MATH 663 | Course Introduction and Application Information - M.SC. in Computer Engineering (Without Thesis)

Course Name

Biomathematics

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 663	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Third 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. Ayşe BELER

Course Objectives

This course introduces many mathematical models in biology. To use the mathematical tools like difference equations, differential equations, probability theory 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

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	will be able to have a grasp of basic mathematics, applied mathematics and theories and applications of statistics.
2	will be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics.
3	will be able to define and analyze problems and to find solutions based on scientific methods.
4	will be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials.
5	will be able to criticize and renew her/his own models and solutions.
6	will be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way.
7	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.
8	will be able to behave in accordance with social, scientific and ethical values while applying solutions.

Course Description

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

Course Category	Core Courses
	Major Area Courses
	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	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5	LO 6	LO 7	LO 8
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	6	84
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury	1	25	25
Project	1	25	25
Seminar / Workshop			0
Oral Exam			0
Midterms			0
Final Exam	1	43	43
		Total	225

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information.		-	-	-	X	-
2	Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations.		-	-	-	-	X
3	Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines.		-	-	-	X	-
4	Is informed about new and upcoming applications in the field and learns them whenever necessary.		-	-	-	-	X
5	Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions.		-	-	-	-	X
6	Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs.		-	-	-	X	-
7	Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process.		-	-	-	X	-
8	Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility.		-	-	-	-	X
9	Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.		-	-	X	-	-
10	Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.		-	-	X	-	-
11	Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications.		-	-	X	-	-
12	Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity.		-	X	-	-	-

MATH 663 | Course Introduction and Application Information

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