• Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Differential Equations I MATH305 FALL 4+0 C 6
    Learning Outcomes
    1-To be able to comprehension the concept of topological space and related basic notions
    2-To be able to comprehension subspace, base, subbase
    3-To be able to expalinthe generalizations of basic notions encountered in analysis to an arbitrary topological
    4-To be able to comprehension the notion of continuity and homeomorphism
  • ActivityPercentage


    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14456
    Classroom study (Pre-study, practice)14684
    Short-Term Exams (exam + preparation) 0000
    Midterm exams (exam + preparation)3011818
    Laboratory 0000
    Final exam (exam + preparation) 6512424
    Other 0000
    Total Workload (hours)   182
    Total Workload (hours) / 30 (s)     6,07 ---- (6)
    ECTS Credit   6
  • Course Content
  • Week Topics Study Metarials
    1 Basic concepts, sets, functions, relations, countable sets, ordered sets
    2 Topology definition and examples
    3 Subspaces, open and closed sets
    4 Metric topology and examples
    5 IR usual space, open and closed sets
    6 Base and subbase for a topology
    7 Neighborhood of a point and local base of a set in topological spaces
    8 Midterm exams
    9 Limit point and closure of a set in topological spaces
    10 Interior and isolated point of a set in topological spaces
    11 Dense set and boundary of a set
    12 Continuity in topological spaces
    13 Some real valued functions
    14 Open-closed functions
    15 Homeomorphisms
    Prerequisites -
    Language of Instruction English
    Coordinator Assist Prof. Dr. Mustafa ASLANTAŞ
    Instructors -
    Assistants -
    Resources Genel Topolojiye Giriş ve Çözümlü Alıştırmalar (3. Baskı), Mahmut Koçak, 2011.
    Supplementary Book Genel Topoloji (7. Baskı), Şaziye Yüksel, Eğitim Akademi Yayınları, 2011, Topolojik uzaylar, Abdugafur Rahimov, Seçkin Yayınları, 2006, Topology (2nd Edition), James R. Munkres, Prentice Hall, Upper Saddle River, 2000 Basic Topology (Undergraduate Texts in Mathematics), M. A. Armstrong, Springer-Verlag, New York, 2010 Elementary Topology Problem Textbook, O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov, American Mathematical Society, 2008 General Topology (Schaums`s Outline Series), Seymour Lipschutz, McGraw-Hill, 2011 A General Topology Workbook, Iain T. Adamson, Birkhauser, Boston, 1996
    Goals Introducing the concept of topological space, demonstrating that real spaces studied in analysis courses are a topological space example and that many basic concepts and properties in these spaces can be generalized to any topological space
    Content Explaining basic concepts, sets, functions, relations, countable sets, ordered sets, Topology definition and examples, Subspaces, open and closed sets, Metric topology and examples ? usual space and open and closed sets, Base and subbase for a topology, Neighborhood of a point and local base of a set in topological spaces, Limit point and closure of a set in topological spaces, Interior and isolated point of a set in topological spaces, Dense set and boundary of a set, Continuity in topological spaces, Some real valued functions, Open-closed functions, Homeomorphisms.
  • Program Learning Outcomes
  • Program Learning Outcomes Level of Contribution
    1 To have a grasp of theoretical and applied knowledge in main fields of mathematics 3
    2 To have the ability of abstract thinking -
    3 To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps 4
    4 To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life -
    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 -
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge -
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time -
    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 -
    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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