Hong Kong Baptist University
Faculty of Science
Department of Mathematics
Title (Units): MATH 1205 Discrete Mathematics (3,3,0)
Course Aims:
This course integrates the fundamental topics in discrete mathematics
and linear system. These topics, including symbolic logic, proof methods,
set theory, combinatorics, graph algorithms, Boolean algebra, and
system of linear equations, are essential for precise processing of
information.
Prerequisite:
None
Course Intended Learning Outcomes (CILOs):
Upon successful completion of this course, students should be able to:
No.
1.
2.
3.
4.
5.
Course Intended Learning Outcomes (CILOs)
Describe the ideas in elementary set theory
Recognize the ideas in elementary graph theory and elementary algebra
Carry out various proofs in symbolic logic, set theory, and algebra
Apply various algorithms to solve the problems in counting, graph theory, and
algebra
Use different discrete models that can be used to represent objects in Computer
Science
Teaching & Learning Activities (TLAs)
CILO
1-5
1-4
2,4,5
TLAs will include the following:
Lecture and tutorial
Instructor will show simple real life problems in lectures to motivate the
concepts, followed by discussions of rigorous technical details. Students will
then be required to consolidate the knowledge by further reading and formulate
their knowledge via discussions and exercises in the tutorials.
In-class activities
Instructor will give some materials for the students to investigate different
aspects of elementary set theory, graph theory and algebra by analyzing various
proofs and arguments presented in class on selected topics, coming up with their
own ideas, and trying to apply them to solve other similar problems.
In-home exercises and assignments
Students will search for the well-known applications of the algorithms in graph
theory and algebra that are used today and formulate their knowledge via
discussions and exercises in the tutorials.
Page 1 of 3
Assessment:
No.
Assessment
Methods
Weighting
1
Continuous
Assessment
30%
2
Final
70%
Examination
CILO
Remarks
Addressed
1,2,3,4,5
Continuous Assessment are designed to
measure how well the students have learned
the logics, set theory, combinatorics, graph
algorithms, Boolean algebra, and system of
linear equations. These continuous
assessments include, but not limited to, in
class discussions and problem solving
exercises.
1,2,3,4
Final Examination questions are designed to
see how far students have achieved their
intended learning outcomes. Questions will
primarily be analysis and skills based to
assess the student's ability in analysis the
problems, formulating the models and
applying the appropriate algorithms to find
the answers.
Course Intended Learning Outcomes and Weighting:
CILO
No.
1,3
2,4,5
1,3
2,4
2,4,5
2,4,5
Contents
I
II
III
IV
V
VI
Symbolic Logic and Proofs
Boolean Algebra
Set Theory
Combinatorics
System of Linear Equations
Graph Algorithms
Teaching
(in hours)
8
5
8
6
5
7
Textbook:
S. Epp, Discrete Mathematics with Applications, 3rd Ed., Brooks Cole,
2003.
References:
K.H. Rosen, Discrete Mathematics and Its Applications, 6th Ed., McGrawHill, 2006.
R. Johnsonbaugh, Discrete Mathematics, 7th Ed., Prentice Hall, 2008.
R.A. Ross and C.R.B. Wright, Discrete Mathematics, 5th Ed., Prentice Hall,
2002.
Page 2 of 3
Course Contents in Outline:
Topics
Hours
I.
Symbolic Logic and Proofs
A. Propositions
B. Conditional Propositional and Logical Equivalence
C. “There exists” and “for all” quantifiers
D. Methods of Proof
E. Mathematical Induction
8
II.
Boolean Algebra
A. Boolean Functions
B. Representing Boolean Functions
C. Logic Gates
D. Minimization of Circuits
5
III.
Set Theory
A. Sets
B. Sequences and Strings
C. Relations
D. Functions
8
IV.
Combinatorics
A. Permutations
B. Combinations
C. The Pigeonhole Principle
D. Recurrence Relations
6
V.
System of Linear Equations
A. Matrix Arithmetic
B. Solutions of Systems of Linear Equations
C. Inverses of Matrices
D. Determinants
5
VI.
Graph Algorithms
A. Terminology of Graphs
B. Path and Cycles
C. Hamiltonian Cycles and the Traveling Salesperson Problem
D. Shortest Path Problem
E. Spanning Trees and Minimal Spanning Trees
7
.
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