MAT 2720
Discrete Mathematics
Spring 2012
Dr. Wai W. Lau
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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
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See course web page
By Appointment
Prerequisites
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MAT 1235 calculus II
What kind of people will pass
this class?
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Have good algebra background
Work hard
Do their homework as soon as possible
What kind of people will pass
this class?
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Follow Instructions on using
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Do not skip steps
• Standard Notations
• Presentation Formats
Calculators
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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)
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Objectives
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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
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The students are expected to cultivate
active learning and the ability of
communicating mathematical ideas.
Use Standard Notations.
Use good Presentation Formats.
Objectives
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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
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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
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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
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DS4. Basics of counting [core]
Minimum core coverage time: 5 hours
Topics:
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Counting arguments
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– Sum and product rule
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– Inclusion-exclusion principle
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– Arithmetic and geometric progressions
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– Fibonacci numbers
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The pigeonhole principle
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Permutations and combinations
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– Basic definitions
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– Pascal’s identity
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– The binomial theorem
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Solving recurrence relations
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– Common examples
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– The Master theorem
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DS5. Graphs and trees [core]
Minimum core coverage time: 4 hours
Topics:
 Trees
 Undirected graphs
 Directed graphs
 Spanning trees
 Traversal strategies
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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
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Exams
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2 Mid-term Exams and a Final Exam.
Homework
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You can choose to do your HW
individually or in a team of two
Team Approach
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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
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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
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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
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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
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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
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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
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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
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You are expected to come to class.
There are classwork in some class
sessions.
Class Participation
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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
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Please respect your instructor and classmates.
Do not talk during the lecture.
Disruptive and disturbing behavior will not be
tolerated.
Class Participation
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No text messaging,
web surfing, email
sending,……
Turn off your phone
before you enter the
classroom***.
Class Participation
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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
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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
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The instructor will not "re-teach" the
lecture in any form including special
appointments.
Make-Up Policies
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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
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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!!
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Talk to me. I am available during office
hours and other times.
Print Privilege
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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.