Spring 2021 - MATH 701 G100
Computer Algebra (3)
Class Number: 3885
Delivery Method: Remote
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.
This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.
You will need a camera to take photographs of your work. A phone is acceptable
The 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.
- Resultants and rational function integration methods.
- Lecture: synchronous- lectures will be held at fixed times, on-line
- Midterm(s): synchronous; date: TBA
- Final exam: synchronous; date: TBA
Note: this is a cross-listed course with MACM 401/ MATH 801
- 5 Assignments (10% each) 50%
- Final Exam (24 hour take-home) 50%
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.
- Access to strong and reliable internet.
- Ability to scan documents (phone app acceptable)
- Access to webcam and microphone (embedded in computer sufficient)
Algorithms for Computer Algebra, 1 / E
Author: KO Geddes, SR Czapor, G. Labahn
Publisher: Kluwer Academic, 1992
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 web site 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
TEACHING AT SFU IN SPRING 2021
Teaching at SFU in spring 2021 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (email@example.com or 778-782-3112).