MAT 330 Abstract Algebra-I
This course defines and investigates the key properties of the mathematical structure called an algebraic group, studying many examples, including groups of numbers, groups of functions, and groups of matrices, with the goal of determining the common properties of all of these mathematical systems. Topics include the basic properties of the integers, permutation groups, subgroups, Lagrange's Theorem, quotient groups, isomorphisms and homomorphisms, and Cayley's Theorem.