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İzmir Ekonomi Üniversitesi

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    GRADUATE SCHOOL

    M.SC. in Computer Engineering (Without Thesis)

    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
    Mode of Delivery -
    Teaching Methods and Techniques of the Course Problem Solving
    Q&A
    Lecture / Presentation
    National Occupation Classification -
    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;

    • 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 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

     

    WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

    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

     

    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

    #
    		 PC Sub Program Competencies/Outcomes
    * Contribution Level
    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
    -
    -
    -

    *1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

     

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