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					                           Capital University of Economics and Business
                                    Overseas Chinese College


Semester and Year             Spring Semester

                              From Mar.3 2008 to July 13 2008

Course Name                   Discrete Math

Course Number                 IT222

Course Credits                4

Instructor                    Xiaoting Zhao

Contact Information           Office Room: C115, Telephone: 51428064

Office Hour                   MTF: 11:00~12:00 am T: 1:00~3:00 pm TH: 4:00~5:00 pm

Leaning Center                TH: 1:00~3:00 pm 6:00~8:00 pm

Time/Place                   Y01 MTTHF 9:00~9:50 Room: A-206

                              Y02 MTTHF 10:00~10:50 Room: A-206

                              Y03 M-TH 3:10~4:00 Room: A-202
Course Description

Discrete mathematics is the gateway to more advanced courses in all parts of the mathematical science.
Discrete mathematics provides the mathematical foundation for many computer science courses,
including data structures, algorithms, data theory, automata theory, formal language, compiler theory,
computer security, and operating systems. Math number theory, linear algebra, abstract algebra,
combinatory, graph theory and probability theory. Also discrete mathematics contains the necessary
mathematical background for solving problems in operations research (including many discrete
optimization techniques), chemistry, engineering, biology, and so on. In the text, the application to some
of these areas will be studied.

Student learning objectives

A discrete mathematics course has more than one purpose. Students should learn a particular set of
mathematical facts and how to apply them; more importantly, such a course should teach students how to
think mathematically. To achieve these goals, this text stresses mathematical reasoning and the different
ways problems are solved. Five important themes are interwoven in this text: mathematical reasoning,

                            Capital University of Economics and Business
                                     Overseas Chinese College

combinatorial analysis, discrete structures, algorithmic thinking, and applications and modeling. A
successful discrete mathematics course should carefully blend and balance all five themes.


Kenneth H. Rosen Discrete Mathematics and Its Applications (Sixth Edition). ISBN: 7 – 111 – 11503 – 1

Reference materials:

Discrete Mathematics and Its Applications ISBN: 7 – 111 – 07577-3/TP

Library Source

Students can find reference books in the library or related materials on the Internet.
Pre-requisite: MATH 102

Teaching methods

This course consists of lectures, discussions and student presentations. Students must be prepared to
finish some small questions and small quiz during the class.

Grade criterion:

Component             Weight      Description

Final Exam            20%         A cumulative final examination will be given based on all of the
                                  contents of the class
Mid-Term Exam         20%         A cumulative mid term examination will be given based on all
                                  of the contents of the first half of the class.
Homework              20%         Homework problems will be assigned throughout the term,
                                  including but not limited to: terminologies, research project, and
                                  reading assignments.
Quiz                  10%         There will be several times quizzes during the semester. The
                                  purpose of the quizzes is to ensure that students keep up with
                                  the readings.
Participation         10%         Individuals will be asked to participate individually in questions
                                  during the semester. Students are required to meet with their
                                  teachers every week. Their performances should be counted in
                                  their participation.
Presentation          10%         Refer to the handouts.
Attendance            10%         Refer to attendance policy listed below.
Total                 100%

Detailed Grade computation

                          Capital University of Economics and Business
                                   Overseas Chinese College

In a semester, the grade of attendance, participation, assignment/homework, and quiz accounts 60 percent
in final grade, the midterm exam and final exam accounts 20 percent in final grade, respectively. 40
percent before midterm, and 60 percent after midterm. That is shown as in the following table:

                                    Before midterm                      After midterm
Attendance                          5%                                  5%
Participation                       5%                                  5%
Homework/assignment                 5%                                  15%
Quiz                                5%                                  5%
Midterm exam                        20%
Final exam                                                              20%
Presentation                                                            10%
Total                               40%                                 60%

Grading Policy

A       100-95    A-     94-90      B+      89–87        B   86-83     B-      82-80 C+          79–77
C       76–73      C-    72-70       D+     69–67        D   66–63      D-      62-60       F 59-0

Quiz/Exam Schedule          Midterm Exam:       May 4 – 9 May. 2008 Final Exam: 7 – 13 July 2008
                            4 July is the deadline for dropping this course with “withdrawal”
                            After completing each chapter, there is a quiz. The quiz time
                            is decided by instructors.

The homework of one class must be submitted before next class. Holiday assignment must be submitted
on the first class after school reopens. No late homework is acceptable. All students should hand in
homework and assignment with hard copies .The score of assignment is determined by the accuracy and
relevance. If students have English problems reading textbook or writing report, they should ask the
teachers in the Learning Center.


