Math 574

Discrete Mathematics
Section 001
University of South Carolina
Fall 2008

Lectures:

LeConte

Contact Information:

LeConte

szekely@math.sc.edu

Covered material and assigned homework:

Aug 22 Section 1.1
Aug 25 Section 1.1 HW: Deadline Sept 3. Section 1.1 problems 2,4,8,10,14,18,20,24,26,34
Aug 27 Section 1.2 HW: Deadline Sept 3. Section 1.2 problems 8,14,20,32,34,40
Aug 29 Section 1.2
Sept 3 Section 1.3 HW: Deadline Sept 10 Wed. Section 1.3 problems 6,8,10,12,14,16,20,34,36,38
Sept 5 Section 1.4 HW: Deadline Sept 10 Wed. Section 1.4 problems 2,8,10,12,24,26,28
Sept 8 Section 1.5 HW: Deadline Sept 17 Wed. Section 1.5 problems 4,8,10,16,20,24
Sept 10 Section 1.6 HW: Deadline Sept 17 Wed. Section 1.6 problems 6,8,10,12,14,20,22
Sept 12 Section 1.6, 1.7 HW: see above
Sept 15 Section 1.6, 1.7 HW: see above
Sept 17 Section 1.6, 1.7 HW: Deadline Sept 24 Wed. Section 1.7 problems 4, 8, 10, 12, 14, 18, 20, 34, 40,
Sept 19 Review HW: see above
Sept 22 first test HW: see above
Sept 24 Section 2.1, HW: Deadline Oct. 1 Wed. Section 2.1 problems 2ab,4,6,8,10,12,18,20,22,34
Sept 26 Section 2.2, HW: Deadline Oct. 1 Wed. Section 2.2 problems 2,4,16,28,30
Sept 29 Section 2.2,2.3
Oct 1 Section 2.3, HW: Deadline Oct. 8 Wed. Section 2.3 problems 2,4ab, 6abd, 10, 12, 14, 16, 26, 28, 34, 36, 38, 40, 70
Oct 3 Section 2.3, HW: see above.
Oct 5 Section 4.1 and 4.2 HW: see above.
Oct 8 Section 4.1 and 4.2 HW: 4.1 4, 6, 8, 10, 18, 20, 32, 40, 48. Deadline Oct 15 Wed
Oct 13 Section 4.1 and 4.2 HW: see above
Oct 15 Section 4.2 HW: 4.2 4, 6, 10, 12, 26, 30, 32 Deadline Oct 22 Wed
Oct 17 Section 5.1 HW: 5.1 2, 4, 6, 8, 18, 20, 24, 26, 30, 40 Deadline Oct 22 Wed
Oct 20 Section 5.1 HW: 5.1 2, 4, 6, 8, 18, 20, 24, 26, 30, 40 Deadline Oct 22 Wed
Oct 22 Section 5.1 HW: 5.1 10, 12, 14, 16, 28, 32, 34, 38, 42, 48, (definition needed: a bit string is a word over the two-letter alphabet consisting of 0 and 1) Deadline Oct 29 Wed
Oct 24 second test HW: see above Deadline Oct 29 Wed
Oct 27 Section 5.3 HW: 5.3 4,12,14,16,18, 20,22,24,28,32,34,40 Deadline Nov 5 Wed
Oct 29 Section 5.3 HW: 5.3 see above Deadline Nov 5 Wed
Oct 31 Section 5.4 HW: 5.4 2,4,8,14,16,20,38 Deadline Nov 5 Wed
Nov 3 Section 5.4, 5.5 HW: see above Deadline Nov 5 Wed
Nov 5 Section 5.5 HW: 5.5 problems 2,4,6,8,10,12,14,16,18,20 Deadline Nov 12 Wed
Nov 7 Section 5.5 HW: 5.5 problems 24,30,38,40,46,50,52,54 Deadline Nov 12 Wed
Nov 10 Section 5.5 HW: see above
Nov 12 Section 5.5, 5.2 HW: Nov 19 Section 5.2 2,4,6,8,14,16,18
Nov 14 review
Nov 17 third test HOMEWORK DEADLINE EXTENDED TO NOV 21 FRIDAY!
Nov 19 Section 5.2, HW see above, deadline Nov 21
Nov 21 Section 5.2
Nov 24 Make-up test

Requirements and extra homework for graduate students:

Graduate requirement: correct solution to 5 graduate problems below. There is no deadline for them. Do not mix them with other homework, give them me marked "graduate homework". An alternative way to satisfy the graduate requirement is to write a 10-pages informative essay on the history of discrete mathematics. Undergraduate students may get extra credit for solving graduate problems, but not for essay writing.

1. Show that the connective "not (p or q)" can express negation, conjunction and disjunction.

2. Section 2.1 ex. 38

3. Section 2.2 ex. 40

4. Section 4.1 ex. 26

5. Section 4.1 ex. 30

6. Section 4.1 ex. 36

7. Section 2.2 ex. 58

8. Section 2.3 ex. 30

9. Section 2.3 ex. 31

10. Section 5.4 ex. 10

10. Section 5.4 ex. 30

Useful Links:

Math 574 Syllabus: http://www.math.sc.edu/~szekely/math574.pdf
Practice Test #1: http://www.math.sc.edu/~szekely/vt5741proba.pdf
Practice Test #2: http://www.math.sc.edu/~szekely/t5742proba.pdf
Practice Test #3: http://www.math.sc.edu/~szekely/t5743proba.pdf

Notes:

The first test has been scheduled to September 22 Monday. Logic and proofs will be covered. The second test has been scheduled to October 24 Friday. Proofs, induction, sets, functions and some counting will be covered. The third test has been scheduled to November 17 Monday. The make-up test is scheduled to November 24 Monday.