Embedding Documents

By way of Kevin Jarret's blog on ed-tech, I'm trying our embedit.in, a web site that allows you to embed many types of documents in your web site. Here's a presentation I recently gave at IMACC 09, a conference of community college educators in Illinois.

Math using Google Earth

From time to time, I teach a freshman level course on liberal arts math. In the section on similarity of figures, there are a few exercises about reading maps and estimating distances. My students saw this as a pointless exercise in the age of GPS and Mapquest. And my comments about being stuck with only a paper map in the boonies usually go nowhere.

Enter Google Earth and its "ruler" tool. I can have them look at a picture of the Pentagon, and with one side measured with the ruler tool, ask them to find its area by subdividing the pentagon into triangles. (Using technology always has the advantage of cranking up the conceptual level of a problem.) There are some interesting math lessons using Google Earth at www.realworldmath.org.

Some articles on faculty development

The March 2009 issue of PRIMUS, a journal for undergrad math education, focuses on faculty development. The articles are an interesting read for those who want to learn more about student centered math classrooms and varying types of assessments.

Also, the January 2009 issue of PRIMUS has three articles on the use of wikis in math classes. The one on the use of wikis in a senior capstone course was authored by me and the other two articles are on the use of wikis in a general math course and in a real analysis course.

The formula that ate your 401(k)

There have been quite a few articles recently discussing the mathematical models of the valuation of mortgage backed securities, and the house of cards that fell as a result. One appeared on WIRED and another in The New York Times .

So what's the take-away for college math education? Most of our math students are not in math intensive majors. However, majors in business and social sciences must have a very good understanding of the mathematics that they do use - typically, a subset of elementary statistics and elementary algebra. It is not clear to me that students are achieving a deeper understanding of these elementary concepts. They should at least understand that mathematical models are limited and there is much more to applying math than simply substituting variables into a range of formulas.

Bits and Bytes : Math of Image Restoration

I've been looking for a simple introduction to image processing that would appeal to students with modest math backgrounds. Most image processing materials are written for electrical engineers and are way above the level of a typical non-math major.

So I was really glad to see this paper from the Electronic Proceedings of the Eighteenth Annual International Conference on Technology in Collegiate Mathematics, Orlando, Florida, March 16-19, 2006.

I'm planning to use it in my math for liberal arts course next time I teach it.

Bits and Bytes: Math Behind the Megapixel Myth

Just about everyone seems enthralled by all things digital - iPods, digital cameras, and so on. But hardly anyone stops to think about the math that's behind the digital craze. About a year ago, I started introducing examples using references to digital items that students are familiar with. They perked up - "hey - this is something I can relate to..."

One of the really interesting examples I use is the "Myth of the Megapixels". Ask anyone about digital cameras and they're likely to tell you that more the megapixels, the better the camera. Well, this is not necessarily true. David Pogue, of The New York Times, posted an article about this. Here's a small excerpt:

Let me tease you first with this question: How much bigger can I print a 10-megapixel photo than a 5-megapixel photo?

Most people answer, “twice as big” or even “four times as big.”

People assume that the length and width of the picture will be doubled.
He shows the math in his article. The gist of the calculation is this: the megapixels refer to the number of pixels in the area of the picture. So even if the area (number of pixels) was doubled, the length and the width of the picture are not doubled. For if the length and the width of the picture were doubled, the area of the picture would be four times as much, not twice. Here are Pogue's calculations:

A 5-megapixel photo might measure 1944 x 2592 pixels. When printed at, say, 180 dots per inch, that’s about 11 by 14 inches.

A 10-megapixel photo (2736 x 3648 pixels), meanwhile, yields a 180-dpi print that’s about 15 by 20 inches—under three inches more on each margin!

The reaction from my students, you ask? "I'll remember that next time I go shopping."
I don't get that reaction when I teach a topic like completing the square!