Abstract Algebra

The Human Face of Abstract Algebra

Fred teaches Abstract Algebra.

An upper-level, university-tier mathematics textbook in Linear Algebra which includes all the standard topics . . .

Binary operations.  Groupoids.  Semigroups.  The Generalized Associative law.  Monoids.  Groups with left and right inverses, right cancelation, permutations.  Symmetric groups.  Cayley's theorem.  Subgroups and the Subgroup test.  Eleven facts about Cosets.  Partitions.  Lagrange's theorem and the order of a group.  Normal groups.  Factor groups.  Three super functions: isomorphisms, homomorphisms, and automorphisms.  Simple groups.  Hamiltonian groups.  Sporadic groups.  The Monster Group.  Inner automorphisms.  Kernels.  Fundamental Isomorphism Theorem of Group Homomorphisms. Center of group.  Centralizers.  Normalizers.  Direct product of groups.  Cyclic groups.  Fundamental Theorem of Finite Abelian Groups.  Sylow's three theorems.  Cauchy's theorem.  Rings.  Subrings.  Centers.  Direct sums.  Ideals.  Quotient rings.  Polynomial rings.  Integral domains.  Norm functions.  Euclidean domains.  Unique factorization domains.  Fields.  Field extentions.  Fundamental Theorem of Field Theory.  Algebraic and Transcendental extensions.  Vector spaces.