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MAT 2720 Discrete Mathematics Spring 2012. Dr. Wai W. Lau Dr. Lau Wai.

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Presentation on theme: "MAT 2720 Discrete Mathematics Spring 2012. Dr. Wai W. Lau Dr. Lau Wai."— Presentation transcript:

1 MAT 2720 Discrete Mathematics Spring 2012

2 Dr. Wai W. Lau Dr. Lau Wai

3 Dr. Wai W. Lau Dr. Lau Wai =

4 Dr. Wai W. Lau Dr. Lau Wai = =

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

6 Course Web Page 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 (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 Exam 180 points Exam 280 points Final80 Points Homework40 Points Class Participation20 Points

37 Final Class Grade 90%A Range 80%B Range 70%C Range 60%D Range Below 60%E

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

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