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Syllabus ( MATH 115 )


   Basic information
Course title: Discrete Mathematics
Course code: MATH 115
Lecturer: Assoc. Prof. Dr. Selçuk TOPAL
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 1, Fall
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: The aim of the course is to introduce students to the fundamentals of discrete structures. Discrete Mathematics is fundamental for mathematical thinking, information technologies and computer sciences. Topics of this course include Logic, Methods of Proof, Sets, Functions, Relations, Counting and Graph theory.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Formulate proofs in basic level and apply elementary logic

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Adapt to a fast-changing technological environment, improving their knowledge and abilities constantly.

    Method of assessment

    1. Written exam
  2. Discuss and use set theoretic techniques

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Using technology as an efficient tool to understand mathematics and apply it.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Solve problems in combinatorics (permutations, combinations, counting)

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
  4. Perform various operations with relations and functions

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Using technology as an efficient tool to understand mathematics and apply it.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
  5. Explain and use the concepts of graphs and trees

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Logic; Propositional Equivalences
Week 2: Predicates and Quantifiers
Week 3: Methods of Proof
Week 4: Sets; Set Operations; Functions
Week 5: The Integers and Division
Week 6: Mathematical Induction
Week 7: The Basics of Counting; The Pigeonhole Principle
Week 8: Permutations and Combinations; Inclusion-Exclusion, Midterm
Week 9: Relations and Their Properties
Week 10: Representing Relations; Recurrence Relations
Week 11: Equivalence Relations
Week 12: Axiomatic Structure of Real Numbers
Week 13: Introduction to Groups, Rings, and Fields
Week 14: Introduction to Graphs; Graph Terminology, Graph Isomorphism, Introduction to Trees
Week 15*: -
Week 16*: Final Exam
Textbooks and materials:
Recommended readings: 1. Kenneth H. Rosen, Discrete Mathematics and Its Applications, Fifth Edition, McGraw-Hill.
2. George Polya, How to Solve It, Princeton University Press.
3. R.P. Grimaldi, Discrete and Combinatorial Mathematics, Addison-Wesley.
4. E.G. Goodaire and M.M. Parmenter, Discrete Mathematics, Prentice Hall
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 30
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 3,5,7,9,11,13 20
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 4 14
Practice, Recitation: 0 0
Homework: 1 6
Term project: 0 0
Term project presentation: 0 0
Quiz: 1 6
Own study for mid-term exam: 15 1
Mid-term: 2 1
Personal studies for final exam: 20 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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