Course Name Code Semester T+U Hours Credit ECTS
Group Theory MAT 536 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Compulsory
Course Coordinator Doç.Dr. MURAT GÜZELTEPE
Course Lecturers
Course Assistants
Course Category
Course Objective To introduce subject of base abstract algebra
Course Content Algebraic structure, Groups
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Students will have acquired a sound understanding of the classification of finitely generated abelian groups. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
2 Students will have acquired knowledge of some fundamental results and techniques from the theory of finite groups. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
3 Students will have acquired knowledge of group actions on sets, simple groups. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 Students will have acquired knowledge of Sylow’s theorems. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
5 Students will have acquired knowledge of various applications of Sylow’s theorems. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
6 Students will have developed an appreciation of the homeomorphism and isomorphism theorems for groups. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Basic consepts
2 Axioms of group
3 Subgroups and cyclic groups
4 Normal subgroups
5 Quotient sets, quotient groups
6 Homomorphism
7 Isomorphism, automorphism
8 Permutation group
9 Direct sum
10 Structure of finite abelian groups
11 Sylow theorems
12 Resolvable groups
13 P-group. Normal series
14 General linear group
Resources
Course Notes
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
2 Student follows the current journals in his/her field and puts forward problems. X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead.
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field.
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research.
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
2. Kısa Sınav 10
1. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Quiz 2 1 2
Assignment 1 15 15
Final examination 1 25 25
Total Workload 158
Total Workload / 25 (Hours) 6.32
dersAKTSKredisi 6