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Syllabus ( MATH 521 )


   Basic information
Course title: Finite Group Theory
Course code: MATH 521
Lecturer: Assist. Prof. Roghayeh HAFEZIEH
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 2/1, Fall and Spring
Level of course: Second Cycle (Master's)
Type of course: Area Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: algebra and group theory
Professional practice: No
Purpose of the course: To understand and use techniques and results in Finite Group Theory.
   Learning outcomes Up

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

  1. They will learn and use the basic techniques and results in the finite group theory

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    4. Work effectively in multi-disciplinary research teams
    5. Design and conduct research projects independently
    6. Develop mathematical, communicative, problem-solving, brainstorming skills.
    7. Defend research outcomes at seminars and conferences.
    8. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Oral exam
    3. Homework assignment
    4. Seminar/presentation
  2. They will solve the problems using techniques and results that they learned in the course and they will also apply to the other areas.

    Contribution to Program Outcomes

    1. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    2. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    3. Acquire scientific knowledge and work independently
    4. Develop mathematical, communicative, problem-solving, brainstorming skills.
    5. Effectively express his/her research ideas and findings both orally and in writing
    6. Defend research outcomes at seminars and conferences.
    7. Write progress reports clearly on the basis of published documents, thesis, etc
    8. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Oral exam
    3. Homework assignment
    4. Seminar/presentation
  3. In this way they will improve the ability of thinking for a better organization.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    4. Acquire scientific knowledge and work independently
    5. Work effectively in multi-disciplinary research teams
    6. Design and conduct research projects independently
    7. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    8. Develop mathematical, communicative, problem-solving, brainstorming skills.
    9. Effectively express his/her research ideas and findings both orally and in writing
    10. Defend research outcomes at seminars and conferences.
    11. Write progress reports clearly on the basis of published documents, thesis, etc
    12. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Oral exam
    3. Homework assignment
    4. Seminar/presentation
   Contents Up
Week 1: Groups, Subgroups, Homomorphisms and Normal subgroups, Automorphisms, Cyclic groups, Commutators.
Week 2: Direct product of groups.
Week 3: The structure of abelian groups
Week 4: Automorphisms of cyclic groups
Week 5: Action and Conjugation
Week 6: Sylow theorems and their applications
Week 7: Some Classification of finite simple groups
Week 8: Midterm exam
Week 9: Semi-direct product, Complements of normal subgroups and Schur-Zassenhaus Theorem
Week 10: Permutation groups, Transitive groups, Frobenius groups
Week 11: Primitive action, The symmetric group
Week 12: Imprimitive groups and Wreath products
Week 13: Composition series.
Week 14: Nilpotent Groups
Week 15*: Solvable Groups.
Week 16*: Final exam
Textbooks and materials: The Theory of Finite Groups, An Introduction by H. Kurzweil and B. Stellmacher.
Recommended readings: finite group theory, I. Martin Isaacs.
  * 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: 8 30
Other in-term studies: 0
Project: 0
Homework: 3,5,7,9,11,13 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: 3 6
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 15 2
Mid-term: 3 1
Personal studies for final exam: 15 2
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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