CISC 822 Algebraic Algorithms
Course meeting time in 107 Memorial Hall:
11:00-12:15 Tuesdays, Thursdays.
May move to Smith 102A or 426.
The textbook "Modern Computer Algebra, 3rd Edition,"
by Joachim von zur Gathen and Juergen Gerhard,
ISBN-13: 978-1107039032 ISBN-10: 1107039037,
will be used. ($120 from bookstore, $104.28 + shipping from Amazon)
Instructor: David Saunders,
home page includes
office location, office hours, phone #s, etc.
Click here for an
evolving summary of course progress
Summary of core topics to be covered.
First Reading assignment:
- Multiplication, inversion, division of integers, polynomials, matrices.
- Integer and polynomial greatest common divisor and factorization.
- Lattice reduction with applications.
- Matrix factorizations and canonical forms.
- Gaussian elimination and blackbox methods for sparse matrix computation.
- Linear system solving for nonsingular and singular systems with dense, sparse, or structured matrices.
- High performance methods in exact linear algebra.
This is rather extensive. Future readings
will be fewer pages (but with the intent of more careful study).
Here "scan" means read through, not necessarily absorbing all details. The point is to have the general idea of what is there so that it can be consulted later as the need arises.
On the other hand, "Read" means to read more carefully, absorb what you see and synthesize it with what you already know.
- Scan Introduction. Purpose: overview of topics, see authors' general view of computer algebra, aka symbolic mathematical computation.
- Scan chapter 1. Purpose: see some sample applications for which
numerical floating point approximation won't do.
Exact or symbolic computation is needed.
- Scan chapter 2.1, 2.2. Purpose: familiarity with notation used.
- Read chapter 2.3. Purpose:
- Review classical methods of arithmetic as
a base case against which to compare faster methods studied later.
- Compare multiplication of polynomials and of integers (algorithms 2.3 and 2.4).
Tentative conclusion: integers are harder to deal with.
- Compare multiplication and division (algorithms 2.3 and 2.5). Tentative conclusion: division is more complicated than multiplication.
- Read chapter 3. Purpose: understand EEA, Extended Euclidean Algorithm.
Viète, a source of our algebraic notational convention [JC, thanks for the link].