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Syllabus ( MATH 210 )


   Basic information
Course title: Algebra II
Course code: MATH 210
Lecturer: Assist. Prof. Roghayeh HAFEZIEH
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 2, Spring
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 ring in detail. The course will introduce the different types and properties of rings.
   Learning outcomes Up

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

  1. Obtain a detail knowledge of algebraic structures, rings, ideals and their properties.

    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. Homework assignment
  2. Furthermore, to be familiar with algebraic field extensions and Galois theory.

    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
    2. Homework assignment
  3. Finally, to be able to do some calculations and applications of prementioned subjects.

    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
    2. Homework assignment
   Contents Up
Week 1: Rings, basic properties of rings
Week 2: Subrings, characteristic of a ring, some examples
Week 3: Ideal, finitely generated ideals, Principal ideal ring
Week 4: Quotient ring, Ring homomorphism
Week 5: The isomorphism theorem, the correspondence theorem
Week 6: Midterm I
Week 7: Sum and direct sum of ideals, minimal, Prime, and maximal ideal
Week 8: Some applications of prime and maximal ideals
Week 9: Nilpotent ideals, irreducible and prime elements of a ring
Week 10: Principal ideal domain, Unique factorization domain, Euclidean domain
Week 11: Midterm II
Week 12: İrreducible polynomials and Eisenstein criterion
Week 13: Algebraic extension of a field
Week 14: Splitting field of a polynomial, algebraic number field
Week 15*: -
Week 16*: Final
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: 6,11 50
Other in-term studies: 0 0
Project: 0 0
Homework: 3,5,7,9,11 10
Quiz: 0 0
Final exam: 16 40
  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: 4 2
Personal studies for final exam: 10 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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