Refresher: Set theory and logic

Yesterday, while I was waiting for my computer to be reimaged due to some serious funk happening with my outlook mail, I had a couple hours to burn. After I killed a longer than normal walk at lunch, I sat down in the lobby with a good book.

Background: my products are reliant on a lot of technology, but one aspect is critical in how they work and are used. This being a PID Servo Control system. While you don’t need to know in depth what that is to use one of our instruments, having a deep knowledge does indeed help you get the most out of it.

Control theory is something you would imagine to be the realm of electrical engineers, but curiously, it seems to be the realm of mechanical engineering. And at the root of it is math. To understand what is really happening, and how it works, you need to know a branch of mathematics called “Discrete Mathematics”. This is the foundation of computers and computer science, dealing with the world broken into discrete pieces and processed algorithmically. (As an aside, my education is in Physics, and there we deal in continuum mathematics, similar, but distinctly different).

So I picked up a textbook. I might have mentioned in the past that Dover publishing does a wonderful job of keeping classic science and math texts in print, and affordable.

The early parts of this text are a deep dive into set theory, function representation, and logic (mathematical logic is not the same as what most people think of logic). Being a child of the 70’s, and the evolution of mathematics elementary education, I had always some concepts of sets, and operations on sets. But beyond this informal early introduction, I never really dove into the subject. Some of my physics topics touched upon it, but again, it was using set theory to get to a solution.

The first chapter was an eye opener. I realize what I had learned earlier was very shallow, and cursory, but now I have a much deeper understanding of these foundations of modern mathematics.

A good way to spend a couple hours.  Next up is counting (combinatorics).

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