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Syllabus ( MATH 209 )

   Basic information
Course title: Algebra I
Course code: MATH 209
Lecturer: Assoc. Prof. Dr. Roghayeh HAFEZIEH
ECTS credits: 6
GTU credits: 3 ()
Year, Semester: 2, Fall
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: none
Professional practice: No
Purpose of the course: To understand algebraic structures, particularly the notion of a group in detail, to introduce types of groups and their properties, and to be able to use the homomorphisms between groups.
   Learning outcomes Up

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

  1. Use the proof techniques and improve them

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    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. improve the ability of abstract thinking

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
  3. Improve problem solving and brain storming skills

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
   Contents Up
Week 1: Sets, relations, binary operations.
Week 2: Semigroups and groups.
Week 3: Homomorphisms, Subgroups.
Week 4: Cosets, Lagrange Theorem.
Week 5: Cyclic and permutation groups.
Week 6: Normal subgroups.
Week 7: Quotient groups.
Week 8: Isomorphism theorems.
Week 9: Automorphisms. Midterm Exam.
Week 10: Conjugation and G-sets.
Week 11: Cayley Theorem. Class equation.
Week 12: Direct product of groups.
Week 13: Sylow Theorem.
Week 14: Some applications of Sylow Theorem.
Week 15*: -
Week 16*: Final Exam.
Textbooks and materials: Basic Abstract Algebra, P.B. Bhattacharya, S. K. Jain, S. R. Nagpaul, ISBN-13: 978-0521466295 ISBN-10: Edition: 2nd. ed. 1994, Cambridge University Press.
Recommended readings: Abstract Algebra, D.S.Dummit, R.M.Foote, ISBN-13: 978-0471433347 ISBN-10: 0471433349 Edition: 3rd
  * 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: 9 40
Other in-term studies: 0 0
Project: 0 0
Homework: 3, 5, 7, 9, 11 0
Quiz: 0 0
Final exam: 16 60
  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: 3 14
Practice, Recitation: 0 0
Homework: 5 5
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 2
Mid-term: 3 1
Personal studies for final exam: 10 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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