RE: Can I just say, and I'm just being honest...
March 6, 2017 at 1:14 am
(This post was last modified: March 6, 2017 at 2:47 am by Kernel Sohcahtoa.)
I just finished reading a section of my abstract algebra book and gained a new appreciation for how beautiful the laws of exponents are, especially as they pertain to groups. I enjoyed the idea that if there is a non-zero integer m such that a^m=e (the identity), then there exists a positive integer n, such that a^n=e, where n (the least positive integer) would be the order of a (Pinter, pg 105)*. Hence, IMO, seeing the concepts of the least positive integer and the division algorithm (cool ideas that I encountered in my studies of discrete math) being used in a way that brought harmony and clarity to the proofs of the theorems covered in the section, just reminded me how cool math is and how constructing proofs and coming up with mathematical ideas requires a mixture of creativity, fun, logic, and a willingness to get one's hands dirty.
Reference
* Pinter, Charles C. (2010). A Book of Abstract Algebra. New York: Dover Publications INC.
Reference
* Pinter, Charles C. (2010). A Book of Abstract Algebra. New York: Dover Publications INC.