Posts Tagged ‘mathematics’

Studying Naked

Sophie Germain (1776-1831), a great French mathematician.

No, not me. Sophie Germain. I took a study break last night and was reading about her.

Unfortunately, I got absorbed in my reading and the next thing I knew, it was 2:30am. I’ve been sleepy all day. I know that I’m too young to be “too old for this,” but today I sure felt like it.

Sophie Germain (1776-1831) was a French mathematician who overcame sexual discrimination to achieve great things. She first got interested in mathematics by reading the books in her father’s library. But her parents disapproved of her interest because it wasn’t considered suitable for a young woman. So she started sneaking the books up to her bedroom at night and reading by candlelight.

When her parents found out — well, I guess it was a different era. And maybe her parents were a little crazy. They took away her clothes and kept her bedroom ice cold, but even being naked and freezing couldn’t stop her from studying mathematics. So they gave up trying to stop her.

French society hadn’t given up, of course. The university wouldn’t admit her as a student because she was a woman. To get her education, she eavesdropped at the doors of lecture halls and borrowed lecture notes from male students.

She started writing mathematical articles, using the pen name of Antoine LeBlanc to hide the fact that she was a woman. Eventually, she wrote to the greatest mathematician of the age, Carl Friedrich Gauss. When Gauss discovered her true identity, he became her dedicated supporter. He wrote that she had “the most noble courage, extraordinary talent, and superior genius.”

Urged by Gauss, in 1831 the University of Gottingen decided to award Germain a doctorate for her work in mathematics. That was an almost unheard-of honor for a woman in a sexist society. Sadly, Germain died before she could receive the award. But her example of courage and determination can still inspire us today. Even when we’re so tired that we feel like we’re “too old for this.” 🙂

(Blog post #195!)

Copyright 2011 by Rinth de Shadley.

Doing It With e

This blog is all about a problem I had with e.

There you are jumping to conclusions again! I’m not talking about the drug you get at raves. I’ve never actually tried that kind of e, though guys have offered it to me. Diet Coke and chocolate are my drugs. 🙂

No, I’m talking about Euler’s number e, which is about 2.71828.

I’ve always been a little scared of e. And horses. And spiders. Don’t ask me what all those things have in common, except that they all scare me.

I recently got a math problem wrong because of e, and I just wanted to share my mistake in case anyone else gets confused like I did.

Calculus books (including mine and a couple others that I looked at) say that when you take the derivative of e, you get the same thing:

And that’s true. Kind of. If you’re not careful, it’s how you will remember the rule. That’s where I went wrong.

What makes it confusing is that the book is showing you a special case. Some books don’t make that clear enough. The derivative of x with respect to x is 1, so what you actually get is:

I hate to admit making a stupid mistake, but maybe I can help other people avoid it. When you differentiate e, the actual rule is this:

In other words, you differentiate the exponent (whatever it is) and then multiply that times e raised to the original exponent.

This blog probably isn’t as much fun as arguing about health care reform, but it’s a lot more useful if you’re a student.

Copyright 2010 by Rinth de Shadley.