Michael Monagan, Simon Fraser University (3 lectures, 6 hours)
Lecture 0 : Gaussian Elimination Video Lec5A Lec5B
Lecture 1 : Determinants: The Schwarz-Zippel Lemma, Gentleman and Johnson's algorithm,
the Bareiss-Edmonds fraction-free algorithm, Hadamard's bound.
Video LecNotesA LecNotesB LecNotesCLecture 2A : Solving Ax=b over ℚ using a modular algorithm and using p-adic lifting with rational number reconstruction.
Video LecNotesA LecNotesBLecture 2B : Rational number reconstruction, maximal quotient rational number reconstruction.
Video LecNotesLecture 3 : The characteristic polynomial, the Berkowitz algorithm.
Video LecNotesA LecNotesB Berkowitz.pdf