Math 574

Lectures:

MWF 10:10-11:00 a.m. in LeConte 112

Contact Information:

Professor L. Székely
Office: LeConte 305
Office Hours: MWF 1:10-2:10 p.m., and by appointment
e-mail: szekely@math.sc.edu

Covered material and assigned homework:

• Aug 21 Section 1.1
• Aug 24 Section 1.1 HW: Deadline Aug 31 Section 1.1 problems 2,4,8,10,14,18,20,24,26,34
• Aug 26 Section 1.1, 1.2
• Aug 28 Section 1.2 HW Deadline Aug 31 Section 1.2 problems 4,8,12,14,32
• Aug 31 Section 1.2
• Sept 2 Section 1.3 HW Deadline Sept 9 Section 1.3 problems 2,and all even problems from 6-24
• Sept 4 Section 1.3 HW Deadline Sept 9 Section 1.3 all even problems from 28-36, 44,45,52
• Sept 9 Section 1.4 HW Deadline Sept 14 Section 1.4 all even problems from 1.4 2-14 and 26-34.
• Sept 11 Section 1.4, 1.5
• Sept 14 Section 1.5
• Sept 16 Section 1.5,1.6 HW Deadline Sept 21 1.5 2-8 even, 14,16,20,23,24; 1.6 2-20 even
• Sept 18 Section 1.6, 1.7
• Sept 21 Section 1.6, 1.7 HW Deadline Sept 28 1.6 22-34 even, 1.7 2-20 even.
• Sept 23 Section 1.7, review
• Sept 25 first test
• Sept 28 1.7, 2.1 HW Deadline Oct 5 2.1 2-30 even
• Sept 30 2.1, 2.2 HW Deadline Oct 5 2.2 2-30 even
• Oct 2 2.2,2.3
• Oct 5 2.3 HW Deadline Oct 12 2.3 2-20 even, 24,26,28,34,36,38,40,50,70,72
• Oct 7 2.3
• Oct 12 2.3
• Oct 14 4.1 HW: Deadline Oct 19 4.1 2-20 even
• Oct 16 4.1
• Oct 19 4.1
• Oct 21 4.2 HW: Deadline Oct 28 4.2 3,4,5,6,29,30,32
• Oct 23 review
• Oct 26 second test
• Oct 28 4.2,4.3
• Oct 30 5.1 HW: Deadline Nov 2 5.1 4,6,8,18,20,24,26,30,32,34,40
• Nov 2 5.1,5.3
• Nov 4 5.3 HW: Deadline Nov 9 5.3 2-12 even, 16,18,22,28,30,32
• Nov 6 5.3, 5.5 HW: Deadline Nov 9 5.5 2-16 even problems, 30
• Nov 9 5.5 HW: Deadline Nov 16 5.5 20,22,24,44,46
• Nov 11 5.4 HW: Deadline Nov 16 5.4 2-8 even problems, 12,14,20,28,38 and
• Nov 13 5.2 HW: Deadline Nov 16 5.2 2-8 even, 18,20,
• Nov 16 review HW: Deadline Nov 23 5.2 22,30,32,40; 5.4 14,15, 16 (note: there is a typo in the text of the problem! for part (a) the denominator is n+1, for part (b) the denominator is 2n+1), 30,38
• Nov 18 third test
• Nov 20 review, making make-up test choices
• Nov 23 make-up test
• Nov 30 counting surjections, Stirling numbers of the second kind
• Dec 2 inequality of arithemtic and geometric means
• Dec 4 Review

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". Work only on those graduate problems whose sections have been already worked through. 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
11. Section 5.4 ex. 30
12. Section 5.5 ex. 32
13. Section 5.5 ex. 38

Useful Links:

• Math 574 Syllabus: http://www.math.sc.edu/~szekely/mathFall574.pdf
• Solution to Section 1.2 ex. 12d: http://www.math.sc.edu/~szekely/1_2_12d.pdf
• Practice Test #1: http://www.math.sc.edu/~szekely/t5741proba.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 25.
• The dropdate is October 1.
• The second test has been scheduled to October 26 Monday. Topics covered: 1.6-7, 2.1-3, 4.1-2
• The third test has been scheduled to November 18 Wednesday.
• The make-up test has been scheduled to November 23 Monday.