• Türkçe
  • English
Course Code: 
MATH 102
Course Period: 
Autumn
Course Type: 
Core
P: 
3
Lab: 
2
Credits: 
4
ECTS: 
8
Course Language: 
İngilizce
Course Objectives: 
To introduce basic algebraic structures and proof techniques
Course Content: 

Operations, number systems, partitions and equivalence classes, groups, subgroups and homomorphisms, cyclic groups, cosets, rings, subrings and ideals, ring homomorphisms, quotient rings, integral domains, polynomial rings, fields, properties of real numbers,vector spaces

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes Teaching Methods Assessment Methods
1) Fasciliates abstract thinking 1,2 A
2) Learns proof techniques 1,2 A
3) Recognizes algebraic structures 1,2 A
4) Interprets relations between algebraic structures 1,2 A

Course Flow

Week Topics Study Materials
1 Operations, number systems, partitions and equivalence classes  
2 Groups, elementary properties of groups  
3 Subgroups, group homomorphisms  
4 Cyclic groups, cosets, Lagrange’s Theorem  
5 Rings, elementary properties of rings  
6 Subrings and ideals  
7 Ring homomorphisms  
8 Quotient rings  
9 Integral domains  
10 Properties of Integers  
11 Rings of polynomials  
12 Fields and properties of real numbers  
13 Vector spaces  
14 Review  

Recommended Sources

Textbook “A Book of Abstract Algebra”, Charles C. PINTER,  “Elementary Abstract Algebra”, W. Edwin CLARK,  “Course Notes of Abstract Algebra”, D.R. WILLIAMS.
Additional Resources  

Material Sharing

Documents  
Assignments  
Exams  

Assessment

IN-TERM STUDIES NUMBER PERCENTAGE
Mid-terms 2 100
Quizzes    
Assignments    
Total   100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE   50
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE   50
Total   100

 

Course’s Contribution to Program

No Program Learning Outcomes Contribution
1 2 3 4 5
1 The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)         x
2 Acquiring fundamental knowledge on fundamental research fields in mathematics         x
3 Ability form and interpret the relations between research topics in mathematics         x
4 Ability to define, formulate and solve mathematical problems         x
5 Consciousness of professional ethics and responsibilty   x      
6 Ability to communicate actively x        
7 Ability of self-development in fields of interest     x    
8 Ability to learn, choose and use necessary information technologies x        
9 Lifelong education     x    

ECTS

Activities Quantity Duration
(Hour)
Total
Workload
(Hour)
Course Duration (14x Total course hours) 14 5 70
Hours for off-the-classroom study (Pre-study, practice) 14 5 70
Mid-terms (Including self study) 2 15 30
Quizzes - - -
Assignments - - -
Final examination (Including self study) 1 20 20
Total Work Load     190
Total Work Load / 25 (h)     7.60
ECTS Credit of the Course     8