# Math 480b Topics

## Linear algebra

- row reduction of matrices
- solving systems of linear equations
- computing determinants and characteristic polynomials
- finding eigenvalues and eigenvectors
- subspaces of vector spaces

## Algebra

- factoring polynomials
- symbolically finding roots of polynomials
- solving systems of polynomial equations
- drawing cayley graphs of groups
- number fields and Galois groups

## Combinatorics, Probability, and Statistics

- plotting graphs (vertices and edges)
- computing invariants of graphs (automorphism group, shortest path, etc.)
- solving Sudoku puzzles and Rubik's cube
- counting and enumerating permutations, combinations, etc.
- generating random numbers and random walks
- computing the mean, variance, standard deviation, and plotting frequency histograms
- predicting missing data (interpolation)

## Calculus

- plotting functions
- computing limits and derivatives
- finding min and max points of functions
- computing symbolic integrals
- computing definite integrals numerically
- numerically finding roots of polynomials
- summing infinite series
- solving differential equations
- parametric curves (plotting, arc length)

## Number theory and Cryptography

- enumerating and counting prime numbers
- exchanging secret messages (Diffie-Hellman and RSA)
- attacking RSA and Diffie-Hellman
- elliptic curve cryptosystems
- determining whether an integer is the area of a rational right triangle