# M 325 Discrete Mathematics Spring 04

INSTRUCTOR: Felipe Voloch (RLM 9.122, ph.471-2674,)

COURSE WEB PAGE: http://www.ma.utexas.edu/users/voloch/disc.html.

CLASS HOURS: MWF 10:00 -- 11:00 RLM 6.114

UNIQUE NUMBER: 55165

OFFICE HOURS: Tue 9:00 -- 11:00 or by appointment.

TEXTBOOK: Epp, Discrete Mathematics with Applications, second edition

TESTS: Midterms on March, 12 (Friday) and April, 26 (Monday). Final on May, 15 (Saturday) 9 to 12. No make-up midterms will be given (see "GRADES" below). First midterm with solutions. Second midterm with solutions.

HOMEWORK: I will assign homework on a weekly basis and it will be due at the beginning of the following week, unless otherwise stipulated. Selected problems (not all problems) will be graded. Homework must be neatly done and stapled if more than one page long. Late or sloppy homework will not be graded.

GRADES: Course grades will be given based on tests and homework as follows: Best midterm 30% + homework 20% + final exam 50% or both midterms (40% each) + homework 20%. The second option can only be selected by the student before the final, in which case the final will not be taken. Students missing a midterm automatically fall into the first option.

COURSE TOPICS: Fundamentals of logic: truth tables, symbolic logic, elementary set theory, laws of set theory, Venn diagrams.

Functions: relations, functions and their properties, Stirling numbers of the second kind, pigeonhole principle.

Relations: relation algebra, matrix representation of relations, directed graphs and relations, partial orders, Hasse diagrams, lattices, equivalence relations, partitions.

Introductory combinatorics: counting principles, permutations with and without repetitions, combinations and distributions.

Introductory graph theory: Euler paths and cycles, planar graphs, Hamilton paths and cycles.

## Homework assignments:

1. Section 1.1 exercises 2,10,13,18,32. Section 1.2 exercises 4,10,13,17,30.
2. Section 1.3 exercises 4,9,18,29,41. Section 2.1 exercises 3,17,30. Section 2.2 exercises 11,19. Due 2/9.
3. Section 2.3 exercises 4,19. Section 3.1 exercises 2,6,26,28. Section 3.2 exercises 7,8,17,24. Due 2/16.
4. Section 4.1 exercises 22,23. Section 4.2 exercises 11,13,17. Section 4.3 exercises 2,5,17. Due 2/23.
5. Section 4.4 exercises 3,4,8,10,13. Section 5.1 exercises 2,3,7,9,10. Due 3/1.
6. Section 5.2 exercises 4,11,12,14,19. Section 5.3 exercises 1,6,12,16,19. Due 3/8.
7. Section 6.1 exercises 11,18,21. Section 6.2 exercises 10,15,34,37. Section 6.3 exercises 10, 23. Due 3/31.
8. Section 6.4 exercises 5,7,16. Section 6.6 exercises 7,11,13. Section 6.7 exercises 4,5,8,16. Due 4/7.
9. Section 7.1 exercises 3,31. Section 7.3 exercises 4,5,9. Section 7.4 exercises 2,11,29. Section 7.5 exercises 5,16. Due 4/14.
10. Section 10.1 exercise 2. Section 10.2 exercises 13,20,28. Section 10.3 exercises 1,5,25. Section 10.5 exercises 7,19. Due 4/21.
11. Section 11.1 exercises 4, 17, 18. Section 11.2 exercises 2,9,15. Due 5/5.

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