Curriculum Arun Ram |
School of Mathematics and Statistics University of Melbourne Parkville VIC 3010 Australia aram@unimelb.edu.au |
This page is built on the philosophy that the way to specify a curriculum is to specify what kinds of tasks will be expected, i.e. what the assessment will be. In other words, a curriculum is determined, whether we admit it or not, by specifying what questions can appear on the exam. If the students are not expecting a question on the exam, then the likelihood that they will learn to do that question is very low.
Some of the material available from the links below is based upon work supported by the Australian Research Council ARC grants DP0986774 and DP087995 and the US National Science Foundation under Grant No. 0353038 and earlier awards. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of these agencies.
Greatest common divisors, Euclid's algorithm, arithmetic modulo m
Fields, RSA cryptography
Bases, linear transformations, eigenvalues, direct sums invariant subspaces
Minimal polynomials, diagonalization
Jordan normal form
Properties and examples of groups, subgroups, cyclic groups orders of elements
Direct product, homomorphisms and isomorphisms, cosets
Normal subgroups, Lagrange's theorem, quotient groups
Inner products
Adjoints, spectral theorem
Group actions, orbit-stabiliser theorem, Sylow theorems