MATHEMATICS (TURKISH, PHD)
PhD	TR-NQF-HE: Level 8	QF-EHEA: Third Cycle	EQF-LLL: Level 8

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT6020	Mathematical Biology	Fall	3	0	3	8

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	Turkish
Type of course:	Departmental Elective
Course Level:
Mode of Delivery:	Face to face
Course Coordinator :	Prof. Dr. CANAN ÇELİK KARAASLANLI
Recommended Optional Program Components:	Matlab
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.

Learning Outcomes

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.

Course Content

Biological applications of linear/nonlinear Difference Equations, theory and examples. Biological applications of Linear/Nonlinear differential equations. Biological applications of partial differential equations.

Weekly Detailed Course Contents

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

Sources

Course Notes / Textbooks:	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.

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Homework Assignments	3	% 10
Midterms	1	% 40
Final	1	% 50
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 50
PERCENTAGE OF FINAL WORK		% 50
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	3	15	45
Homework Assignments	3	15	45
Midterms	1	30	30
Final	1	38	38
Total Workload			200

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

Program Outcomes

Level of Contribution