MA 330-01, Foundations of Mathematics, Spring 2008

Course Description and Goals

This is a basic course on the foundations of mathematics, primarily intended for students in mathematics, science, engineering, and philosophy. Topics include

• symbolic logic and the algebra of logical operations, including conjunction, disjunction, negation, implication and equivalence
• methods of proof, including direct proof, counterexamples, and mathematical induction
• sets and the algebra of set operations, including union, intersection, complement, and Cartesian product
• abstract functions
• equivalence relations and their properties
• partial order relations and their properties
• cardinality, including finite sets, countably infinite sets, and uncountable sets

Course goals include

• an improved ability to think abstractly, and in particular, a basic understanding of mathematical structures defined axiomatically
• the ability to construct careful, correct, succinct proofs of simple theorems
• the ability to recognize fallacious arguments and logical flaws
• an improved understanding of the interplay between conjecture, example, counterexample, and proof
• a basic understanding of the central role of sets, functions, and relations in mathematics
• an improved ability to read, write, speak, and think in mathematical terms

Prerequisites

• MA 172, Calculus B
• one MA course at the 200 level or above

Credit

• 3 Semester Hours

Course Materials

• Introduction to Advanced Mathematics second edition, by William Barnier and Norman Feldman, published by Prentice Hall, 1990.
• Class website: http://www.math.uah.edu/siegrist/teaching/2008Spring/MA330/index.html

Text syllabus

• Chapter 1. Introduction to Logic
• Chapter 2. Methods of Proof
• Chapter 3. Set Theory
• Chapter 4. Cartesian Products and Functions
• Chapter 5. Relations
• Chapter 6. Cardinality

Instructor Information

• Instructor: Kyle Siegrist
• Office: 258K Shelby Center
• Voice: 824-6486
• Fax: 824-6173
• E-mail: siegrist@math.uah.edu

Class Schedule

• Monday, Wednesday, Friday 11:30 - 12:25
• 205 Shelby Center

Office Hours

• Monday, 10:15 - 11:15
• Tuesday, 2:15 - 3:45
• Wednesday, 10:15 - 11:15
• Thursday, 2:15 - 3:45
• Friday, 10:15 - 11:15

Grade Determination

• Quizzes and homework: 1/6
• Three class tests 1/2
• Final Exam: 1/3

Test Schedule

• Test 1: Friday, February 1
• Test 2: Friday, February 29
• Test 3: Friday, April 4
• Final Exam: Monday, April 28, 11:30 - 2:00

Grading Scale (%)

1. 90-100
2. 80-89
3. 70-79
4. 60-69
6. 0-59

Policies

• No make-up tests or quizzes will be given except for documented cases of illness or emergency.
• Consult the Student Handbook for information about the grievance procedure, accommodations for students with disabilities, or academic misconduct.

Quizzes and Tests

Note: The quizzes and tests are written in the Mathematics Markup Language (MathML). You will need Mozilla Firefox (version 2.0 or later), with the MathML fonts installed, to properly view the quizzes and tests.

Quizzes

1. Quiz 1
2. Quiz 2
3. Quiz 3
4. Quiz 4
5. Quiz 5
6. Quiz 6
7. Quiz 7
8. Quiz 8
9. Quiz 9
10. Quiz 10
11. Quiz 11
12. Quiz 12
13. Quiz 13
14. Quiz 14
15. Quiz 15
16. Quiz 16
17. Quiz 17
18. Quiz 18
19. Quiz 19
20. Quiz 20
21. Quiz 21
22. Quiz 22
23. Quiz 23
24. Quiz 24
25. Quiz 25
26. Quiz 26

Tests

1. Test 1
2. Test 2
3. Test 3

Assignments

Week 1

• Monday, January 7. Read Section 1.1 and work problems 1-21, odd.
• Wednesday, January 9. Read Section 1.2 and work problems 1-10, 15, 17, 19
• Friday, January 11. Read Section 1.3 and work problems 1-7, 9, 11, 13, 17, 18.

Week 2

• Monday, January 14. Continue with the assignment in Section 1.3. Work Chapter 1 supplementary problems 5-8, 9, 11.
• Wednesday, January 16. Read Section 2.1 and work problems 1 - 9 odd, 15, 17, 19.
• Friday, January 18. Read Section 2.2 and work problems 1, 3, 7, 9, 11-15.

Week 3

• Monday, January 21. No class
• Wednesday, January 23. Read Section 2.3 and work problems 1, 3, 7, 9, 11, 17, 19, 21, 23.
• Friday, January 25. Read Section 2.4 and work problems 1-15 odd, 19, 21, 23.

Week 4

• Monday, January 28. Read Section 2.5 and work problems 1-21 odd.
• Wednesday, January 30. Study for Test 1 on Friday, over chapters 1 and 2.
• Friday, February 1. Read Section 3.1 and work problems 1-19 odd, 23, 25

Week 5

• Monday, February 4. Read Section 3.2 and work problems 1-19 odd.
• Wednesday, February 6. Read Section 3.3 and work problems 1-17 odd.
• Friday, February 8. Read Section 3.4 and work problems 1-21 odd, 16.

Week 6

• Monday, February 11. Continue with the assignment in Section 3.4.
• Wednesday, February 13. Read Section 4.1 and work problems 1-21 odd.
• Friday, February 15. Read Section 4.2 and work problems 1-23 odd.

Week 7

• Monday, February 18. Read Section 4.3 and work problems 1-13 odd, 15-23.
• Wednesday, February 20. Continue with the assignment in Section 4.3.
• Friday, February 22. Read Section 4.4 and work problems 1-19 odd.

Week 8

• Monday, February 25. Continue with the assignment in Section 4.4.
• Wednesday, February 27. Study for Test 2 on Chapters 3 and 4.
• Friday, February 29. Read Section 5.1 and work problems 1-31 odd.

Week 9

• Monday, March 3. Continue with the assignment in Section 5.1.
• Wednesday, March 5. Read Section 5.2 and work problems 1-21 odd, 12.
• Friday, March 7. Continue the assignment in Section 5.2.

Week 10

• Monday, March 10. Read Section 5.3 and work problems 1-11 odd, 13-18, 19, 21, 23, 24.
• Wednesday, March 12. Continue with the assignment in Section 5.3
• Friday, March 14. Continue with the assignment in Section 5.3. Have a nice spring break.

Week 11, Spring Break

• Monday, March 17. No class
• Wednesday, March 19. No class
• Friday, March 21. No class

Week 12

• Monday, March 24. Continue with the assignment in Section 5.3.
• Wednesday, March 26. Read Section 6.1 and work problems 1, 3, 5-9, 11, 13, 17, 19, 30
• Friday, March 28. Continue with Section 6.1 and problems 1, 3, 5-9, 11, 13, 17, 19, 23, 25, 27, 30, 31.

Week 13

• Monday, March 31. Continue with Section 6.1.
• Wednesday, April 2. Study for Test 3 over Chapter 5 and Section 6.1 on Friday.
• Friday, April 4. Read Section 6.2 and work problems 1-15 odd, 16-22

Week 14

• Monday, April 7. Continue with the assignment in Section 6.2
• Wednesday, April 9. Continue with the assignment in Section 6.2. Read 6.3
• Friday, April 11. Continue with the assignments in Section 6.2, 6.3.

Week 15

• Monday, April 14. Continue with the assignments in Sections 6.2, 6.3.
• Wednesday, April 16. Continue with the assignments in Chapter 6.
• Friday, April 18. Study for the final exam on Monday, April 28, 11:30 - 2:00