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Syllabus ( MATH 565 )

   Basic information
Course title: Combinatorial Design Theory
Course code: MATH 565
Lecturer: Prof. Dr. Sibel ÖZKAN
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 1/2, Fall and Spring
Level of course: Second Cycle (Master's)
Type of course: Area Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: Combinatorial designs have applications in many other fields such as statistics, cryptology and coding theory. The purpose of this course is to cover commonly used combinatorial designs and show their applications. Topics include methods for the construction of different combinatorial structures, such as difference sets, symmetric designs, projective geometries, orthogonal Latin squares, transversal designs, Steiner systems, and tournaments.
   Learning outcomes Up

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

  1. Make combinatorial proofs

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment

    Method of assessment

    1. Written exam
  2. Grasp and use main combinatorial construction methods

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. See the relation between the combinatorial designs within and with other disciplines

    Contribution to Program Outcomes

    1. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    2. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    3. Acquire scientific knowledge and work independently
    4. Work effectively in multi-disciplinary research teams
    5. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
    6. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
    2. Term paper
   Contents Up
Week 1: Introduction and History
Week 2: Basics and Terminology
Week 3: Balanced Incomplete Block Designs (BIBDs)
Week 4: Symmetric BIBDs
Week 5: Transversal Designs
Week 6: Difference Sets
Week 7: Hadamard Matrices
Week 8: Resolvable BIBDs
Week 9: Latin Squares
Week 10: Orhtogonal Latin Squares
Week 11: Pairwise Balanced Designs
Week 12: Steiner Systems
Week 13: t-Designs
Week 14: Orthogonal Arrays and Codes
Week 15*: Applications
Week 16*: Final Exam
Textbooks and materials:
Recommended readings: 1. D.R. Stinson , Combinatorial Designs: Constructions and Analysis , Springer-Verlag
2. C.C. Lindner, C.A. Rodger, Design Theory, CRC Press
  * 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 25
Other in-term studies: 0
Project: 14 25
Homework: 3,5,7,9,11,13 20
Quiz: 0
Final exam: 16 30
  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: 2 14
Practice, Recitation: 0 0
Homework: 2 6
Term project: 4 14
Term project presentation: 2 1
Quiz: 0 0
Own study for mid-term exam: 10 2
Mid-term: 1 1
Personal studies for final exam: 10 2
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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