MATHEMATICS
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT1003	Abstract Mathematics I	Fall	3	2	4	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Instructor MAHMOUD JAFARI SHAH BELAGHI
Recommended Optional Program Components:	None
Course Objectives:	To enable the student to obtain skills and logical perspectives that prepare them for subsequent courses inside the department,to understand and use the language and notation of mathematics, to communicate using mathematical language, to comprehend and construct mathematical arguments,to introduce fundamental concepts of mathematics which are essential for mathematical thinking and.to provide most common methods of mathematical proofs , to develop the mathematical maturity of the student,for further studies in mathematics.

Learning Outcomes

The students who have succeeded in this course;
The students who succeeded in this course;
o will be able to describe prof methods.
o will be able to conclude validity of propositions.
o will be able to apply concepts of logic to proof methods.
o will be able to formulate and develop mathematical statements.
o will be able to distinguish mathematical implications.
o will be able to adopt proof techniques to fundamental topics:set theory, graphs, correspondences, functions, relations, construct sets and relations of given property.
o will be able to compare sets (with respect to cardinality etc. ),compare functions (with respect to injectivity, surjectivity, invertibility, the properties of image and preimage under them etc.),demonstrate basic abstract structures.

Course Content

The language of mathematics. Theorems, Theory of logics. Statements and Proofs. Quantifiers. Sets. Product of sets. Correspondances and functions. Images under graphs and functions. Composite graphs and functions. Sections, retractions, injections and surjections. Relations. Equivalence and Ordering. Ordering. Partially ordering. Total ordering. Well ordering. Directed sets. Intervals. Axiom of choice.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	The language of mathematics.
2)	Theorems, Theory of logics.
3)	Statements and Proofs.
4)	Quantifiers.
5)	Sets. Product of sets. Graphs.
6)	Correspondances and functions.
7)	Union and Intersection of a family of sets, coverings and partitions.
8)	Inverses of Graphs ,correspondances and functions. Images of the family of sets under graphs and functions.
9)	Composite functions, graphs and correspondences. Sections, retractions,injections and surjections.
10)	Product of a family of sets.
11)	Relations.Equivalence relations.
12)	Ordering. Partially ordering. Total ordering.
13)	Well ordering. Directed sets. Intervals.
14)	Axiom of choice. Summary of the course topics, directions and notices for the final exams.
15)	Final exams.
16)	Final exams.

Sources

Course Notes / Textbooks:	Naive Set Theory, Halmos P R, The Theory of Sets, Bourbaki N , Schaum’s Outline , Theory and Problems of Finite Mathematics, Seymour Lipschutz.
References:

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Midterms	2	% 45
Final	1	% 55
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 45
PERCENTAGE OF FINAL WORK		% 55
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	5	70
Midterms	2	2	4
Final	1	2	2
Total Workload			118

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics	5
2)	To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods,	5
3)	To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials,	3
4)	To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,	2
5)	To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way,	5
6)	To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,	1
7)	To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,	3
8)	To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,	1
9)	By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,	5
10)	To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning,	3
11)	To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school,	5
12)	To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.	1