Being late for 15 minutes will result in unexcused absence. Each unexcused absence will result in 10%
reduction of attendance grade. Five hours of unexcused absences will result in the lowering of grade by
one level, i.e. A to A-. 12 hours (20% of total class hours) of absences under any circumstances forces a
withdrawal from the course and get a grade of “F”. An excused absence must be discussed directly with
the teacher. An incomplete grade (I) will be considered in case of medical or family emergencies.

                           Capital University of Economics and Business
                                    Overseas Chinese College


Students should participate in classes actively. Half of participation grade is determined by their
presentation in class. They are encouraged to ask questions relevant to the subject and express their own
opinions. Every student should respect the ideas, opinions, and questions of their classmates. Students
should also use office hour to ask questions or talk with the instructor for good communication and
effective learning. Any misbehavior and non-class related activities in class will result in the lowering of
the participation grade, including ringing beepers and cell phones. All above behaviors will be solely
evaluated by the instructor for scoring.

Topical Course Outline

Week Index                 Content
                           1.1 Logic
   Week 1 (Mar.3~7)
                           1.2 Propositional Equivalences
                           1.3 Predicates and Quantifiers
                           1.4 Nested Quantifiers
                           1.5 Methods of Proof
 Week 2 (Mar.10~14)
                           1.5 Methods of Proof
                           1.6 Sets
                           1.7 Set Operations
                           1.8 Functions
 Week 3 (Mar.17~21)
                           10.1 Boolean Functions
                           10.2 Representing Boolean Functions
                           10.3 Logic Gates
 Week 4 (Mar.24~28)
                           10.4 Minimization of Circuits
                           10.4 Minimization of Circuits
Week 5 (Mar.31~Apr.4)
                           2.1 Algorithms
                           2.2 The Growth of Functions
                           2.3 Complexity of Algorithms
                           2.4 The Integers and Division
  Week 6 (Apr.7~11)
                           2.5 Integers and Algorithms
                           2.7 Matirces
                           3.1 Proof Strategy
 Week 7 (Apr.14~18)
                           3.2 Sequences and Summations
                           3.3 Mathematical Induction
                           3.4 Recursive Definition and Structural Induction
  Week 8(Apr.21~25)
                           4.1 The Basics of Counting
                           4.2 The Pigeonhole Principle
     Week 9 (Apr.          Exercises
      28~May2)             Exercises

                           Capital University of Economics and Business
                                    Overseas Chinese College


  Week 10 (May 4~9)
                                                        Mid-term Exam

                           4.3 Permutations and Combinations
                           4.4 Binomial Coefficients
 Week11 (May 12~16)
                           5.1 An Introduction to Discrete Probability
                           6.1 Recurrence Relations
                           6.5 Inclusion-Exclusion
 Week 12(May19~23)
                           7.1 Relations and Their Properties
                           7.3 Representing Relations
                           7.5 Equivalence Relations
 Week13 (May 26~30)        7.6 Partial Orderings
                           8.1 Introduction to Graph
                           8.2 Graph Terminology
                           8.3 Representing Graphs and Graph Isomorphism
  Week 14 (Jun.2~6)        8.4 Connectivity
                           8.5 Euler and Hamilton Paths
  Week 15 (Jun.9~13)       Quiz
                           9.1 Introduction to Trees
                           9.2 Application of trees
                           9.3 Tree Traversal
 Week 16 (Jun.16~20)       9.4 Spanning Trees
                           9.5 Minimum Spanning Trees
 Week 17 (Jun.23~27)       Exercises

Week 18 (Jun.30~Jul.4)                                    Presentation

  Week 19 (Jul.7~13)                                    Final-term exam

Teacher’s Office Hour
The instructor’s office hour is shown in the front of the office door. Students are required to use the
instructor’s office hour to ask questions or talk with the instructor once at least per week for good
communication and effective learning, which is recorded in the students’ participation. The time can be
scheduled by instructors or students, or both.

Withdrawal Policy

                           Capital University of Economics and Business
                                    Overseas Chinese College

Students can drop the class in the first week of the semester without leaving any marks to the final grade.
Students can withdraw from any class before July 4th 2008 and get a W for withdrawal. However anyone
with 12 absences automatically receives an F.
Cheating and Plagiarism

Cheating is not tolerated. Any student caught cheating on a quiz; test or exam will be given a mark of
zero (0) for the particular work. At the beginning of the semester the definition of plagiarism will be
carefully explained, When any thoughts or writings of another person are used, they must be clearly
identified (usually one uses quotation marks) and the source notes. If any student is caught cheating on
any homework assignment, the highest score the student can earn in that course is a "C".

Note: This syllabus is tentative and may be changed or modified throughout the semester. All students
will be notified and a new syllabus will be given.


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