APPLIED MATHEMATICS (TURKISH, THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5002 Abstract Algebra II Fall 3 0 3 12
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Assoc. Prof. ATABEY KAYGUN
Recommended Optional Program Components: None
Course Objectives: To provide the necessary algebraic tools and techniques to a graduate student.

Learning Outcomes

The students who have succeeded in this course;
A student who finishes this class successfully will have acquired the minimum background to be able to follow a graduate level algebra course.

Course Content

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Rings and ideals. Morphisms of rings.
2) Fields and vector spaces.
3) Examples of rings and fields.
4) Zero divisors. Principal Ideal Domains and Integral Domains.
5) Euclidean Domains. Unique Factorizations Domains.
6) Principal ideals, primary ideals, prime ideals and maximal ideals.
7) Radicals of ideals and rings. Nil radical and Jacobson radical.
8) Local and semi-local rings.
9) Basics of Lie algebras and Lie brackets. Structure constants. Jacobi identity.
10) Residue field and the cotangent space of a local ring.
11) The lattice of ideals of a ring, and operations in this lattice.
12) Alexandroff topology in a poset. Distributive lattices and Birhoff transform.
13) Selected topics from ring theory.
14) Selected topics from ring theory.

Sources

Course Notes / Textbooks: Instructor's own lectures notes.
S. Lang, "Algebra"
References:

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Project 1 % 20
Midterms 1 % 30
Final 1 % 50
Total % 100
PERCENTAGE OF SEMESTER WORK % 30
PERCENTAGE OF FINAL WORK % 70
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 6 84
Project 1 49 49
Midterms 1 12 12
Final 1 13 13
Total Workload 200

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) Ability to assimilate mathematic related concepts and associate these concepts with each other. 5
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. 5
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. 5
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. 4
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. 5
10) To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data.
11) 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. 4
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, 3