Syllabus ( MATH 312 )
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Basic information
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| Course title: |
Group Theory |
| Course code: |
MATH 312 |
| Lecturer: |
Assoc. Prof. Dr. Ayten KOÇ
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| ECTS credits: |
6 |
| GTU credits: |
3 (3+0+0) |
| Year, Semester: |
4, Fall |
| Level of course: |
First Cycle (Undergraduate) |
| Type of course: |
Area Elective
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| Language of instruction: |
Turkish
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| Mode of delivery: |
Face to face
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| Pre- and co-requisites: |
None |
| Professional practice: |
No |
| Purpose of the course: |
To teach simple proof techniques. |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Develop skills of simple proof techniques
Contribution to Program Outcomes
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Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
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Ability to work in interdisciplinary research teams effectively.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
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Exhibiting professional and ethical responsibility.
Method of assessment
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Written exam
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Practise at abstract-thinking
Contribution to Program Outcomes
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Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
Method of assessment
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Written exam
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Homework assignment
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Experience at brainstorming
Contribution to Program Outcomes
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Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
Method of assessment
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Written exam
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Homework assignment
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Contents
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| Week 1: |
Definition of group and Examples of Groups
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| Week 2: |
Dihedral Groups – Symmetric Groups - Matrix Groups
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| Week 3: |
The Quaternion Groups - Homomorphisms and Isomorphisms
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| Week 4: |
Group Actions - Subgroups: Definition and Examples
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| Week 5: |
Centralizers and Normalizers, Stabilizers and Kernels |
| Week 6: |
Cyclic Groups and Cyclic Subgroups
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| 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 Multiplication-Cayley's Theorem-Groups Acting on Themselves by Conjugation - |
| Week 11: |
The Class Equation- Automorphisms - The Sylow Theorems |
| Week 12: |
The Sylow Theorems (continue) - (p-Groups) - 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: |
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| 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 |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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| Method of assessment |
Week number |
Weight (%) |
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| Mid-terms: |
7, 13 |
40 |
| Other in-term studies: |
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0 |
| Project: |
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0 |
| Homework: |
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0 |
| Quiz: |
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0 |
| Final exam: |
16 |
60 |
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Total weight: |
(%) |
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Workload
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| Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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| Courses (Face-to-face teaching): |
3 |
14 |
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| Own studies outside class: |
4 |
14 |
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| Practice, Recitation: |
0 |
0 |
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| Homework: |
0 |
0 |
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| Term project: |
0 |
0 |
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| Term project presentation: |
0 |
0 |
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| Quiz: |
0 |
0 |
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| Own study for mid-term exam: |
10 |
2 |
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| Mid-term: |
6 |
2 |
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| Personal studies for final exam: |
15 |
1 |
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| Final exam: |
3 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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