Abstract Algebra(MAT204)
Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
---|---|---|---|---|---|---|---|
MAT204 | Abstract Algebra | 4 | 5 | 0 | 0 | 5 | 7 |
Prerequisites | |
Admission Requirements |
Language of Instruction | French |
Course Type | Compulsory |
Course Level | Bachelor Degree |
Course Instructor(s) | Begüm Gülşah ÇAKTI (Email) Can Ozan OĞUZ canozanoguz@gmail.com (Email) |
Assistant | |
Objective | To introduce some basic algebraic structures (groups and rings) and how to study them |
Content |
Groups as symmetry measuring constructs, subgroups, normal subgroups, quotient groups, group homomorphisms, isomorphism theorems, group actions Rings, subrings and ideals, isomorphism theorems |
Course Learning Outcomes | To understand basic algebraic structures and to be able to put them to use |
Teaching and Learning Methods | |
References |
Toute l'Algebre de la Licence, Jean-Pierre Escofier Abstract Algebra: Theory and Applications, Thomas W. Judson, Robert A. Beezer http://abstract.ups.edu/aata/aata.html An Inquiry Based Approach to Abstract Algebra, Dana C. Ernst https://danaernst.com/teaching/mat411f20/IBL-AbstractAlgebra.pdf Cebir I - Temel Grup Teorisi, Ali Nesin https://nesinkoyleri.org/wp-content/uploads/2019/05/cebir.pdf |
Theory Topics
Week | Weekly Contents |
---|---|
1 | Notion of symmetry, definition of a group |
2 | Group examples, subgroups, homomorphisms, equivalence relations |
3 | Cosets, Lagrange's Theorem, Normal subgroups |
4 | Isomorphism theorems |
5 | Isomorphism theorems |
6 | Cyclic and symmetric groups |
7 | Group actions |
8 | Midterm |
9 | Sylow Theorems |
10 | Applications of Sylow Theorems |
11 | Classificaiton of finite abelian groups |
12 | Introduction to ring theory, sub rings, ideals |
13 | Quotient rings |
14 | Rings of polynomials |
Practice Topics
Week | Weekly Contents |
---|
Contribution to Overall Grade
Number | Contribution | |
---|---|---|
Contribution of in-term studies to overall grade | 11 | 60 |
Contribution of final exam to overall grade | 1 | 40 |
Toplam | 12 | 100 |
In-Term Studies
Number | Contribution | |
---|---|---|
Assignments | 10 | 30 |
Presentation | 0 | 0 |
Midterm Examinations (including preparation) | 1 | 30 |
Project | 0 | 0 |
Laboratory | 0 | 0 |
Other Applications | 0 | 0 |
Quiz | 0 | 0 |
Term Paper/ Project | 0 | 0 |
Portfolio Study | 0 | 0 |
Reports | 0 | 0 |
Learning Diary | 0 | 0 |
Thesis/ Project | 0 | 0 |
Seminar | 0 | 0 |
Other | 0 | 0 |
Toplam | 11 | 60 |
No | Program Learning Outcomes | Contribution | ||||
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | ||
1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | X | ||||
7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | X | ||||
8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | X | ||||
9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X |
Activities | Number | Period | Total Workload |
---|---|---|---|
Class Hours | 14 | 5 | 70 |
Working Hours out of Class | 14 | 3 | 42 |
Assignments | 10 | 3 | 30 |
Midterm Examinations (including preparation) | 1 | 10 | 10 |
Final Examinations (including preparation) | 1 | 20 | 20 |
Total Workload | 172 | ||
Total Workload / 25 | 6,88 | ||
Credits ECTS | 7 |