Bologna Information System

  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Learning Outcomes
    1-To explain metric spaces, complete metric spaces and properties of complete metric spaces
    2-To explain some basic structures like open-closed sets and limit of sequences
    3-To explain the concepts of normed spaces, linear operators and linear functionals on normed spaces
    4-To explain the fundamental theorems of functional analysis like hahn-banach theorem, banach steinhauss theorem, open mapping and closed graphs theorems
  • ActivityPercentage


    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14456
    Classroom study (Pre-study, practice)12784
    Short-Term Exams (exam + preparation) 1021530
    Midterm exams (exam + preparation)3011616
    Laboratory 0000
    Final exam (exam + preparation) 5012020
    Other 0000
    Total Workload (hours)   234
    Total Workload (hours) / 30 (s)     7,8 ---- (8)
    ECTS Credit   8
  • Course Content
  • Week Topics Study Metarials
    1 Metric and Metric spaces, neighborhood of a point , open and closed sets in metric spaces
    2 Sequences in metric spaces and their convergence, Hölder and Minkowski inequalities, Classical sequence spaces
    3 Complete metric spaces, First and second countable metric spaces, Baire Category Theorem
    4 Continuous functions between metric spaces and their properties
    5 Vector space, subspace, norm, normed space, Banach space, examples of normed spaces,
    6 Finite dimensional normed spaces
    7 Bounded and continuous linear operators
    8 Linear operators and functionals in finite dimensional spaces, Normed operator spaces, Dual space
    9 Hahn-Banach Teorem, Hahn-Banach Theorem for normed spaces
    10 Applications of bounded linear functionals defined on continuous function spaces, Reflexive spaces
    11 Banach-Steinhaus Theorem and its applications
    12 Open Mapping Theorem and its applications
    13 Closed linear operators
    14 Closed Graph theorem and its applications
    Prerequisites -
    Language of Instruction Turkish
    Course Coordinator Prof. Dr. Hüseyin IRMAK

    1-)Doktor Öğretim Üyesi Gülsüm Ulusoy Ada

    Assistants -
    Resources Fonksiyonel Analize Giriş I, Erwin Kreyszig den uyarlayan Prof. Dr. Öner Çakar, Ankara Üniversitesi Yayınları, 2007.
    Supplementary Book [1] Yüksel SOYKAN, Fonksiyonel Analiz, Nobel yayın dağıtım. 2008, Ankara. [2] Erdoğan S. Şuhubi, Fonksiyonel analiz, İTÜ vakfı yayınları, 2001. [3] Tosun Terzioğlu, Fonksiyonel Analizin Yöntemleri, Matematik Vakfı, 1998.
    Document Lecture notes
    Goals -
    Content -
  • Program Learning Outcomes
  • Program Learning Outcomes Level of Contribution
    1 To have a grasp of theoretical and applied knowledge in main fields of mathematics 5
    2 To have the ability of abstract thinking 4
    3 To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps 5
    4 To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life 2
    5 To have the qualification of studying independently in a problem or a project requiring mathematical knowledge 3
    6 To be able to work compatibly and effectively in national and international groups and take responsibility -
    7 To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge 5
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge 5
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time 3
    10 To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally 4
    11 To be able to produce projects and arrange activities with awareness of social responsibility -
    12 To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level -
    13 To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results -
    14 To have the awareness of acting compatible with social, scientific, cultural and ethical values -
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