https://mmwelch.net/The personal blog of Michael Welch. Rarely updated. It contains random exercises and thoughts I had mostly about programming. 2023-02-01T21:45:06-06:00 Michael Welch https://mmwelch.net/ Jekyll © 2023 Michael Welch /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png 2012-03-10T00:00:00-06:00 2023-02-01T21:04:19-06:00 https://mmwelch.net/2012/03/10/abstract-algebra-is-refactoring/ Michael Welch

In my previous post I presented a little introduction to abstract algebra. The easiest way for me to explain abstract algebra to a software developer is that it’s a lot like refactoring. What do I mean by this? Well in my last post I proved two propositions that looked very similar. However, initially, the two proofs were completely different. By stepping back and looking at what the two alg...

2012-03-07T00:00:00-06:00 2012-03-07T00:00:00-06:00 https://mmwelch.net/2012/03/07/what-is-abstract-algebra/ Michael Welch

I’ve recently begun a study of abstract algebra (also known as modern algebra) using the text  A Book of Abstract Algebra by Charles C. Pinter. I’ll give you a brief introduction to abstract algebra by way of an example. I will write two simple proofs. The first is a proof about addition of real numbers. The second is a proof about the exclusive or operation on Boolean1 values. The proofs wi...