MM213 : Set Theory

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

03

Prerequisite

MM102MM317

Overview

This course introduces the student to the basic concepts of groups. It also deals with proving some theorems on groups. It also aims to know indexed groups. This course aims to develop the student's ability to define relationships, functions, number theory, and congruence.

Intended learning outcomes

By the end of the course, the student should be able to:

1. Recognize groups, subgroups, and operations on groups

2. Mention the concept of indexed groups, their generalized union and their generalized intersection

3. Enumerate the conditions of the equivalence relationship

4. Distinguish the terms of the unilateral, superscript and inverse function

5. Explain countable groups and their theorems

6. Enumerate the terms of the partial and total ordered group

7. Explain the major and minor elements of an ordered group.

8. Analyze issues related to group operations

9. Explain the union and intersection of indexed groups

10. Deduce the terms of the equivalence relationship

11. Find out the difference between the monadic, superscript and inverse function

12. Analyze the concept of countable and uncountable groups. And finite groups and non-finite groups

13. Connect the partial and total ordered group

14. Compare the major and minor elements of an ordered set.

15. The concept of groups, subgroups, and operations on groups is used to solve single-idea and multi-idea problems

16. There is an intersection and union of indexed groups

17. It applies the conditions of unary and meta functions

18. Use the terms of the equivalence relationship to find out the type of relationship

19. The concept of countability is used to determine the type of group

20. Partial and total ordered group conditions apply

21. The concept of major and minor elements is used to extract them from any ordered group.

Teaching and learning methods

1. Theoretical lectures

2. Discussion and dialogue

3. Brainstorm

4. Using mathematical proof methods

5. Exercises, trainings, and multi-idea problem solving

Methods of assessments

1. A written exam (essay + objective) = 25 marks, or its assessment is left to the course instructor

2. Short tests (written or oral), demonstration tasks, applications, exercises, and presentation = 15 marks or left to the course instructor

3. Written final exam (essay + objective) = 60 marks

Course content:

Week	Scientific topic	Number of hours	Lecture	Exercises	Discussion
1-2	groups	6	ü	ü	ü
2-3-4	Operations on groups	10	ü	ü	ü
5	First midterm exam (2 hours)
5-6	Indexed Collections	4	ü	ü	ü
6-7	Cartesian Product and Ordered Pairs	4	ü	ü	ü
7-8-9	Relationships	10	ü	ü	ü
10	Second midterm exam (2 hours)
10-11	Functions	6	ü	ü	ü
12	Finite and infinite sets	4	ü	ü	ü
13	Countable and uncountable groups	4	ü	ü	ü
14	Groups ranked	4	ü	ü	ü
15-16	final exam
	Total	56

References

, , , where it is

Title of references	publisher	version	author	located
set theory	first new book house	2003 d	Dr. Ramadan Mohamed Juhayma Dr. Ali Saleh Al-Ruwaini Library Department	Mathematics department library

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