Course Code:
MATH 321
Semester:
Fall
Course Type:
Core
P:
3
Lab:
0
Laboratuvar Saati:
0
Credits:
3
ECTS:
7
Course Language:
English
Course Objectives:
To teach as much about groups as one can in a first course to constitute a firm foundation for more specialized work and to provide valuable experience for any further axiomatic study of mathematics.
Course Content:

Binary operations, groups, subgroups, cyclic groups and generators. Permutation groups. Orbits, cycles and alternating groups. Cosets and Lagrange theorem. Direct products. Finitely generated Abelian groups. Isomorphism theorems. Cayley's theorem. Factor groups, simple groups, series of groups, group action. Sylow theorems and applications. Free groups. Group representations.

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) Classifies finite abelian groups 1,2 A 2) Finds the Sylow subgroups of a group 1,2 A 3) Compute factor groups 1,2 A 4) Finds group homomorphisms 1,2 A 5) Determines if groups are isomorphic or not 1,2 A 6) Determines if a group is simple 1,2 A

### Course Flow

 Week Topics Study Materials 1 Groups, subgroups, cyclic groups Textbook 2 Permutation groups, orbits, cycles, alternating groups Textbook 3 Cosets and the theorem of Lagrange Textbook 4 Direct product and finitely generarted abelian groups Textbook 5 Homomorphisms, factor groups Textbook 6 Simple groups Textbook 7 Group action on a set Textbook 8 Isomorphism theorems Textbook 9 Series of groups Textbook 10 Sylow theorems Textbook 11 Applications of the Sylow theory Textbook 12 Free abelian groups Textbook 13 Free groups Textbook 14 Groups presentations Textbook

### Recommended Sources

 Textbook A First Course in Abstract Algebra, J. Fraleigh. 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 40 CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE 60 Total 100

 COURSE CATEGORY Expertise/Field 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 3 42 Hours for off-the-classroom study (Pre-study, practice) 14 5 70 Mid-terms (Including self study) 2 16 32 Quizzes - - - Assignments - - - Final examination (Including self study) 1 20 20 Total Work Load 164 Total Work Load / 25 (h) 6.56 ECTS Credit of the Course 7