• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

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

1. Construct and use resolvable designs

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
   3. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   4. Analyze critically and evaluate his/her findings and those of others,
   5. Question and find out innovative approaches.
   6. Acquire scientific knowledge and work independently,
   7. Develop mathematical, communicative, problem-solving, brainstorming skills.
   8. Effectively express his/her research ideas and findings both orally and in writing

   Method of assessment

   1. Written exam
   2. Homework assignment
   3. Term paper
2. Get a deep understanding of Frame techniques and use them in other constructions

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
   3. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   4. Analyze critically and evaluate his/her findings and those of others,
   5. Acquire scientific knowledge and work independently,
   6. Design and conduct research projects independently
   7. Develop mathematical, communicative, problem-solving, brainstorming skills.
   8. Effectively express his/her research ideas and findings both orally and in writing

   Method of assessment

   1. Written exam
   2. Homework assignment
   3. Term paper
3. Construct difference families and difference sets, also grasp the necessary algebraic and geometric tools

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Gain original, independent and critical thinking, and develop theoretical concepts and tools,
   3. Understand relevant research methodologies and techniques and their appropriate application within his/her research field,
   4. Question and find out innovative approaches.
   5. Acquire scientific knowledge and work independently,
   6. Design and conduct research projects independently
   7. Develop mathematical, communicative, problem-solving, brainstorming skills.
   8. Support his/her ideas with various arguments and present them clearly to a range of audience, formally and informally through a variety of techniques

   Method of assessment

   1. Written exam
   2. Homework assignment
   3. Term paper
4. Apply designs and difference families to other areas such as coding theory

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics in a specialized way
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Work effectively in multi-disciplinary research teams
   4. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
   5. Support his/her ideas with various arguments and present them clearly to a range of audience, formally and informally through a variety of techniques
   6. Be aware of issues relating to the rights of other researchers and of research subjects e.g. confidentiality, attribution, copyright, ethics, malpractice, ownership of data

   Method of assessment

   1. Written exam
   2. Homework assignment
   3. Term paper

Contents
Week 1:	Review of Balanced Incomplete Block Designs
Week 2:	Group Divisible Designs
Week 3:	Recursive Frame Constructions
Week 4:	Direct Frame Constructions
Week 5:	Near Resolvable Designs
Week 6:	Constructing Resolvable Designs using Finite Geometries
Week 7:	Constructing Resolvable Designs using Frames
Week 8:	Constructing Resolvable Designs using Color Classes
Week 9:	Automorphism of Designs and Group Actions
Week 10:	Difference Families and Designs
Week 11:	Difference Sets and Designs
Week 12:	Bruck -Ryser -Chowla Theorem
Week 13:	Multipliers
Week 14:	Difference sets from Geometry. Optical Orthogonal Codes and Difference Families.
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	S. Furino, Y. Miao, J. Yin, Frames and Resolvable Designs, CRC Press
Recommended readings:	E. H. Moore, H. S. Pollatsek, Difference Sets: Connecting Algebra, Combinatorics and Geometry, American Mathematical Society
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:		0
Other in-term studies:		0
Project:	13, 14	25
Homework:	3,5, 7,9, 11	40
Quiz:		0
Final exam:	16	35
	Total weight:	(%)

Workload
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:	9	5
Term project:	2	14
Term project presentation:	1	2
Quiz:	0	0
Own study for mid-term exam:	0	0
Mid-term:	0	0
Personal studies for final exam:	10	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)