| Learning Outcomes |
PO |
MME |
| The students who succeeded in this course: |
|
|
| LO-1 |
Can understand the most general and fundamental notions of structure of groups. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts.
|
Examination
|
| LO-2 |
Can know and use cyclic groups |
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data.
|
Examination
|
| LO-3 |
Can know and use theorems of isomorphism |
PO-5 Develop suitable material for a subject on a mathematical area, to use the knowledge and experience gains with different methods
|
Examination
|
| LO-4 |
Can know Sylow theorems and apply on problems. |
PO-10 With the knowledge of foreign language required the field of mathematics, use and follow information technologies by the level of European Language Portfoy B1.
|
Examination
|
PO: Programme Outcomes
MME:Method of measurement & Evaluation |
| Course Contents |
| Groups, Subgroups, Permutations, Cyclic Groups, Direct Products, Finete Generated Abelian Groups, Cosets, Normal Subgroups and Quotient Groups, Homomorphisms, The Izomorphism Theorems, Group Actions, Sylow Theorems and Applications, Free Serbest Abelian Grups. |
| Weekly Course Content |
| Week |
Subject |
Learning Activities and Teaching Methods |
| 1 |
Groups, Subgroups
|
problem-solving |
| 2 |
Permutations |
problem-solving |
| 3 |
cyclic groups |
problem-solving |
| 4 |
direct product |
problem-solving |
| 5 |
Finete Generated Abelian Groups, |
problem-solving |
| 6 |
cosets |
problem-solving |
| 7 |
Normal Subgroups, Quotient Groups |
problem-solving |
| 8 |
mid-term exam |
|
| 9 |
Homomorphisms
|
problem-solving |
| 10 |
The İzomorphism Theorems |
problem-solving |
| 11 |
Group Actions |
problem-solving |
| 12 |
Sylow Theorems and Applications
|
problem-solving |
| 13 |
Sylow Theorems and Applications
|
problem-solving |
| 14 |
Free Serbest Abelian Grups.
|
problem-solving |
| 15 |
Free Serbest Abelian Grups.
|
problem-solving |
| 16 |
final exam |
|
| Recommend Course Book / Supplementary Book/Reading |
| 1 |
1. 1. A First Course in Abstract Algebra , John B. Fraleigh, Addision-Wesley Publishing Company. 1994 |
| 2 |
2. Algebra, Thomas W. Hungerford, Holtü, Rinehart and Winston, inc. New York Chicago San Francisco, 1974, |
| 3 |
3. Abstract Algebra David S. Dummit, Richard M. Foote, John Wiley & Sons, inc. 2004. |
| 4 |
4. Soyur Cebir, Taşcı D., Ankara 2010. |
| Required Course instruments and materials |
| Books of abstract algebra |
