| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6020 | Mathematical Biology | Fall Spring |
3 | 0 | 3 | 8 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | Tr |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Prof. Dr. CANAN ÇELİK KARAASLANLI |
| Course Objectives: | This course introduces many mathematical models in biology. To use the mathematical tools like difference equations, differential equations to model various biological phenomena, and also understand the basic analytical method based on calculus and algebra, qualitative analysis based on elementary geometry and computer aid numerical method to completely analize some basic models. These mathematical tools will be useful for life sciences major students in any quantitative and qualitative analysis in the future. Biological applications include various population growth models. |
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The students who have succeeded in this course; The students who succeeded in this course; will be able to have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. will be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics. will be able to define and analyze problems and to find solutions based on scientific methods. will be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials. will be able to criticize and renew her/his own models and solutions. will be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way. will be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively. will be able to behave in accordance with social, scientific and ethical values while applying solutions. |
| Biological applications of linear/nonlinear Difference Equations, theory and examples. Biological applications of Linear/Nonlinear differential equations. Biological applications of partial differential equations. |
| Week | Subject | Related Preparation | |
| 1) | Mathematical models: Linear Models: | ||
| 2) | Discrete and continuous dynamical systems : overview | ||
| 3) | Continuous Population Models | ||
| 4) | Delay Modelss | ||
| 5) | Discrete Logistic Models | ||
| 6) | Models for Interacting Populatıons | ||
| 7) | Infectious diseases models, SIS models. | ||
| 8) | Bifurcation Anaysis, Center Manifold Reduction | ||
| 9) | Population genetics and evolution | ||
| 10) | Age-structured models | ||
| 11) | Pattern formation, Turing Instability | ||
| 12) | Activator-Inhibitor Systems | ||
| 13) | Tumor-Growth Models | ||
| 14) | Reaksiyon ve yayılma denklemleri | ||
| Course Notes: | 1-Mathematical Bıology: an introduction, J. D. Murray, 1993. 2-Mathematical Models in Biology: L. Edelstein-Keshet,SIAM, 2005. 2-Steven Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering", Publisher: Perseus Books Publishing, ISBN-10: 0-7382-0453-6. |
| References: | 1- An introduction to Mathematical Biology, L.J.S. Allen, 2007, Pearson Education. |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | 3 | % 10 |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 1 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 3 | 15 | 45 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 3 | 15 | 45 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 30 | 30 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 38 | 38 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |