Since then, the material has gotten quite sophisticated. Simultaneously, significant events in my personal life have taken my focus away from the subject. Moments of clarity have been few and far between. I am using strange rules to justify arguments that I don't believe. I am blind in a world where visualization has always been my most valuable tool. Now what do I do?
Earlier in the course I could see the structures I was learning about in my mind. I could watch the elements interact, and manipulate their behavior to simulate a result. It was not easy to do, but I was operating on some level of intuition. That intuition is now completely gone, and I'm finding this type of mathematics a most frustrating endeavor. I'm memorizing rules and trying to remember when I am supposed to use them. Algebra is not supposed to be like this. The only things that keep me going are the hope that I will finally understand the material (better late than never), and the fact that I'm not going to let this subject best me.
I wonder if there are few math-o-phobes who have tried learning the subject blindly by memorizing rules and techniques. I recall a few high school math lessons where teachers would recite, "Well, if you see a question like this then you do this. See? It works." How dreadfully boring! If I had learned all math that way, I would have sworn off the subject a long time ago. It's an awful way to go. There is no fun in it! It's easy to see how frustrating this method of learning is when I'm actively doing it.
So, to end on a positive note, here is a graph theory question that everyone can have a crack at. It's intuitive, it requires logic, and most of all, its FUN! It was on my last assignment. Don't worry; it's a relatively easy question and it doesn't require any formal training in graph theory.
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| Suppose you wanted to colour the lines on this diagram. (This is called the Petersen graph, in case you were interested.) Here are the rules: each line gets exactly one colour. You may use the same colour for two different lines if you wish, but only if those lines do not share a dot. Can you convince yourself that it is impossible to do it with only three colours? (I.e. you need at least four colours.) |
