Rapor Tarihi: 13.04.2026 03:09
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Abstract Mathematic II | MAT122 | Turkish | Compulsory | 2. Semester | 2 + 2 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing, exemplification, problem solving, and conceptual discussion. |
| Course Coordinator | Dr. Öğr. Üyesi Hasan KARA |
| Instructor(s) | Dr. Öğr. Üyesi Hasan KARA (Bahar) |
| Goals | To introduce fundamental concepts of algebraic and numerical structures in abstract mathematics, to develop students’ abstract thinking skills, and to enable them to establish connections between different mathematical structures. |
| Course Content | Algebraic operations and their basic properties, modular structures, algebraic systems, structure-preserving mappings, number systems and their properties, countability and equivalence concepts. |
| # | Öğrenme Kazanımı |
| 1 | Ability to understand and interpret fundamental structures and concepts in abstract mathematics. |
| 2 | Ability to establish relationships between different mathematical structures and adapt them to various situations. |
| 3 | Ability to approach problems using mathematical thinking and abstraction skills. |
| 4 | Ability to generalize mathematical concepts and evaluate them in different contexts. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Finite Math systems (Group, Ring and Field) Definition and Properties | Preparation, After Class Study, Research, Practice |
| 2. Week | Establishment of Numbers, One-to-One Mapping of Natural Numbers between Has-Peano and Finite Sets, Establishment through Equation Correlation | Preparation, After Class Study, Research, Practice |
| 3. Week | Definitions of operations in natural numbers (addition and multiplication operations, subtraction and division operations) | Preparation, After Class Study, Research, Practice |
| 4. Week | In natural numbers, the largest common divisor and the smallest common divider and their properties | Preparation, After Class Study, Research, Practice |
| 5. Week | Establishment of integers and related definitions | Preparation, After Class Study, Research, Practice |
| 6. Week | Homomorphisms | Preparation, After Class Study, Research, Practice |
| 7. Week | Isomorphisms | Preparation, After Class Study, Research, Practice |
| 8. Week | Naturel Numbers | Preparation, After Class Study, Research, Practice |
| 9. Week | Naturel Numbers | Preparation, After Class Study, Research, Practice |
| 10. Week | Integers | Preparation, After Class Study, Research, Practice |
| 11. Week | Operations in Rational numbers and their properties | Preparation, After Class Study, Research, Practice |
| 12. Week | Representation of rational numbers (Decimal and Cyclic decimal) | Preparation, After Class Study, Research, Practice |
| 13. Week | Establishment of irrational numbers and comparison with rational numbers | Preparation, After Class Study, Research, Practice |
| 14. Week | General applications of Numbers Set | Preparation, After Class Study, Research, Practice |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 2 | Explains the historical development of mathematical concepts, their relationship with other branches of science, and their application areas. | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| 5 | Formulates and interprets real-life problems by performing mathematical modeling. | ✔ | |||||
| 6 | Effectively uses information technologies and mathematical software in data analysis and computation processes. | ✔ | |||||
| 7 | Takes responsibility in individual or team work; plans and executes projects. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 9 | Expresses mathematical ideas verbally and in writing clearly and in accordance with academic rules. | ✔ | |||||
| 10 | Acts in accordance with professional and academic ethical values; acts with a sense of social responsibility. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 |
|---|---|---|---|---|
| PY1 | 4 | 4 | 4 | 4 |
| PY2 | 5 | 5 | 5 | 5 |
| PY3 | 5 | 5 | 5 | 5 |
| PY4 | 3 | 3 | 3 | 3 |
| PY5 | 4 | 4 | 4 | 4 |
| PY6 | 2 | 2 | 2 | 2 |
| PY7 | 5 | 5 | 5 | 5 |
| PY8 | 4 | 4 | 4 | 4 |
| PY9 | 2 | 2 | 2 | 2 |
| PY10 | 5 | 5 | 5 | 5 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 4 | 56 |
|
Ders Dışı |
Homework | 14 | 1 | 14 |
| Preparation, After Class Study | 14 | 1 | 14 | |
| Research | 14 | 1 | 14 | |
| Interview | 14 | 1 | 14 | |
| Practice | 14 | 1 | 14 | |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Final | 1 | 2 | 2 | |
| Total Workload | 130 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
