ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE

Syllabus ( MATH 517 )


   Basic information
Course title: Ring Theory I
Course code: MATH 517
Lecturer: Assoc. Prof. Dr. Ayten KOÇ
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 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: none
Professional practice: No
Purpose of the course: To understand the structure of rings.
   Learning outcomes Up

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

  1. Explain the structure of rings, subring, ideal and factor ring.

    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. Acquire scientific knowledge and work independently

    Method of assessment

    1. Written exam
  2. Develop awareness for simple and semisimple modules

    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. Acquire scientific knowledge and work independently

    Method of assessment

    1. Written exam
  3. Identify Polynomial rings with multi indeterminates

    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. Acquire scientific knowledge and work independently

    Method of assessment

    1. Written exam
   Contents Up
Week 1: Rings: some specific examples of rings.
Week 2: Subrings.
Week 3: Ideals.
Week 4: Factor rings.
Week 5: Ring homomorphisms.
Week 6: Isomorphism theorems for rings.
Week 7: Prime and maximal ideals.
Week 8: Euclid rings. Midterm Exam.
Week 9: The Jacobson radical of a ring.
Week 10: Simple and semisimple rings.
Week 11: Prime and semiprime rings.
Week 12: Polynomial rings.
Week 13: Polynomial rings.
Week 14: Polynomial rings with multi indeterminates.
Week 15*: -
Week 16*: Final Exam.
Textbooks and materials: 1.) Algebra; T. Hungerford, New York 1971
2.) Modules and rings; Kasch-Vallace, Academic Press, 1982.
Recommended readings: 1.) Cebir I-II; Abdullah Harmancı, Hacettepe Üniv. Yayınları
2.) Abstract Algebra I-II; Beachy J.A., Lectures Notes on Rings and Modules, 1995.
3.) Rings and Categories of Modules; Anderson-Fuller, Springer-Verlag, New York 1974.
  * 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 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 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: 8 14
Practice, Recitation: 0 0
Homework: 0 0
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 15 1
Mid-term: 2 1
Personal studies for final exam: 20 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)
-->