Category Archives: advice to math students

Why are you sitting around base camp while the mountain awaits?

This is a message to a certain kind of math major, although it applies with few alterations to many other disciplines. You'll have to decide for yourself how much of this applies to you. We live in an age not only of supreme scientific and technological development, but also of unprecedented access to knowledge. Our university libraries are networked with other libraries and online databases so that almost any book or article is not far away. Scholars have taken time and care to write gentle introductions to their fields…

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A Case Study in Problem Solving: Rubik's Cube

Let's be honest: Rubik's cube is actually a terrible puzzle. It's not hard to get one layer correct, but beyond that it gets ridiculously complicated. Most moves you try to get the next layers mess up what you've already put right. And all those kids on TV who solve it in under 20 seconds? They've all memorized moves from books or from the internet. It would be interesting to know what percentage of people who have picked up a cube have actually solved it without outside…

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To math majors, with useful advice for other students

Have you ever gone into an exam feeling good about your understanding, only to draw a blank? I remember a third-year algebra test that went that way. I read through my notes again and again until I felt I knew them backwards and forwards. But when the exam came, and I actually had to make use of that information, it simply wasn't there. Since then, I've come to realize how ineffective such a study method is, for it practices and practices the first step of studying,…

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Read as much as you can. Read as little as you can.

In math, as in any subject, there is definitely an advantage to being widely and well read, so that every known fact about your topic of study is immediately available for recall. Thus, so long as the result of your reading is that you actually retain new and useful knowledge, the first sentence in the title is indeed sound advice. However, I have noticed that math students often find it very difficult to learn from reading. They spend time with their math book, but come away with…

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