MM317 : Mathematical Logic

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

03

Prerequisite

MM101

Overview

The course introduces students to the study of the logic of propositions and the study of informal logical systems. It also aims to study logical systems and prove their theorems that depend on definitions as inference rules. It also deals with the study of logical systems and proving their theorems that depend on logical equivalences as inference rules, and quantum logic.

Intended learning outcomes

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

1. Determine the type of logical case

2. Recognize the concept of logical equivalence, logical arguments, and the rules of logical inference

3. Recognize the concept of the comprehensive quantifier and the partial quantifier

4. Learn some method of proof

5. The student distinguishes between the correct and logical propositions, and between simple and compound propositions

6. The student compares the truth tables for each of the logical conjunctions

7. Explain how truth tables are formed

8. Explain the logical equivalence of logical propositions

9. Explain ways of proving logical arguments

10. Compare the concept of the comprehensive quantifier and the partial quantifier

11. Compare the methods of proof

12. The concept of the logical case is used to know the type of any declarative statement

13. Use validity tables to study the validity of logical propositions

14. Use truth tables to determine the type of logical case

15. Employ the laws of logical equivalence to prove the validity of logical propositions

16. Use the laws of mathematical reasoning to prove the validity of the logical argument

17. The universal quantifier and the partial quantifier are used to form mathematical expressions

18. Apply the proofs steps to prove the validity of the mathematical relationship

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:

The week	Scientific subject	The number of hours	A lecture	Exercise	Discussion
1	Logical case and its types	2
2-3-4 5 6	Boolean joins and truth tables First midterm exam ( 2 hours ) Logical correctives and contradictions	6 2
7-8	Logical equivalence	4
9 10 11-12	Logical arguments and rules of inference Second midterm exam (2 hours) Logical arguments and rules of inference	2 4
13 14-15	Comprehensive quantifier and partial quantifier Proof methods	2 2
16	Final exam The total	28

The reviewer:

References address	Publisher	Release	Author	Where it is located
Discrete mathematics Easy Chum Briefs	International House Cultural Investment Egypt	The first 2006	Dr..Seymour Lipchter Dr..Mark Lebussen Translation Dr..Intisar MuhammadAl-shabki	Department library

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