Download MATH 251

FACULTY OF INFORMATION
TECHNOLOGY
Course Specifications:
(MATH 251)
Month, Year: Fall 2008
University: Misr University for Science and Technology
Faculty : Faculty of Information Technology
Course Specifications for Discrete Mathematics
Program(s) on which the course is given: Undergraduate
Computer Science & Information Systems
Department offering the program: Computer Science
Department offering the course: Computer Science
Academic year / Level: CS Level seven/ IS Elective Course
Date of specification approval
A- Basic Information
Title: Discrete Mathematics
Credit Hours: 3
Tutorial: 2
Code:
math 251
Lecture : 2
Practical:
Total: 4
B- Professional Information
1. Course Description: The course provides an introduction to
mathematical structures fundamental to computer science. Topics
discussed include logic of compound and quantified statements,
number theory and methods of proof, mathematical induction,
counting methods, finite state automata, functions and relations.
2. Course Objectives (Overall Aims of Course):
Upon completion of this course, students should be able to:
1. Use logic to determine the validity of an argument.
2. Construct the proof of a theorem.
3. Understand the terminology, operations, and symbols of set
theory.
4. Use combinatorial techniques when needed in solving
problems.
5. Identify a function; specifically,
6. Identify relation, reflexive, symmetric, and transitive
relations. Included too equivalence relations.
7. Understand the terminology, operations, and symbols of
finite state automata and minimum language accepted.
3. Learning Outcomes :
Upon completion of this course the student will be able to
understand logic of compound and quantified statements, number
theory and methods of proof, mathematical induction, counting
methods, finite state automata, functions and relations
1. Knowledge and understanding :
- Fundamental knowledge needed for mathematical
structures.
- Use logic to determine the validity of an argument.
- Identify functions, and relation.
- Finite state automata.
2. Intellectual skills:
- Learning of mathematical structures
- Design of finite state automata .
- Use of functions, and relation.
- Construct proof of a theorem.
- Recognize and use various types of reasoning and
methods of proof
-How to use abstract algebraic structures in solving
problems expressed by symbols
3. Professional and practical skills:
- Use combinatorial techniques when needed in
solving problems.
- Use of logic to determine the validity of an argument.
- Construct a proof of a theorem using mathematical
induction
- Learn the deductive nature of mathematics, the roles of
definitions, axioms, and theorems to - construct viable
arguments
- How to develop conjectures and draw appropriate
conclusions
4. General and transferable skills.
- Learning of quantified statements, number theory and
methods of proof, and mathematical induction,
counting methods, permutation.
- Emphasis operation on finite state automata.
- Formulate mathematical ideas using the appropriate
mathematical notation
- Judge the validity of mathematical arguments
4. Course Contents
Week
1
2
3
Topics
Digital Logic of statement.
-Logical forms .
-logical equivalence,
-conditional statement,
-Valid and invalid
arguments
Logic of quantified statement
-predicate and quantified
statement
4
5
6
7
8
9
10
11
12
13
14
15
Elementary Number theory and
method of proof.
-Direct proof and counter
example, rational numbers.
-Mathematical Induction
Counting, Permutation,
permutation of selected
elements
Revision
Mid-Term Exam
Mid-Term Exam
-Functions.
-One to one, Onto Functions
-Inverse functions,
-Composition of functions
Basic Relations.
-Relations on sets,
-Reflexivity, symmetry,
and transitivity.
-Equivalence relations.
Finite-State automata Machines
:Transition diagram, annotated
next state table, minimum
language accepted by the
automaton.
Revision
Total/
hours
4
Lecture/
hr
2
Tutorial/hr
4
2
2
4
2
2
4
2
2
4
4
2
2
2
2
4
2
2
4
2
2
4
2
2
4
2
2
4
4
2
2
2
2
4
2
2
2
5– Teaching and Learning Methods
5.1-Lectures
5.2-Exercises
6- Student Assessment Methods
6.1 Written Exams: to assess Concepts related to Discrete
Mathematics
6.2 Exercises to assess understanding of Discrete Mathematics
topics.
6.3 Presentation: to assess workgroup collaboration and
communication skills.
Weighting of Assessments
Mid-Term Examination
20%
Final-term Examination
60%
Semester Work and Project
20%
__________________________________
Total
100%
6- List of References
6.1- Course Notes
-given on board by instructor.
6.2- Essential Books (Text Books)
Required Book:
Sussana Epp, Discrete Mathematics with Applications, 3rd
Edition , Thomson Learning, 2004.
6.3- Recommended Books:
Judith L. Gersting, Mathematical Structures for Computer
Science, 6th ed., W. H. Freeman Press, 2006.
7- Facilities Required for Teaching and Learning
Data show, computer Lab
Course coordinator: Prof. Assem Deif
Date : 20 /4 /2008