Ebook: Abstract Algebra: Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography

Traditionally, mathematics has been separated into three main areas: algebra, anal-
ysis, and geometry. Of course, there is a great deal of overlap between these areas.
For example, topology, which is geometric in nature, owes its origins and problems
as much to analysis as to geometry. Furthermore, the basic techniques in studying
topology are predominantly algebraic. In general, algebraic methods and symbolism
pervadeall of mathematics,and it is essentialfor anyonelearninganyadvancedmath-
ematics to be familiar with the concepts and methods in abstract algebra.