Syllabus ( CSE 626 )
|
|
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:
-
Understand the difference between numeric and symbolic computation.
Contribution to Program Outcomes
-
Define and manipulate advanced concepts of Computer Engineering in a specialized way
-
Use advanced knowledge of mathematics, science, and engineering
Method of assessment
-
Written exam
-
Use symbolic computation for applications in engineering and sciences.
Contribution to Program Outcomes
-
Use advanced knowledge of mathematics, science, and engineering
-
Formulate and make analytical and experimental researches, and analyze the complicated issues during design and application process
-
Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment,
Method of assessment
-
Homework assignment
-
Analyze non-numeric algorithms and design algebraic, geometric and combinatorial algorithms.
Contribution to Program Outcomes
-
Define and manipulate advanced concepts of Computer Engineering in a specialized way
Method of assessment
-
Written exam
-
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)
|
|
|
-->
