Topic Index of Computer Algebra Lecture Videos

Algebraic numbers [L1]
Analysis of algorithms [L2]

Ben–Or Tiwari sparse interpolation [L3A]
Berkowitz algorithm [L3]
Berlekamp–Hensel factorization procedure [L1]
Binary powering with remainder [L3]
Black box polynomial representation [L1]
Brown's GCD algorithm [L1A, L1B]
Buchberger's Groebner basis algorithm [L4A]

Cantor–Zassenhaus factorization algorithm [L2]
Chinese remainder algorithm [L1]

Determinants [L1] [Bareiss Edmonds algorithm] [Gentleman Johnson algorithm] [Hadamard bound]
Diophantine equations [L2]
Dixon's Lemma [L3A]

Euclidean algorithm [L3] [L1]
Euclidean domain [L4] [L1]

Fast Fourier Transform [L1] and [L3A]
Fast polynomial multiplication [L1]
Fast polynomial division [L4A]
Fast multipoint evaluation [L4B]

Gaussian Elimination [L0]
Graded lexicographical order [L2A]
Greatest common divisors [Integer] [Polynomial] [Modular] [Brown's algorithm] [Zippel's algorithm]
Groebner bases [Applications] [Buchberger's Algorithm] [Definition] [Properties]

Hadamard bound [L1]
Heaps (algorithms) [L4A]
Hensel lifting [L3]
Hermite reduction [L1]
Hilbert basis theorem [L3B]
Homomorphism [L1]
Horowitz' algorithm [L1]

Ideals (in polynomial rings) [L1]
Integer multiplication [L1] [L2]
Integer GCD [L3]
Integer square–root [L1]
Integral domains [L4]
Integration [Rational Function] [Elementary Function]
Intermediate expression swell [L3]

Karatsuba's algorithm [L1]

Lexicographical order [L2A]
Linear Algebra [Determinants] [Characteristic polynomials] [Gaussian elimination] [Solving A x = b]

Maple tutorial [L2]
Mignotte bound [L1B]
Modular GCD algorithm [L3]
Monomial orderings [L2A]
Multivariate polynomials [L2]

Norms of algebraic numbers [L3]

P–adic representations [L1]
Polynomial (multivariate) data structures in Maple, Singular, Pari and Trip [L4B]
Polynomial division
[Univariate] [Multivariate] [Pseudo Division] [Groebner Bases] [Using a heap]
Polynomial factorization [Square free] [Berlekamp–Hensel] [Cantor–Zassenhaus] [Trager] [Tutorial]
Polynomial GCD algorithms [Euclid] [Primitive] [Modular] [Hensel lifting] [Brown] [Zippel]
Polynomial interpolation [L2] [Ben–Or Tiwari] [Zippel]
Polynomial multiplication using [the CRT] [the FFT] [merging] [divide–conquer] [a heap]
Polynomial square–root [L2]
Primitive Elements [L2]
Primitive Euclidean algorithm [L3]
Pseudo division [L3]

Rational number reconstruction [L2B]
Resultant [Computation] [Sylvester] [Trager–Rothstein]
Rational function integration [L1,L2]
Risch integration procedure [L3,L4,L5]

Schwartz–Zippel Lemma [L1]
Square–free factorization [L1]
Solving polynomial systems using Groebner bases [L4B]
Sparse polynomial data structures in Maple, Singular, Pari and Trip [L4B]
Sparse polynomial interpolation
[L1]
Stein's binary GCD algorithm
[L3]
Symbolic differentiation [L3]

Univariate polynomials [L1]
Unlucky primes [L4] and [L1A]
Unlucky evaluation points [L1B]

Vandermonde systems (solving) [L2]

Zero divisors [L4]
Zippel's sparse interpolation algorithm [L2]