Information Package / Course Catalogue
| Course Code | : MAT403 |
| Course Type | : Area Elective |
| Couse Group | : First Cycle (Bachelor's Degree) |
| Education Language | : Turkish |
| Work Placement | : N/A |
| Theory | : 2 |
| Prt. | : 2 |
| Credit | : 3 |
| Lab | : 0 |
| ECTS | : 6 |
The main objective of this course is to study the properties, behavior and relations of algebraic objects such as commutative rings and modules. Thus, the course prepares students for applications in algebraic geometry, cryptography, coding theory and number theory.
Rings and ring homomorhisms, Ideals and Quotient rings, Prime ideals, Maximal ideals, Nilpotent elements and Nil Radical, Jacobson radical, Operations on ideals, Modules and Quotient modules, Finitely generated modules, Rings and Modules with Ascending Chain Condition, Hilber Basis Theorem
| 1. | To explain the notions of ideal, maximal ideal and prime ideal |
| 2. | To learn the notions of nil and Jacobson radicals. |
| 3. | To learn basic concepts of local rings and primary ideals |
| 4. | To understand the structure of modules on commutative rings |
| 5. | To identify links and modules with chain condition |
| 1. | Atiyah M.F., MacDonald I.G., Çevirenler: Harmancı A., Tutalar H.İ., Akgül M., Taş K. “Değişmeli Cebire Giriş”, Hacettepe Üniv. Fen. Fak.Yayınları, 1980. |
| 2. | R.Y. Sharp, “Steps in Commutative Algebra”, London Mathematical Society Student Texts, Cambridge University Press, 2000. |
| 3. | M. Reid, “Undergraduate Commutative Algebra”, Cambridge University Press, 1995. |
| Type of Assessment | Count | Percent |
|---|---|---|
| Assignment | 1 | %5 |
| Term Assignment | 1 | %5 |
| Midterm Examination | 1 | %30 |
| Final Examination | 1 | %60 |
| Activities | Count | Preparation | Time | Total Work Load (hours) |
|---|---|---|---|---|
| Lecture - Theory | 14 | 0 | 2 | 28 |
| Lecture - Practice | 14 | 0 | 2 | 28 |
| Assignment | 1 | 1 | 1 | 2 |
| Term Project | 1 | 1 | 1 | 2 |
| Individual Work | 14 | 0 | 2 | 28 |
| Midterm Examination | 1 | 24 | 2 | 26 |
| Final Examination | 1 | 34 | 2 | 36 |
| TOTAL WORKLOAD (hours) | 150 | |||
PÇ-1 | PÇ-2 | PÇ-3 | PÇ-4 | PÇ-5 | PÇ-6 | PÇ-7 | PÇ-8 | PÇ-9 | PÇ-10 | PÇ-11 | PÇ-12 | PÇ-13 | PÇ-14 | PÇ-15 | PÇ-16 | PÇ-17 | PÇ-18 | |
OÇ-1 | 3 | 4 | 3 | 3 | 2 | 3 | ||||||||||||
OÇ-2 | 3 | 3 | 4 | 3 | 3 | 3 | ||||||||||||
OÇ-3 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | |||||||||||
OÇ-4 | 3 | 3 | 4 | 3 | 3 | 3 | 3 | |||||||||||
OÇ-5 | 3 | 3 | 4 | 3 | 3 | 3 | ||||||||||||