Applied Mathematics(MAT416)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT416 | Applied Mathematics | 8 | 3 | 0 | 0 | 4 | 5 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| Course Type | Elective |
| Course Level | Bachelor Degree |
| Course Instructor(s) | |
| Assistant | |
| Objective | The objective of this course is to study the basics of 3 important subjects of Applied mathemetics: Fixed Point Theory, Approximation Theory and Optimisation Theory with their applications in Data science, Physics and Economics |
| Content |
(1) Banach Fixed Point Theory and its applications: Newton's Method, Cobweb Thm, Picard Thm, Gauss-Seidel Iteration, Fredholm-Volterra Thm. Applications in economics (2) Approximation Theory. Uniform and approximation in the sense of . Convexity, Haar's condition. Applications. (3) Optimisation Theory basics with numerical viewpoint by usual algorithmes |
| Course Learning Outcomes | Student who succeed this course will learn about 3 important theories in Applied Mathematics and learn how they are used (with data, algorithmes and coding) in different areas of application. |
| Teaching and Learning Methods | Course and recitation hours |
| References |
Introductory Functional Analysis with Applications, E. Kreyszig, Wiley An Introduction to Real Analysis, T. Terzioğlu, ODTÜ Fonksiyonel Analizin Yöntemleri, T. Terzioğlu, Matematik Vakfı Fonksiyonel Analiz, E. Şuhubi, İTÜ Vakfı Bir Analizcinin Defeterinden Seçtikleri, T.Terzioğlu, Nesin Matematik Köyü Real Analysis with Economic Applications, Efe A. Ök, Princeton University Press Numerical Optimization , J. Nocedal & S. J. Wright, Springer , 1999. ve 2. basım: Introduction to Global Optimization , R. Horst , P. M.Pardolas &N. V. Thoai , Kluwer Academic Publishers , The Princeton Companion to Applied Mathematics , Edited by Nicholas J. Higham , Princeton University Press , 2015 https://nhigham.com/2016/03/29/the top 10 algorithms in applied mathematics A gentle introduction to optimization / B. Guenin , J. Könemann , L. Tunçel Cambridge University Press |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | Examen Partiel |
| 9 | |
| 10 | |
| 11 | |
| 12 | |
| 13 | |
| 14 |
Practice Topics
| Week | Weekly Contents |
|---|---|
| 8 | Examen Partiel |
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 3 | 60 |
| Contribution of final exam to overall grade | 0 | 40 |
| Toplam | 3 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 1 | 25 |
| Midterm Examinations (including preparation) | 1 | 25 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 1 | 10 |
| 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 |
| 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 | 3 | 42 |
| Working Hours out of Class | 3 | 10 | 30 |
| Assignments | 1 | 10 | 10 |
| Presentation | 1 | 5 | 5 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 1 | 3 | 3 |
| Final Examinations (including preparation) | 1 | 25 | 25 |
| 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 |
| Make-up | 0 | 0 | 0 |
| Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Bütünleme | 0 | 0 | 0 |
| Total Workload | 125 | ||
| Total Workload / 25 | 5.00 | ||
| Credits ECTS | 5 | ||