GRADUATE SCHOOL
PH.D. In Applied Mathematics and Statistics
MATH 663 | Course Introduction and Application Information
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
|
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Mode of Delivery | - | |||||
Teaching Methods and Techniques of the Course | Problem SolvingQ&ALecture / Presentation | |||||
Course Coordinator | - | |||||
Course Lecturer(s) | ||||||
Assistant(s) |
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 |
The students who succeeded in this course;
|
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. |
|
Core Courses | |
Major Area Courses |
X
|
|
Supportive Courses | ||
Media and Management Skills Courses | ||
Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
Week | Subjects | Related Preparation |
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 |
EVALUATION SYSTEM
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 |
ECTS / WORKLOAD TABLE
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
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
1
|
2
|
3
|
4
|
5
|
||
1 | To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies, |
X | ||||
2 | To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts, |
X | ||||
3 | To have the ability of defining and verifying problems in Mathematics and Statistics, |
X | ||||
4 | With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application, |
X | ||||
5 | In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently, |
X | ||||
6 | To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way, |
X | ||||
7 | To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way, |
X | ||||
8 | To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual. |
X | ||||
9 | To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently, |
X | ||||
10 | To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics, |
X | ||||
11 | As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values, |
X | ||||
12 | As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them, |
X | ||||
13 | To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results, |
X | ||||
14 | To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science, |
X | ||||
15 | In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule. |
X |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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