Course Code:
MATH 102
Semester:
Spring
Course Type:
Core
P:
3
Lab:
2
Laboratuvar Saati:
0
Credits:
4
ECTS:
8
Course Language:
English
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 CATEGORY Core Courses

### 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