Bologna Information System

  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Learning Outcomes
    1-To be able to express an idea in the language of mathematics
    2-To be able to apply methods of proof
    3-To be able to use basic properties of sets, relations and functions
  • ActivityPercentage


    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14342
    Classroom study (Pre-study, practice)14570
    Short-Term Exams (exam + preparation) 102510
    Midterm exams (exam + preparation)30188
    Laboratory 0000
    Final exam (exam + preparation) 5011212
    Other 0000
    Total Workload (hours)   152
    Total Workload (hours) / 30 (s)     5,07 ---- (5)
    ECTS Credit   5
  • Course Content
  • Week Topics Study Metarials
    1 Basic notions about propositions and introduction to algebra of propositions (conjunction and disjunction)
    2 Implication (conditional) and equivalence (biconditional)
    3 Quantifiers
    4 The notions of axiom, theorem and proof, introduction to methods of proof (proof by truth table and direct proof)
    5 Indirect proof methods, proof by contrapositive and proof by contradiction, falsification methods (giving counterexample, finding conflict)
    6 Mathematical induction
    7 More examples about methods of proof
    8 Basic notions of sets, Boolean operations on sets
    9 Finite-infinite intersections and unions, products of sets and basic notions about product sets
    10 Relations and their basic properties
    11 Equivalance relation
    12 Order relations
    13 Functions and their basic notions
    14 Equivalance Sets
    Prerequisites -
    Language of Instruction Turkish
    Course Coordinator Assist. Prof. Dr. Nihal Bircan
    Instructors -
    Assistants -
    Resources Matematiğin Temelleri, Halil İbrahim Karakaş, ODTÜ Geliştirme Vakfı Yayınları, 2011
    Supplementary Book Soyut Matematik, Hüseyin Irmak, Pegem Akademi, 2008
    Document -
    Goals To gain the student the ability of expressing an idea in the language of mathematics and proof skills, to teach the notions of set, relation and function
    Content Basic notions on propositions. If and if and only if connectives. Quantifiers. Notions of axiom, theorem, and proof, introduction to proof techniques. Indirect proof techniques. Proof by induction. Eamples to proof techniques. Basic notions on sets. Finite-infinite intersections and unions, basic notions on product sets. Relation and basic properties. Equivalence relation. Ordering relations. Functions and basic notions on them. Equivalent sets.
  • 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 5
    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 3
    5 To have the qualification of studying independently in a problem or a project requiring mathematical knowledge 2
    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 2
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge 2
    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 3
    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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