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

Basic information
Course title:	Symbolic Computation
Course code:	CSE 626
Lecturer:	Assist. Prof. Zafeirakis ZAFEIRAKOPOULOS
ECTS credits:	7,5
GTU credits:	3 (3+0+0)
Year, Semester:	2016, Fall
Level of course:	Third Cycle (Doctoral)
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:	This course aims to introduce the basic concepts and tools of symbolic computation to graduate students. By the end of this course, students will know how to model a problem coming from engineering or sciences and apply tools from symbolic computation in order to solve it. The students will learn how to design algorithms for the computation of exact solutions and how to use symbolic computation in applications.

Learning outcomes

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

1. Understand the difference between numeric and symbolic computation.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Computer Engineering in a specialized way
   2. Use advanced knowledge of mathematics, science, and engineering

   Method of assessment

   1. Written exam
2. Use symbolic computation for applications in engineering and sciences.

   Contribution to Program Outcomes

   1. Use advanced knowledge of mathematics, science, and engineering
   2. Formulate and make analytical and experimental researches, and analyze the complicated issues during design and application process
   3. Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment,

   Method of assessment

   1. Homework assignment
3. Analyze non-numeric algorithms and design algebraic, geometric and combinatorial algorithms.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Computer Engineering in a specialized way

   Method of assessment

   1. Written exam
   2. Homework assignment

Contents
Week 1:	History and importance of symbolic computation
Week 2:	Combinatorial Counting
Week 3:	Groups, Rings, Fields and Polynomial Rings
Week 4:	Exact Arithmetic and Fast Algorithms: Matrix Multiplication, FFT, GCD etc.
Week 5:	Univariate polynomial solving
Week 6:	Multivariate polynomials: division, ideals, varieties, Groebner Bases
Week 7:	Polynomial Systems: Modeling and Solving (Kinematics, Biology, Graph theory)
Week 8:	Midterm
Week 9:	Parallel Symbolic Computation
Week 10:	Parallel Symbolic Computation
Week 11:	Recurrences
Week 12:	Applications and Research Problems
Week 13:	Project Presentations
Week 14:	Project Presentations
Week 15*:	Review
Week 16*:	Final Exam
Textbooks and materials:	Joachim Von Zur Gathen and Jurgen Gerhard. 2003. Modern Computer Algebra (2 ed.). Cambridge University Press, New York, NY, USA.
Recommended readings:	None
	* 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:	8	25
Other in-term studies:		0
Project:		40
Homework:	3,6,10,12	10
Quiz:		0
Final exam:	16	25
	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	6
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	12	1
Mid-term:	3	1
Personal studies for final exam:	12	1
Final exam:	3	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)