Credits -- 3 (3-0-0)
Term Offered -- Fall
- Possible Text
-- - Algebra by M.
Artin
- Topics
-- -
-- Matrix Operations: row reduction, determinants, permutation matrices,
Cramer's rule
-- Groups: basic definitions, subgroups, isomorphisms, homomorphisms,
equivalence relations and partitions, cosets, products, modular
arithemtic, quotient groups
-- Vector Spaces: Abstract fields, bases, dimension, computation with
bases, infinite-dimensional spaces, direct sums
-- Linear Transformations: dimension formula, matrices, linear operators
and eigenvectors, characteristic polynomials, orthogonal matrices and
rotations, diagonalization
-- Symmetry: plane figures, motions of the plane, finite and discrete
groups of motions, abstractgroup actions, coset actions, the counting
formula, permutation representations, finite subgroups of SO (3).
-- More Group Theory: group actions of the group, class equations, the
Sylow theorems, classification of groups of order p, p2, pq, etc.