Fundamentals of Mathematics (MAT115)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT115 | Fundamentals of Mathematics | 1 | 3 | 2 | 0 | 5 | 8 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Serap GÜRER serapgurer@gmail.com (Email) |
| Assistant | |
| Objective | To introduce the subjects and technics of pure mathematics |
| Content |
Logic, Proof methods, Notion of set, Family of sets, Product of sets, Relations, Functions, One to one, surjective functions, composition of functions, equivalence relation, equivalence classes, quotient sets, Order relations |
| Course Learning Outcomes |
1. Knowledge of proof methods 2. Set notion 3. Define notions of relation and function 4. Composing functions 5. Define equivalence relation, order relation 6. Explain notions of partial ordering, well ordering |
| Teaching and Learning Methods | |
| References |
Deschamps et Warusfel , Mathématiques 1ère année, Cours et exercices. Gary Chartrand, Albert D. Polimeni, Ping Zhang, Mathematical Proofs: A Transition to Advanced Mathematics |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Set theory |
| 2 | Introduction to logic |
| 3 | Introduction to logic |
| 4 | Proof methods |
| 5 | Proof methods |
| 6 | Proof methods |
| 7 | Relations |
| 8 | Mid-term examination |
| 9 | Order relations |
| 10 | Modular arithmetic |
| 11 | Functions |
| 12 | Mid-term examination, functions |
| 13 | Cardinalities of sets |
| 14 | Cardinalities of sets |
Practice Topics
| Week | Weekly Contents |
|---|
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) | 2 | 50 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 4 | 5 |
| 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 | 6 | 55 |
| 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; | |||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | |||||
| 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; | |||||
| 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 | 4 | 56 |
| Working Hours out of Class | 0 | 0 | 0 |
| Assignments | 9 | 4 | 36 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 30 | 60 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 30 | 30 |
| Quiz | 2 | 5 | 10 |
| 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 |
| Make-up | 0 | 0 | 0 |
| Total Workload | 192 | ||
| Total Workload / 25 | 7.68 | ||
| Credits ECTS | 8 | ||