Syllabus ( MATH 312 )

Basic information


Course title: 
Group Theory 
Course code: 
MATH 312 
Lecturer: 
Assoc. Prof. Dr. Ayten KOÇ

ECTS credits: 
6 
GTU credits: 
3 (3+0+0) 
Year, Semester: 
4, Fall 
Level of course: 
First Cycle (Undergraduate) 
Type of course: 
Area Elective

Language of instruction: 
Turkish

Mode of delivery: 
Face to face

Pre and corequisites: 
None 
Professional practice: 
No 
Purpose of the course: 
To teach simple proof techniques. 



Learning outcomes


Upon successful completion of this course, students will be able to:

Develop skills of simple proof techniques
Contribution to Program Outcomes

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Ability to work in interdisciplinary research teams effectively.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Exhibiting professional and ethical responsibility.
Method of assessment

Written exam

Practise at abstractthinking
Contribution to Program Outcomes

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.
Method of assessment

Written exam

Homework assignment

Experience at brainstorming
Contribution to Program Outcomes

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.
Method of assessment

Written exam

Homework assignment


Contents


Week 1: 
Definition of group and Examples of Groups 
Week 2: 
Dihedral Groups – Symmetric Groups  Matrix Groups 
Week 3: 
The Quaternion Groups  Homomorphisms and Isomorphisms

Week 4: 
Group Actions  Subgroups: Definition and Examples

Week 5: 
Centralizers and Normalizers, Stabilizers and Kernels 
Week 6: 
Cyclic Groups and Cyclic Subgroups 
Week 7: 
Subgroup Generated by Subset of a Group  The Lattice of Subgroups of a Group, Midterm 1 
Week 8: 
Quotient Groups and Homomorphisms 
Week 9: 
Composition Series and the Holder Program  Transpositions and the Alternating Group 
Week 10: 
Group Actions and Permutation Representations Groups Acting on Themselves by Left MultiplicationCayley's TheoremGroups Acting on Themselves by Conjugation  
Week 11: 
The Class Equation Automorphisms  The Sylow Theorems 
Week 12: 
The Sylow Theorems (continue)  (pGroups)  Finitely Generated Abelian Groups 
Week 13: 
Midterm 2 and Solutions 
Week 14: 
Nilpotent Groups  Solvable Groups  Free Groups 
Week 15*: 
 
Week 16*: 
Final Exam 
Textbooks and materials: 

Recommended readings: 
1) Soyut cebir, Fethi Çallıalp 2) A First Course in Abstract Algebra / 6th ed., John B. Fraleigh 3) Topics in Algebra, I. N. Herstein 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
7, 13 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 

0 
Quiz: 

0 
Final exam: 
16 
60 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
4 
14 

Practice, Recitation: 
0 
0 

Homework: 
0 
0 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
10 
2 

Midterm: 
6 
2 

Personal studies for final exam: 
15 
1 

Final exam: 
3 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



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