday, October 1, Section 4.3, 36 -- 47.

Wednesday, October 3, Section 4.3, Problem 54. Use the hint that I gave in class. Hand in the following two problems on Friday. Remember to write careful explanations. Use complete sentences, not phrases. (1) problem 51 on page 92; (2) prove that the common log of 20 (that is, logarithm base 10 of 20) is irrational or else prove that the cube root of 4 is irrational. Your choice!

Friday, October 5, Section 4.5, 86 -- 91.

Wednesday, October 10, Section 5.1, 1 -- 11.

Friday, October 12, Section 5.2, 17 -- 28 (two-day assignment).

Monday, October 15, complete Friday's assignment.

Wednesday, October 17, Section 5.4, 51, 52.

Friday, October 19, Section 5.4, 53 -- 59.

Monday, October 22, Click here for mathematical induction problems given in class.

Wednesday, October 24, Section 5.5. 73 -- 76.

Friday, October 26, Section 5.5, 66 -- 70.

Monday, October 29, Section 6.1, 1 -- 14.

Wednesday, October 31, Section 6.2, 15 -- 29.

Wednesday, November 7, Hand in problems 30 and 33 on page 145 next Monday.

Monday, November 12, Section 6.3, 39 -- 51.

Wednesday, November 14, Finish Monday's assignment. The quiz on Friday will cover relations.

Friday, November 16, Section 6.4, 59 -- 63.

Monday, November 19, Section 6.4, 64 -- 74; Section 6.5, 79 -- 91.

The last written assignment (see November 7) may be revised and resubmitted on Monday. Find concise but convincing ways to make your arguments.

Monday, November 26, Section 7.1, 1 -- 8; Section 7.2, 17 -- 24.

Wednesday, November 28, Section 7.3, 31 -- 40.

Friday, November 30, Section 7.4, 51 -- 59.