Faculty of Education · Secondary School Mathematics Education · Undergraduate
ECTS: 2 T+P+L: 2+0+0 Compulsory
Coordinator: Dr. Öğr. Üyesi Hatice İNANKIL
Instructors: Dr. Öğr. Üyesi Hatice İNANKIL
Course Objective
To be able to carry out ideas about abstract concepts, to comprehend the basic concepts of algebra, to have information about theorems and proof methods, to be able to understand problem solutions, to comprehend the body structures of groups.
Course Content
Binary operations, group definition and basic properties, subgroups, permutation groups, cyclic groups, cyclic permutations, odd and even permutations, homomorphisms, Kosets and Lagrange's theorem, isomorphism theorems, rings, subrings and ideals, prime and maximal ideals, homomorphisms of rings.
Course Learning Outcomes
- Knows subgroups and their examples.
- Knows the cyclic subgroups and gives some examples about that.
- Learns isomorphisms for group and ring theory.
- To be able to carry out ideas about abstract concepts
- To be able to comprehend and practice group structure
- Knows the ring structure in general terms.
Core Area Distribution
(46) Mathematics and Statistics%100
Teaching Methods
ExpressionQuestion-AnswerDiscussionExercise and PracticePresentationBrain StormingSelf studyProblem Solving
Assessment & Evaluation
Testing (Essay / Tests: True-Falls, multiple-choice, short answer, matching)
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 1 | 14 | 14 |
| Out of Class Study Period | 4 | 4 | 16 |
| Midterm | 1 | 8 | 8 |
| Quiz | 0 | 0 | 0 |
| Assignment | 0 | 0 | 0 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 12 | 12 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | Binary operations and binary operation | Studying from the required source 1 to the relevant section |
| 2 | Groups | Studying from the required source 1 to the relevant section |
| 3 | Subgroup | Studying from the required source 1 to the relevant section |
| 4 | Group Homomorphisms | Studying from the required source 1 to the relevant section |
| 5 | Cyclic Subgroups | Studying from the required source 1 to the relevant section |
| 6 | Cosets and Lagrange's Theorem | Studying from the required source 1 to the relevant section |
| 7 | Normal Subgroups | Studying from the required source 1 to the relevant section |
| 8 | Midterm | Midterm |
| 9 | Isomorphism Theorems for Group Theory | Studying from the required source 1 to the relevant section |
| 10 | Symmetric Groups | Studying from the required source 1 to the relevant section |
| 11 | Odd and even Permutations on Symmetric Groups | Studying from the required source 1 to the relevant section |
| 12 | Ring Theory | Studying from the required source 1 to the relevant section |
| 13 | Subrings and ideals of a ring | Studying from the required source 1 to the relevant section |
| 14 | Prime and maximal ideals | Studying from the required source 1 to the relevant section |
| 15 | Homomorphisms of a ring | Studying from the required source 1 to the relevant section |
| 16 | Final Exam | Final Exam |