# Algebra (MATH541) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Algebra MATH541 3 0 0 3 5
Pre-requisite Course(s)
N/A
Course Language English N/A Natural & Applied Sciences Master's Degree Face To Face Lecture, Question and Answer. The course is designed to give the fundamentals of main algebraic structures: Groups, Rings, Fields and Modules. The students who succeeded in this course; Understand and use the main theorems on groups, rings, modules and fields Define and construct examples of basic algebraic structures given in the content of the course Be able to apply homomorphism theorems, Sylow theorems and the fundamental theorem of Galois theory Be able to reproduce simple proofs of some simple theorems in algebra Groups: quotient groups, isomorphism theorems, direct products, finitely generated abelian groups, actions, Sylow theorems, nilpotent and solvable groups; rings: ring homomorphisms, ideals, factorization in commutative rings, rings of quotients, polynomial rings; modules: exact sequences, vector spaces, tensor products; fields: field extensions, th

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Groups, Subgroups, Homomorphisms Read related sections in references
2 Permutation Groups, Symmetric and Alternating Groups, Sylow theorems Read related sections in references
3 Solvable groups, Normal and Subnormal series, Direct Products Read related sections in references
4 Nilpotent Groups, Finite Abelian Groups, Free groups Read related sections in references
5 Rings, Ring homomorphisms, Ideals Read related sections in references
6 Field of fractions of an integral domain, Polynomials Read related sections in references
7 Midterm Exam
8 Polynomials in several indeterminates, Divisibility and Factorization Read related sections in references
9 Chinese Remainder Theorem, Hilbert Basis Theorem Read related sections in references
10 Field extensions, The fundamental theorem of Galois theory Read related sections in references
11 Normality and Seperability, Galois Theory of Equations Read related sections in references
12 Symmetric Functions, Norm and Trace Read related sections in references
13 Modules, Direct sums, Free Modules Read related sections in references
14 Finitely Generated Modules over PID Read related sections in references
15 Tensor Products Read related sections in references
16 Final Exam

### Sources

Course Book 1. Algebra, Larry C. Grove, Dover Publications, 2004 2. Algebra, Thomas W. Hungerford, Springer, 2005 3. Abstract Algebra, David S. Dummit - Richard M. Foote, Wiley and Sons, Inc. 2004 4. Cebir Dersleri, H. İbrahim Karakaş, TÜBA, 2008

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 7 100
 Percentage of Semester Work 70 30 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area.
2 Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research.
3 Can apply gained knowledge and problem solving abilities in inter-disciplinary research.
4 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary.
5 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study.
6 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework.
7 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility.
8 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation.
9 Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields.
10 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge.
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 3 15
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 10 10
Prepration of Final Exams/Final Jury 1 10 10