• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Formulate proofs in basic level and apply elementary logic

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Adapt to a fast-changing technological environment, improving their knowledge and abilities constantly.

   Method of assessment

   1. Written exam
2. Discuss and use set theoretic techniques

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
   3. Using technology as an efficient tool to understand mathematics and apply it.
   4. Exhibiting professional and ethical responsibility.

   Method of assessment

   1. Written exam
3. Solve problems in combinatorics (permutations, combinations, counting)

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
   3. Using technology as an efficient tool to understand mathematics and apply it.

   Method of assessment

   1. Written exam
4. Perform various operations with relations and functions

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
   3. Using technology as an efficient tool to understand mathematics and apply it.
   4. Exhibiting professional and ethical responsibility.

   Method of assessment

   1. Written exam
5. Explain and use the concepts of graphs and trees

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Using technology as an efficient tool to understand mathematics and apply it.

   Method of assessment

   1. Written exam

Contents
Week 1:	Logic; Propositional Equivalences
Week 2:	Predicates and Quantifiers
Week 3:	Methods of Proof
Week 4:	Sets; Set Operations; Functions
Week 5:	The Integers and Division
Week 6:	Mathematical Induction
Week 7:	The Basics of Counting; The Pigeonhole Principle
Week 8:	Permutations and Combinations; Inclusion-Exclusion, Midterm
Week 9:	Relations and Their Properties
Week 10:	Representing Relations; Recurrence Relations
Week 11:	Equivalence Relations
Week 12:	Axiomatic Structure of Real Numbers
Week 13:	Introduction to Groups, Rings, and Fields
Week 14:	Introduction to Graphs; Graph Terminology, Graph Isomorphism, Introduction to Trees
Week 15*:	-
Week 16*:	Final Exam
Textbooks and materials:
Recommended readings:	1. Kenneth H. Rosen, Discrete Mathematics and Its Applications, Fifth Edition, McGraw-Hill. 2. George Polya, How to Solve It, Princeton University Press. 3. R.P. Grimaldi, Discrete and Combinatorial Mathematics, Addison-Wesley. 4. E.G. Goodaire and M.M. Parmenter, Discrete Mathematics, Prentice Hall
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:	8	40
Other in-term studies:		0
Project:		0
Homework:		0
Quiz:		0
Final exam:	16	60
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	4	14
Practice, Recitation:	0	0
Homework:	0	0
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	17	1
Mid-term:	2	1
Personal studies for final exam:	25	1
Final exam:	2	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)