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Syllabus ( MATH 312 )

   Basic information
Course title: Group Theory
Course code: MATH 312
Lecturer: Assoc. Prof. Dr. Fatma KARAOĞLU CEYHAN
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 3, Fall
Level of course: First Cycle (Undergraduate)
Type of course: Elective
Language of instruction: Turkish
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: To introduce the concept of groups and to equip students with knowledge in topics such as subgroups, cyclic groups, Lagrange's theorem, normal groups, quotient groups, group homomorphisms, and Sylow theorems.
   Learning outcomes Up

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

  1. Develop skills of simple proof techniques

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Ability to work in interdisciplinary research teams effectively.
    3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
  2. Practise at abstract-thinking

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Experience at brainstorming

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
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 Exam.
Week 8: Quotient Groups and Homomorphisms.
Week 9: Composition Series and the Holder Program. Transpositions and the Alternating Groups.
Week 10: Group Actions and Permutation Representations. Groups acting on themselves by left multiplication. Cayley's Theorem.
Week 11: The Class Equation. Automorphisms. The Sylow Theorems.
Week 12: The Sylow Theorems (continued). p-Groups. Direct Products.
Week 13: Finitely Generated Abelian Groups.
Week 14: Nilpotent Groups. Solvable Groups. Free Groups.
Week 15*: -
Week 16*: Final Exam.
Textbooks and materials: Soyut Cebir, Fethi Çallıalp
Topics in Algebra, I. N. Herstein
Recommended readings: A First Course in Abstract Algebra / 6th ed.,
John B. Fraleigh
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 7 30
Other in-term studies: 0
Project: 0
Homework: 5,10,14 20
Quiz: 0
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 4 14
Practice, Recitation: 0 0
Homework: 6 3
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 2 1
Personal studies for final exam: 15 1
Final exam: 2 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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