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İzmir Ekonomi Üniversitesi

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    GRADUATE SCHOOL

    M.SC. in Computer Engineering (Without Thesis)

    IE 501 | Course Introduction and Application Information

    Course Name
    Mathematics for Operations Research
    Code
    Semester
    Theory
    (hour/week)
    Application/Lab
    (hour/week)
    Local Credits
    ECTS
    IE 501
    Fall/Spring
    3
    0
    3
    7.5

    Prerequisites
    None
    Course Language
    English
    Course Type
    Elective
    Course Level
    Second Cycle
    Mode of Delivery -
    Teaching Methods and Techniques of the Course -
    National Occupation Classification -
    Course Coordinator
    Course Lecturer(s)
    Assistant(s) -
    Course Objectives The objectives of this course are to enable the students to review basic theoretical concepts of linear algebra, optimization, real analysis and functional analysis, to be exposed of operational research applications of these mathematical concepts. This course introduces the key role of mathematics in optimization and linear systems. It explains effective procedures for performing mathematical tasks that arise in many fields, including operations research, engineering, systems sciences, statistics, and economics.\nWe emphasize the basic concepts and methodologies, and include dozens of examples and applications.
    Learning Outcomes

    The students who succeeded in this course;

    • Be able to resolve linear independence and find null spaces and factors of matrices.
    • Be able to determine existence of restricted solutions to linear equations and inequalities.
    • Be able to resolve definiteness of Hermitian and real symmetric matrices by Gaussian pivoting.
    Course Description The course basically covers sets, functions, countability, compact sets, lim sup and lim inf, convergence in R, convergence in metric spaces, normed spaces, inner product spaces, convexity, and functions of several variables

     



    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 Proof, contrapositives, converses, sets Course notes
    2 Sets, functions, countability Course notes
    3 Properties of R Course notes
    4 Sequences in R, subsequences, limits of sequences Course notes
    5 Infimum and supremum of a set, lim inf and lim sup Course notes
    6 lim inf and lim sup, series Course notes
    7 Metric spaces, open and closed sets Course notes
    8 Compact sets, connected sets Course notes
    9 Convergence in metric spaces Course notes
    10 Continuous functions Course notes
    11 Properties of continuous functions Course notes
    12 Uniform continuity Course notes
    13 Vector spaces Course notes
    14 Normed spaces, inner product spaces Course notes
    15 Functions of several variables Course notes
    16 Course review

     

    Course Notes/Textbooks

    Course notes
    Suggested Readings/Materials

    - Erhan Çınlar and Robert J. Vanderbei, Mathematical Methods of Engineering Analysis, free e-book, 2000.

    - Walter Rudin, Principles of Mathematical Analysis, 3rd edition, McGraw-Hill, 1976, ISBN: 0-07-054234-X

    - Kenneth A. Ross, Elementary Analysis:The Theory of Calculus, 2nd edition, Springer, 2013, ISBN: 978-1-4614-6270-5

    - Rangarajan K. Sundaram, A First Course in Optimization Theory, Cambridge University Press, 1996, ISBN:978-0-521-49770-1

     

    EVALUATION SYSTEM

    Semester Activities Number Weigthing
    Participation
    Laboratory / Application
    Field Work
    Quizzes / Studio Critiques
    Portfolio
    Homework / Assignments
    6
    20
    Presentation / Jury
    Project
    Seminar / Workshop
    Oral Exams
    Midterm
    1
    35
    Final Exam
    1
    45
    Total

    Weighting of Semester Activities on the Final Grade
    55
    Weighting of End-of-Semester Activities on the Final Grade
    45
    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
    15
    6
    90
    Field Work
    0
    Quizzes / Studio Critiques
    0
    Portfolio
    0
    Homework / Assignments
    6
    10
    60
    Presentation / Jury
    0
    Project
    0
    Seminar / Workshop
    0
    Oral Exam
    0
    Midterms
    1
    10
    10
    Final Exam
    1
    17
    17
        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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