Purpose of Abstract Algebra

There is a tough course that most math majors must take called abstract algebra or modern algebra.

1. What is abstract algebra?

2. What is the importance of abstract algebra in the real world?

 

abstract algebra is a branch of mathematics in which algebraic concepts are generalized by using symbols to represent basic arithmetical operations
abstract algebra courses introduce students to advanced mathematical concepts such as group theory and lattices

Roughly speaking, abstract algebra is the study of what happens when certain properties of number systems are abstracted out; for instance, altering the definitions of the basic arithmetic operations result in a structure known as a ring, so long as the operations are consistent.
Some of the real-life applications of abstract algebra : Vector Space in Physics and Groups in Differential Geometry: The development of vector spaces has helped physicists solve the complex space and location problem.

A significant amount of abstract algebra is used in cryptography generally. Group theory has many applications. One example is in robotics Group Theory application in Robotics, Computer Vision and Computer Graphics.

 

Thank you. I will not study abstract algebra. I would be overjoyed to develop a decent understanding of calculus l, ll, and lll. What more do I need in my late 50s?