Syllabus ( MATH 209 )

Basic information


Course title: 
Algebra I 
Course code: 
MATH 209 
Lecturer: 
Assist. Prof. 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 corequisites: 
Yok 
Professional practice: 
No 
Purpose of the course: 
To understand algebraic structures, particularly the notion of a group in detail. The course will introduce the different types and properties of groups and will give the ability to use the homomorphisms between them. 



Learning outcomes


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

use the proof techniques and improve them
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

improve the ability of abstract thinking
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

improve problem solving and brain storming skills
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


Contents


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 and quotient groups 
Week 7: 
Isomorphism theorems 
Week 8: 
Automorphisms 
Week 9: 
Midterm and solutions 
Week 10: 
Conjugation and Gsets 
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 
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: 
9 
40 
Other interm studies: 
0 
0 
Project: 
0 
0 
Homework: 
3, 5, 7, 9, 11 
0 
Quiz: 
0 
0 
Final exam: 
16 
60 

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: 
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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