Lecture Notes in Computer
Algebra at NC State
University
These notes are all currently in PDF
format.
I typeset them using LyX.
If you would like a copy of
them in LyX, LATEX
or PostScript format, email
me.
Note: The PDF files to which these link appear to be corrupt. I will attempt to obtain correct versions in due course.
Dr. Agnes Szanto's lectures on
Solving polynomial
systems over the complex numbers (MA792K, Spring 2004):
- Finding roots of univariate
systems
- Univariate Newton's method and point estimates for approximate zeroes
- The Fundamental Theorem of Algebra
- A Homotopy Algorithm for finding zeroes of polynomials
- Finding roots of multivariate systems
Some of Dr. Hoon Hong's lectures
on Computer Algebra:
- One polynomial equation, in
one variable
- Linear equations, the quadratic formula, and the general solution of the cubic
- The general solution of the quartic
(Other lectures were removed due to a class he
taught, and I
have since lost them.)
Dr.
Michael Singer's lectures on
Symbolic
Computation (MA591U, Spring 2001) (not in chronological order, but in
an
order which made organizational sense to me):
- Foundational Material
- Introduction
- Squarefree
factorization
- Resultants
- Galois Theory of Polynomials
- Integration
- Liouville's Theorem (Introduction)
- Liouville's Theorem (Extensions of Differential Fields)
- Liouville's Theorem (Proof)
- Liouville's Theorem (Applications)
- Risch's Algorithm
- Linear Differential Equations
- Linear Differential Equations (Rational Solutions of LDEs)
- Differential Galois Theory