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Description
MAT 2720 Discrete Mathematics
Spring 2012
Dr. Wai W. Lau
Dr. Lau
Wai
Dr. Wai W. Lau
Dr. Lau
Wai =
Dr. Wai W. Lau
Dr. Lau
Wai = =
Dr. Wai W. Lau
Dr. Lau
Wai = =
It is the “wai” in “Hawaii” and “Waikiki”
Course Web Page
http://myhome.spu.edu/lauw Link to this document and other course information
Office Hours
See course web page By Appointment
Prerequisites
MAT 1235 calculus II
What kind of people will pass this class?
Have good algebra background Work hard Do their homework as soon as possible
What kind of people will pass this class?
Follow Instructions on using
Do not skip steps
• Standard Notations • Presentation Formats
Calculators
No calculators will be allowed in all exams.
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)
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.
Objectives
The students are expected to cultivate active learning and the ability of communicating mathematical ideas. Use Standard Notations. Use good Presentation Formats.
Objectives
This course partially fulfill the Discrete Structure requirements (in Computer Science Body of Knowledge) recommended by ACM/IEEE Computing Curricula 2008.
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
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
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
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
DS5. Graphs and trees [core] Minimum core coverage time: 4 hours Topics: Trees Undirected graphs Directed graphs Spanning trees Traversal strategies
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
Exams
2 Mid-term Exams and a Final Exam.
Homework
You can choose to do your HW individually or in a team of two
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.
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.
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.
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.
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.
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.
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.
Class Participation
You are expected to come to class. There are classwork in some class sessions.
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.
Class Participation
Please respect your instructor and classmates. Do not talk during the lecture. Disruptive and disturbing behavior will not be tolerated.
Class Participation
No text messaging, web surfing, email sending,…… Turn off your phone before you enter the classroom***.
Class Participation
Annoying behaviors will reduce the maximum participation points that you can get.
Points Distribution Exam 1
80 points
Exam 2
80 points
Final
80 Points
Homework
40 Points
Class Participation
20 Points
Final Class Grade 90% 80% 70% 60% Below 60%
A Range B Range C Range D Range E
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).
Missing Classes
The instructor will not "re-teach" the lecture in any form including special appointments.
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.
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.
Help!!
Talk to me. I am available during office hours and other times.
Print Privilege
Open Computer Lab 253 M, T, W, Th:
7:30am - 9:30pm
F:
7:30am - 6:00pm
S:
8:00am - 5:00pm
Do not use the printer in this lab unless you have permission to do so.
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