Summer 2019 - MATH 895 G100
Class Number: 1991
Delivery Method: In Person
COURSE-LEVEL EDUCATIONAL GOALS:
1 The Fast Fourier Transform
- The FFT as an affine transformation.
- The polynomial Newton iteration.
- Fast division using the FFT.
- Fast multi-point evaluation using the FFT.
2 Computational Linear Algebra
- The Bareiss fraction-free algorithm for computing det(A) and solving Ax=b.
- The Berkowitz division free algorithm for computing det(A - lambda I)
- Solving Ax=b over Q using p-adic lifting + rational reconstruction.
3 Multivariate Polynomial Interpolation
- Browns' algorithm for multivariate polynomial GCDs.
- The Black Box model of computation.
- Zippel's sparse interpolation.
- Ben-Or/Tiwari sparse interpolation.
4 Algebraic Number Fields
- Representation of elements in Q(alpha) and calculating norms.
- The Trager-Kronecker algorithm for factoring polynomials in Q(alpha)[x].
- A modular gcd algorithm for Q(alpha)[x]
- Cyclotomic fields and solving Ax=b over Q(alpha).
5 Polynomial Data Structures and Algorithms
- Multivariate polynomial representations and term orderings.
- Polynomial multiplication and division using heaps.
- The Kronecker substitution.
6 Course Project and Additional Topics
- Course project selection.
- Writing papers using LaTex.
- Multivariate Hensel Lifting.
- 5 Assignments, 1 per topic 60%
- Course Project (presentation as a written report) 40%
MATERIALS + SUPPLIES:
Modern Computer Algebra by von zur Gathen and Gerhard
Algorithms for Computer Algebra by Geddes, Czapor and Labahn
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.
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ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS