Part One, Linear Algebra: Orthogonal matrices, Bilinear forms, The spectral theorem.






Part Two, Groups: The Sylow Theorem, Generators and relations, The Todd-Coxeter Algorithm, The group of motions of the plane, Finite subgroups of the rotation group, The classical linear groups, The Lie algebra.






Part Three, Rings: Maximal and prime ideals, Algebraic geometry, Algebraic integers, Ideal factorization, Some Diophantine Equations.






Part Four, Fields: Constructions with Ruler and compass, Finite fields, Function fields, The main theorem of Galois theory, primitive elements, Kummer extensions, Cyclotomic extensions.






Part Five, Modules: Diagonalization of integer matrices, The structure theorem for abelian groups, Application to linear operators.






Part Six, Group representations: Permutation representations, Regular representations, Unitary representations, Characters, Schur lemma, Orthogonality Relations.






Part Seven, Other topics: