MAT 2720 Discrete Mathematics

1. MAT 2720Discrete Mathematics Spring 2012

2. Dr. Wai W. Lau • Dr. Lau • Wai

3. Dr. Wai W. Lau • Dr. Lau • Wai = Y

4. Dr. Wai W. Lau • Dr. Lau • Wai = = Y Why?

5. Dr. Wai W. Lau • Dr. Lau • Wai = = • It is the “wai” in “Hawaii” and “Waikiki” Y Why?

6. Course Web Page http://myhome.spu.edu/lauw Link to this document and other course information

7. Office Hours • See course web page • By Appointment

8. Prerequisites • MAT 1235 calculus II

9. What kind of people will pass this class? • Have good algebra background • Work hard • Do their homework as soon as possible

10. What kind of people will pass this class? • Follow Instructions on using • Standard Notations • Presentation Formats • Do not skip steps

11. Calculators • No calculators  will be allowed in all exams.

12. Texts • Johnsonbaugh, Discrete Mathematics, 7th ed. (ISBN 0131593188, $108 at Amazon) • e-book version available at http://www.coursesmart.com/9780132082853 (180 days, $55.99)

13. Objectives • This course is an introduction to the concepts of discrete mathematics.  • One of the main goals is to extend students' mathematical maturity and ability to deal with abstraction. • This course serves as a stepping stone to advanced courses in mathematics and computing sciences.

14. Objectives • The students are expected to cultivate active learning and the ability of communicating  mathematical ideas. • Use Standard Notations. • Use good Presentation Formats.

15. Objectives • This course partially fulfill the Discrete Structure requirements (in Computer Science Body of Knowledge) recommended by ACM/IEEE Computing Curricula 2008.

16. DS1. Functions, relations, and sets [core] • Minimum core coverage time: 6 hours Topics: • Functions (surjections, injections, inverses, composition) • Relations (reflexivity, symmetry, transitivity, equivalence relations) • Sets (Venn diagrams, complements, Cartesian products, power sets) • Pigeonhole principle • Cardinality and countability

17. DS2. Basic logic [core] • Minimum core coverage time: 10 hours Topics: (Logic System Design) • Propositional logic • Logical connectives • Truth tables • Normal forms (conjunctive and disjunctive) • Validity • Predicate logic • Universal and existential quantification • Modus ponens and modus tollens • Limitations of predicate logic

18. DS3. Proof techniques [core] • Minimum core coverage time: 12 hours Topics: • Notions of implication, converse, inverse, contrapositive, negation, and contradiction • The structure of formal proofs • Direct proofs • Proof by counterexample • Proof by contraposition • Proof by contradiction • Mathematical induction • Strong induction • Recursive mathematical definitions • Well orderings

19. DS4. Basics of counting [core] • Minimum core coverage time: 5 hours Topics: • Counting arguments • – Sum and product rule • – Inclusion-exclusion principle • – Arithmetic and geometric progressions • – Fibonacci numbers • The pigeonhole principle • Permutations and combinations • – Basic definitions • – Pascal’s identity • – The binomial theorem • Solving recurrence relations • – Common examples • – The Master theorem

20. DS5. Graphs and trees [core] • Minimum core coverage time: 4 hours Topics: • Trees • Undirected graphs • Directed graphs • Spanning trees • Traversal strategies

21. DS6. Discrete probability [core] • Minimum core coverage time: 6 hours Topics: (Probability Theory) • Finite probability space, probability measure, events • Conditional probability, independence, Bayes’ theorem • Integer random variables, expectation

22. Exams • 2 Mid-term Exams and a Final Exam.

23. Homework • You can choose to do your HW individually or in a team of two

24. Team Approach • You can work with at most one classmate on the HW. • Turn in one paper for each team. • Team paper need to be typed in MS WORD with proper format.

25. Team Approach • You need to state clearly on the front page the percentage of contributions of each team member. • This approach is intended for you to have discussions over the HW. • Do not take turn to do HW.

26. Individual Approach • Your homework must be neat and easy to read. Otherwise, no points will be given. Sloppy handwriting will not be tolerated. • You will get bonus points at the end of the quarter if most of your papers are typed.

27. Homework • You are not allowed to discuss your HW with anyone (except your team parnter and the instructor).  • Discussing or copying homework is considered as an act of academic dishonesty. • Your only references are the textbook and lecture notes. Do not use other references such as books, WIKI, and other web resources.

28. Homework • You must show all of your work − a correct answer with no justification will also be worth NO credit. • When explanations are called for on the homework, you should respond in complete sentences with proper grammar, spelling, and punctuation.

29. Homework • Staple your Homework. Points will be taken off if you fail to do so. • Homework is due at the beginning of the class. Absolutely no late homework. • Excuses such “the printer is not working” will not be accepted.

30. Reading Assignment • You are required to read the textbook before class everyday. I will ask questions during the class period to check your reading progress.

31. Class Participation • You are expected to come to class. • There are classwork in some class sessions.

32. Class Participation • At the end of the quarter, your grades on class participation will be determined by the above activities and other observations by the instructor.

33. Class Participation • Please respect your instructor and classmates. • Do not talk during the lecture. • Disruptive and disturbing behavior will not be tolerated.

34. Class Participation • No text messaging, web surfing, email sending,…… • Turn off your phone before you enter the classroom***.

35. Class Participation • Annoying behaviors will reduce the maximum participation points that you can get.

36. Points Distribution

37. Final Class Grade

38. Missing Classes • You are responsible to catch up all the materials if you miss classes for whatever reasons (sickness, family issues, family Hawaii vacation, alien abduction etc).

39. Missing Classes • The instructor will not "re-teach" the lecture in any form including special appointments.

40. Make-Up Policies • If a student has a  documented conflict that will prevent him or her from taking an exam at the scheduled time, he/she must arrange IN ADVANCE with the instructor to take the exam early. 

41. Make-Up Policies • Makeups are NOT AUTOMATIC. • Do NOT assume that because you miss an exam that you will get to make it up. A makeup exam must be APPROVED by me. Lying to avoid taking an exam is considered as an act of academic dishonesty.

42. Help!! • Talk to me. I am available during office hours and other times.

43. Print Privilege • Open Computer Lab 253 • Do not use the printer in this lab unless you have permission to do so. M, T, W, Th:        7:30am - 9:30pm F:                        7:30am - 6:00pm S:                        8:00am - 5:00pm