Abstract Algebra(MAT204)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT204 | Abstract Algebra | 3 | 3 | 2 | 0 | 5 | 8 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Gönenç ONAY gonay@gsu.edu.tr (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, irreducible and prime elements |
| Course Learning Outcomes | To understand basic algebraic structures and to be able to put them to use |
| Teaching and Learning Methods |
Inquiry based learning Weekly exercice sessions |
| References |
Mathématique L3 Algèbre, Aviva Szpirglas 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 |
| 2 | Axiomatic definition of a group, group examples, operation tables, subgroup |
| 3 | Group homomorphisms, operations on groups |
| 4 | Kernel et image of homomorphisms, quotient of a group by a subgroup, Lagrange's theorem |
| 5 | Normal subgroups, quotient groups, Isomorphism theorems |
| 6 | Semi-direct products |
| 7 | Group actions on sets |
| 8 | Midterm |
| 9 | Orbit-stabiliser theorem, Sylow Theorems |
| 10 | Sylow Theorems and applications |
| 11 | Rings, ring homomorphisms, kernel and image of homomorphisms, subrings and ideals |
| 12 | Quotient rings, isomorphism theorem |
| 13 | Prime and irreducible elements |
| 14 | Unique Factorization Domains |
Practice Topics
| Week | Weekly Contents |
|---|---|
| 2 | Notion of symmetry |
| 3 | Axiomatic definition of a group, group examples, operation tables, subgroup |
| 4 | Group homomorphisms, operations on groups |
| 5 | Kernel et image of homomorphisms, quotient of a group by a subgroup, Lagrange's theorem |
| 6 | Normal subgroups, quotient groups, Isomorphism theorems |
| 7 | Semi-direct products |
| 9 | Group actions on sets |
| 10 | Orbit-stabiliser theorem, Sylow Theorems |
| 11 | Sylow Theorems and applications |
| 12 | Rings, ring homomorphisms, kernel and image of homomorphisms, subrings and ideals |
| 13 | Quotient rings, isomorphism theorem |
| 14 | Prime and irreducible elements |
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 3 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 4 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 30 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 2 | 30 |
| 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 |
| Make-up | 0 | 0 |
| Toplam | 3 | 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 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 20 | 20 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Total Workload | 172 | ||
| Total Workload / 25 | 6.88 | ||
| Credits ECTS | 7 | ||