This semester I'm taking Math 290: Elementary Linear Algebra. It started back in August, but somehow I neglected to mention it.
This time I managed to save a lot of money on the textbook. I bought it online at Abe Books. I had been warned to double check that I got the right edition, including number and country. The Chinese editions are dirt cheap, but somewhat different from the U.S. versions. I ended up paying less than $50 for a new book, while the K.U. Bookstore (I'm sure they'll be happy I linked to them) was charging $96 for a used copy.
And on Abe Books, if you go for an edition only 2 or 3 years old, the price drops drastically, on some textbooks down to just a dollar (plus shipping, of course).
There is definitely a problem with textbook pricing at the University level. I have no problem with the authors making money on textbooks that they have written, but too often students are forced to spend hundreds of dollars for books that they only open to get the homework problems. In my summer class, that was definitely the case. On the few occasions that I attempted to learn something from the book, I found that I was better off with my class notes. For this class, I've only looked a couple of times to clarify some word usage. It seems to be a little better written than my last book. At least it didn't leave me dazed and confused. And it has one thing I like: each chapter starts with a brief essay (3-4 paragraphs) about a notable mathematician who has contributed in some way to the material at hand. It's a nice reminder that we haven't always just known this math, and a lot of it is less than 200 years old.
This suggests a goal for math teachers: to find the next Fourier, or Laplace, or Gauss, or Kepler. Someone to seriously stretch the concept of mathematics. Maybe your heart doesn't skip a beat when you hear those names. Mine doesn't, exactly. But when I think about how they pioneered the concepts that I struggle to follow, I can't help but be impressed. As difficult as it is to follow the book or lecture, at least my answers are checked by the grader. Those guys had no one to tell them they were right, though I doubt it was hard to find naysayers.
And while some of these famous mathematicians did nothing but math, many of them were working on applying math to the real world. In other words, science. When men stood on the moon, it was math that took them there. When you turn the key in your car and the engine starts, it is math that designs the parts the move so smoothly and determines how much gasoline to explode with each cycle. When drugs are developed to fight chronic diseases, it is math that tells us how the population as a whole may be effected. And if you are reading this, it was composed on a computer. Scads of math tied up there.
America has been raising its children to automatically think math is hard, boring, and pointless. This will cause serious problems not too far down the line. It is true: people no longer need to crunch numbers by hand. The digital watch we sell at Wal-Mart for $5.87 can do more computations in a day than a human can in a week. The newest computer you buy today is roughly twice as fast, with twice as much memory as the newest computer you could have bought a year ago. To heck with slide rules and abacus... Abacuses. Abaci. Abracadabra. Most people don't need to be able to do math in their heads any more, which is fine.
But without an understanding of what is happening inside your calculator or computer, there is absolutely no way that you can hope to expand on it.
I just finished my third test in Math 290 yesterday. I had to use my calculator on about half of the problems, and I finished in about 30 minutes. The teacher (Jeff Lang) commented that not so long ago, this would have been a two hour test, because of the matrix crunching. And the grading would have been tedious, too, following minor errors to award partial credit.
[Incidentally, Prof. Lang is a Muslim, which I didn't find out until I Googled him for the above link. There's an interesting interview with Jeff Lang on YouTube which gives some feeling for his lecture style. Don't click that link unless you have a good enough internet connection to watch a 10 minute video, and maybe the other three parts as well. There are also links to some fragments of lectures he has given on Islam. He's much more serious about that than he is about matrices. The other big difference is that in class he frequently raises his chalk to his mouth and takes a drag.]
This is good. (The test thing, not the extra bits about my prof.) I can demonstrate a wider range of skills by virtue of being able to complete tasks more quickly. And hopefully I demonstrated them well. If I get an A on this test, I won't have to take the final exam. I'll still go to class and do homework, but I won't have to sweat another test. Good deal. I'll find out Monday.
Getting back to the idea of learning math: I rarely meet a kid who likes math anymore. And I have met many, many adults who say they never liked it. While I know that part of the problem is that they are not "naturally" good at it, I believe that the biggest problem is that they haven't been taught well. They've had homework piled on, they've sat through boring lectures, they've felt nitpicked, and they've seen no connection between math and life. Why bother?
I hope that I can make some of them see that there is a connection. I want them to understand why the details are important, and why it's worth practicing to become better. I want them to come out of class excited, feeling that they have conquered math, and are ready to take on next year's math. I want them to believe that if they can play video games well, they can do math. If they can keep track of who likes who and what couples are together, they can do math. If they can throw, catch and run without falling down all the time, they can do math. Because all of those things have math underneath, whether just below the surface, or so deep that we haven't found it yet.
In short: Love doesn't make the world go round. Math does.