Reading

One last stall and I promise we'll get to the good stuff. I'm going to roughly follow a book by Joseph Gallain called Contemporary Abstract Algebra. I don't think its the best book out there for the purposes of learning group theory, but it is the book that I own so I'm going to be using it as a reference and I don't see any reason not to share that with you. In the spirit of following textbooks, though, I'd like to talk about reading mathematics for a little bit.

I took this class last spring called Mathematical Models and it was taught by one of my favorite professors, Dr. Curtis Clemons. The class was useless and I was only in it for a few days, but on the first day of class Dr. Clemons asked someone if they had any experience with differential equations and the person said "no, I've just never had the time." Dr. Clemons looked a little taken by that, then he paused for a second before saying "If its something that you want to know, do the work. You've got your whole life - learn it." That's definitely something that's stuck with me, because that's how you have to approach mathematics. If you're serious about learning math then the best thing you can do is find a textbook and read until you get it.

Reading a textbook isn't like reading a novel, though. Its difficult and a lot of people have trouble with it, but it is an acquired skill and its worth doing because eventually it will pay off. I've read a lot of textbooks in my lifetime and if you care to know, I'd like to share a little bit about what I've learned. Before you can start reading you have to pick a book. Ideally, the beginning of the book is some things that you already know, and about 20 pages in should be things that are completely new. If you're having trouble picking one, talk to me and we can figure out where to start. Once you've got a book, you really need to dedicate some time to it. Its going to take a really long time and you're going to get stuck. The way I read a book is I start at the beginning and I first read until I can't keep up any more. Like I said, the beginning is familiar and then as it gets more complicated I start forgetting things and getting confused. When it starts to get so frustrating that it inhibits my learning I start the book over at the beginning. Then I start reading again and understand some more and the second time through I get a little farther before I have to start over. Eventually, I've read through the whole book and I've gathered a pretty good understanding of what I was reading.

This doesn't mean that I read without stopping. I stop all the time and reread whole pages if I need too. I stop to take notes, I flip back for reference, and sometimes I do the exercises. And most importantly, I ask questions all the time. No point in pressing forward if you don't understand where you started. You should try my suggestions and develop whatever habits work best for you. Its a process and practice makes perfect.

References

Text Reference: Gallain