Abstract Algebra
Abstract algebra (also known as modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras.
In an introductory course on abstract algebra and its application, one may teach the following topics:
Definition of binary operations
Definition of semigroups, monoids, and groups
Subgroups
Normal subgroups and quotient groups
Group homomorphisms
Automorphisms
Cayley's theorem
Sylow's theorems
Definition of rings
Ring homomorphisms
Ideals and quotient rings
Prime and maximal ideals of rings
The field of quotients of an integral domain
Euclidean rings
Polynomial and formal power series rings
For more details, refer to the following book:
Herstein, I. N. (2006). Topics in algebra. John Wiley & Sons.
For applications of abstract algebra, one may choose some topics from the following general themes:
Coding Theory
Cryptography
For more details, refer to the following book:
Lidl, R., Pilz, G. (2012). Applied Abstract Algebra. Springer Science & Business Media.
See also the following pages: