## Discrete Mathematics

Instructor: Thomas Hull, Mendel 256, x4334, thull@merrimack.edu

Text: An Introduction to Discrete Mathematics, 3rd Edition, by Michael J. Bradley, McGraw Hill (Primis Custom Publishing), 2000.

Description: This course will expose you to a variety of topics in discrete mathematics. Of particular importance are topics relevant to further study in computer science and mathematics, including logic and proofs.

Prerequisites: You will need a mind that is imaginative, creative, disciplined, and open to new ideas in mathematics. A mastery of high school algebra is also required, as is a willingness to read the text and to work each week on this course. Occasional silliness will be tolerated.

Course Outline: We'll be covering every chapter in the book!

1. Introduction (15 minutes)

2. Symbolic Logic: simple and compound statements, and, or, not, truth tables, equivalent statements, tautologies and contradictions, Boolean algebra, Venn diagrams, circuit diagrams. (2.5 weeks)

3. Proof Techniques: direct proof, dis-proof by counterexample, proof by contrapositive, proof by mathematical induction. (2.5 weeks)

4. Relations: representing relations by sets of ordered pairs, by graphs, by adjacency matrices; reflexive, symmetric, transitive, irreflexive, and antisymmetric properties; partial orderings; Hasse diagrams; equivalence relations; modular arithmetic; matrix stuff. (2.5 weeks)

5. Trees and Graphs: binary search trees - creating and using searches; traversal algorithms for binary trees - preorder, postorder, inorder, levelorder; minimal spanning trees - Prim's and Kruskal's greedy algorithms. (2.5 weeks)

6. Probability: sample points, counting techniques, mn rule, equiprobable sample points, probabilities with and without repetition, sampling with and without replacement, factorials, combinations, hypergeometric and binomial random variables, conditional probabilities using tree diagrams. (2 weeks)

Grading and exams: There will be 4 tests and a cumulative final (worth 2 test grades). No makeups unless you are dying. In addition, 25% of your grade will be based on assigned homework problems.

Schedule:
Thur Feb. 7 Test #1 on Chapter 2
Thr Feb. 28 Test #2 on Chapter 3
Tu Mar. 26 Test #3 on Chapter 4
Tu Apr. 16 Test #4 on Chapter 5

Final Exams:
Section D Friday, May 10, 1:30pm
Section E Minday, May 6, 1:30pm

Please come by and see me if you have any questions! Or if anything happens to you that makes this course difficult, or if you're having any trouble, or if you just want to gripe, feel free to stop by. Except for when I'm teaching and lunchtime, I'm usually in my office.

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