Spring 2023 - MATH 701 G100
Computer Algebra (3)
Class Number: 5318
Delivery Method: In Person
Course Times + Location:
Tu 2:30 PM – 4:20 PM
AQ 5037, Burnaby
Th 2:30 PM – 3:20 PM
AQ 5037, Burnaby
Exam Times + Location:
Apr 21, 2023
9:00 AM – 9:00 AM
TAKE HOME-EXAM, Burnaby
1 778 782-4279
Data structures and algorithms for mathematical objects, including long integers, polynomials, and general mathematical formulae. Topics include computing polynomial greatest common divisors, the Fast Fourier transform, Hensel's lemma and p-adic methods, differentiation and simplification of formulae, and polynomial factorization. Students will use a computer algebra system such as Maple for calculations and programming. Students may not take a 700-division course if it is being offered in conjunction with a 400-division course which they have taken previously.
Course DescriptionThe focus of the course is on the algebra of and computing with long integers, polynomials, rational functions, and the elementary functions. We will use Maple for calculations.
The main topics covered will be:
- Algorithms for long integer multiplication and GCD.
- Non-unique factorization and unique factorization.
- Euclidean domains, the Euclidean algorithm and applications.
- How do systems like Maple represent a formula on the computer?
- Simplification and differentiation of a formula.
- The Fast Fourier Transform and applications.
- The Chinese remainder theorem and polynomial GCD computation.
- The P-adic Newton iteration.
- Probabilisitic algorithms for polynomial factorization over finite fields.
- Hensel's lemma and polynomial factorization over the integers.
- The Sylvester Resultant.
Note: this is a cross-listed course with MACM401/MATH 801.
- 6 Assignments 50%
- Course Project 10%
- Final Exam 40%
Note: all 3 courses (MATH 401, MATH 701, MATH 801) run Tuesday 2:30 - 4:20 plus Thursday 2:30 - 4:20 (lecture 2:30 - 3:20 plus tutorial 3:30 - 4:20).
THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.
Course notes will be provided.
Algorithms for Computer Algebra, 1 / E
Author: KO Geddes, SR Czapor, G. Labahn
Publisher: Kluwer Academic, 1992
Students are not required to purchase this text. For those who wish to purchase a physical copy, the text is available on Amazon.
Modern Computer Algebra
Author: von zur Gathen, J & Gerhard, J.
As above, purchase of this text is not required.
REQUIRED READING NOTES:
Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.
Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html