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 corequisites: 
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


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

Obtain a detail knowledge of algebraic structures, rings, ideals and their properties.
Contribution to Program Outcomes

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.

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Exhibiting professional and ethical responsibility.
Method of assessment

Written exam

Homework assignment

Furthermore, to be familiar with algebraic field extensions and Galois theory.
Contribution to Program Outcomes

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.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.
Method of assessment

Written exam

Homework assignment

Finally, to be able to do some calculations and applications of prementioned subjects.
Contribution to Program Outcomes

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.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.
Method of assessment

Written exam

Homework assignment


Contents


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, ISBN13: 9780521466295 ISBN10: Edition: 2nd. ed. 1994, Cambridge University Press. 
Recommended readings: 
Abstract Algebra, D.S.Dummit, R.M.Foote, ISBN13: 9780471433347 ISBN10: 0471433349 Edition: 3rd 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
6,11 
50 
Other interm studies: 
0 
0 
Project: 
0 
0 
Homework: 
3,5,7,9,11 
10 
Quiz: 
0 
0 
Final exam: 
16 
40 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface 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 midterm exam: 
10 
2 

Midterm: 
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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