MAT 2720 Discrete Mathematics

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MAT 2720Discrete Mathematics

• Spring 2012

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Dr. Wai W. Lau

• Dr. Lau
• Wai

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Dr. Wai W. Lau

• Dr. Lau
• Wai

Y
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Dr. Wai W. Lau

• Dr. Lau
• Wai

Y
Why?
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Dr. Wai W. Lau

• Dr. Lau
• Wai
• It is the wai in Hawaii and Waikiki

Y
Why?
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Course Web Page

• http//myhome.spu.edu/lauw
• Link to this document and other course
  information

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Office Hours

• See course web page
• By Appointment

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Prerequisites

• MAT 1235 calculus II

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What kind of people will pass this class?

• Have good algebra background
• Work hard
• Do their homework as soon as possible

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What kind of people will pass this class?

• Follow Instructions on using
• Standard Notations
• Presentation Formats
• Do not skip steps

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Calculators

• No calculators  will be allowed in all exams.

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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

• 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.

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Objectives

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

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Objectives

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

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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
• Counting arguments
• Sum and product rule
• Inclusion-exclusion principle
• Arithmetic and geometric progressions
• Fibonacci numbers
• The pigeonhole principle
• Permutations and combinations
• Basic definitions
• Pascals identity
• The binomial theorem
• Solving recurrence relations
• Common examples
• 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

• 2 Mid-term Exams and a Final Exam.

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Homework

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Class Participation

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

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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.

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Class Participation

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

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Class Participation

• No text messaging, web surfing, email sending,
• Turn off your phone before you enter the
  classroom.

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Class Participation

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

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Points Distribution
Exam 1 80 points
Exam 2 80 points
Final 80 Points
Homework 40 Points
Class Participation 20 Points
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Final Class Grade
90 A Range
80 B Range
70 C Range
60 D Range
Below 60 E
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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).

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Missing Classes

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

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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. 

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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.

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Help!!

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

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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        730am - 930pm F            
            730am - 600pm S                    
    800am - 500pm