University of Cebu
Main Campus

SYLLABUS IN DISCRETE MATHEMATICS

Instructor: Mr. Jonathan O. Etcuban
College: Information and Computer Science
Email: sir_etcuban@yahoo.com
Website:  www.geocities.com/sir_etcuban

Credit Hours: 3 Hrs./Wk. 
Lec: 3 Hrs./Wk     

 I.  C O U R S E     D E S C R I P T I O N 

	A 3-unit subject that covers the essential core of mathematics which includes logic, sets, relations and functions, combinations, probability and graphs.

            Whereas calculus concerns itself with continuous mathematics, this course will introduce you to the fundamental ideas of discrete mathematics.  These fundamental ideas (which include sets, functions, logic, relations, graphs, matrices, trees, induction, and recursion) form the building blocks for much higher-level material in both mathematics and computer science.  

II.   R E C O M M E N D E D   B A C K G R O U N D 

Prerequisite: 
Math 1 – College Algebra
Math 21 – Probability and Statistics
IT 12   – C Programming

Required Course Materials: 

• Discrete Mathematics 
       By: Washburn, Marlowe, Ryan
• Discrete Mathematics 
       By: Richard Johnsonbaugh

Method of Instruction: 

Lecture notes, homework, and assignments will include reading. Students will be monitored for activity via online communication methods, such as on-line discussion groups, email, and chat rooms.  A final requirement will be given to learners as fulfillment to the course.   

Attendance: 

Attendance is necessary to pass this course. Attendance will be monitored daily. “A student absences equivalent to two weeks of instruction in a summer class may be dropped by the instructor.”  Please consult the Student’s Manual for details.  Students with excessive absences will be automatically dropped from the course with notification. You will be required to keep pace with homework and other assignments.  Email me regularly and keep me posted on your progress with the course.  

Homework and Computer Assignments: 

Homework and programming assignments will be sent to me as attachments via email or hard copy. You must keep pace with the course calendar of events. Late assignments will not be accepted.

Exams: 

Exams and quizzes will be administered in person. Please refer to the calendar of course events and/or bulletin boards for more information on exam dates.

Course Expectations: 

You are required to read each topic before you attempt to take the review examination. You will be quizzed after each topic. If you diligently follow the course guidelines and complete all the required assignments, you will be adequately prepared to take the course exams. The calendar of events is subjected to change, make sure you refer to the calendar every day. 
 
Final Grade: 

Each student’s grade will be calculated as follows: 
Class Standing  		 50% 
Major Exams     		 35%
Programming Project             15%

III.   C O U R S E   C O N T E N T 

1.	Propositions and their types					
2.	Logical Operations and their Truth Tables			
3.	Quantifiers							
4.	Types of Proofs						
Review Test 							

5.	Sets and its Types						
6.	Operations on Sets						
7.	Properties of Sets						
8.	De Morgan’s Law						
9.	Power Set Partition						
10.	 Sequences and Strings					
11.	 Number Systems						
 Review Test							
 Midterm Examination
	
12.	Relations							
13.	Equivalence Relations						
14.	Relational Databases						
15.	Functions							
Review Test							

16.	Algorithms							
17.	Notation for Algorithms					
18.	Euclidean Algorithms						
19.	Recursive Algorithms						
Review Test							

20.	Basic Counting Principles					
21.	Permutations							
22.	Combinations							
Review Test							

23.	Graph Theory							
Final Examination

IV.    L E A R N I N G   O U T C O M E S 

At the end of this course, the student shall be able to:

1.   Discuss fundamental concepts in modern mathematics such as logic, sets, relations and 
          functions.
2.   Develop these concepts in the context of combinations, probability and graph theory.
3.	To introduce basic techniques of proof and reasoning, in particular, those for solving discrete    
          problems. 
4.	To enhance modes of thinking essentials to mathematics. 
5.	To teach techniques widely used in computer science and related fields.