MATH 400 | Course Introduction and Application Information - Department of Mathematics

Course Name

Biomathematics

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 400	Fall/Spring	3	0	3	7

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	First Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	Problem Solving Q&A Lecture / Presentation
National Occupation Classification	-
Course Coordinator	-
Course Lecturer(s)	Doç. Dr. Sevin GÜMGÜM
Assistant(s)	Araş. Gör. Dr. Ayşe BELER Araş. Gör. Merve KAHRAMAN ARİMAN Araş. Gör. Sıla Selenay KOÇ

Course Objectives

In this course, how to use basic mathematical concepts such as some basic concepts in analysis and algebra, difference equations, probability theory in different biological cases will be given. On the other hand, qualitative analysis of geometry and numerical computation techniques will be done on computers.

Learning Outcomes

The students who succeeded in this course;

will be able to analyze models theoretically and visually.
will be able to interpret population models.
will be able to do biology applications in data analysis.
will be able to solve linear or nonlinear dynamic systems.
will be able to solve biology problems with graph theory.

Course Description

Biological applications of difference and differential equations. Biological applications of nonlinear differential equations. Biological applications of graph theaory.

Course Category	Core Courses
	Major Area Courses	X
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Linear differential equations: theory and examples, introduction, basic definitions and notation, first-order linear systems	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 4.1, 4.2, 4.7
2	Phase Analysis, an example: Pharmacokinetics model	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 4.8, 4.10
3	Application to population growth models, delay logistic equation	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 5.3, 5.9
4	Biological applications of differential equations; harvesting a single population, predator-prey models, competiton models	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 6.2, 6.3, 6.4
5	Chemostat model, epidemic models	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 6.7, 6.8
6	Excitable systems	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 6.9
7	Reaction-diffusion equation, spread of genes and traveling waves	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 7.3, 7.6
8	Euler method	"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 2
9	Systems of differential equations	"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 3
10	The backward Euler method and the trapezoidal method	"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 4
11	Taylor and Runge–Kutta methods	"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 5
12	Applications to biological models
13	Applications to biological models
14	Applications to biological models
15	Semester Review
16	Final Exam

Course Notes/Textbooks

"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163

Suggested Readings/Materials

"An Invitation to Biomathematics" by Raina Stefanova Robeva, James R. Kirkwood, Robin Lee Davies, Leon Farhy, Boris P. Kovatchev, Academic Press, 1st Edition, 2007. ISBN-13: 978-0120887712

"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury	1	30
Project	1	30
Seminar / Workshop
Oral Exams
Midterm
Final Exam	1	40
Total

Weighting of Semester Activities on the Final Grade	2	60
Weighting of End-of-Semester Activities on the Final Grade	1	40
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	4	56
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury	1	30	30
Project	1	30	30
Seminar / Workshop			0
Oral Exam			0
Midterms			0
Final Exam	1	46	46
		Total	210

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.		-	-	-	-	X
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.		-	-	-	X	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.		-	-	-	X	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.		-	-	-	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.		-	-	X	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.		-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.		-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.		-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.		-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.		-	-	-	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.		-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.		-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.		-	-	-	-	-