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Archive for May, 2009

I read a book this weekend called “What the Dormouse Said.” It tells the story of the birth of the computer industry in Silicon Valley during the 1960s and 1970s.  Most of the people involved were connected in some way with Stanford University because of all the computer research being done there.  Much of this work was government funded, with the bulk of the funding coming from the Pentagon.

There was a naval air station in Sunnyvale throughout WW II that led to the need for research in advanced aeronautical technology and electronics.  A number of corporations set up offices in the area to help fill the need for advanced technological research.

Lockheed and Honeywell both set up research operations in Sunnyvale.

Shockley Semiconductor in Mountain View did extensive research in developing silicon chip technology and led to the founding of both Fairchild Semiconductor and Intel.

Ampex was based in San Carlos.

Hewlett Packard was founded in Palo Alto.

Xerox PARC (Palo Alto Research Center) was in Palo Alto.

Mathematics is essential to computer programming – Math is the the language that computers speak.

I’m getting ready to talk to MTH 060 about graphing in a few days and the connection between computer graphics and the Cartesian Plane occured to me.  All computer graphics are based on the pixels of the screen and what color they need to be to represent the object.

To communicate to the computer what to do with each pixel, the programmer must identify the pixel by its position on the screen.  This is usually done a little differently than the standard Cartesian Plane, but it is exactly the same idea.

In addition, any type of object that is projected on the screen can be moved by describing the movement to the computer as a series of mathematical formulas.  The more difficult movements are often established using motion capture technology in which real performers wear black bodysuits with white disks at key points of the body.  Those key points are the ones involved in making the movement appear natural.

There are a number of courses on Mathematics and Computer Graphics

At the University of Illinois Urbana-Champaign

At Georgia Tech

Here are links to several books on the subject

Mathematics for Computer Graphics by John Vince

Essential Mathematics for Games and Interactive Applications by James Van Verth and Lars Bishop

Mathematics for 3D Game Programming by Eric Lengyel

There is also a nice pdf on Mathematics and Computer Graphics here.

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Wolfram Alpha is up and running!

Here is some discussion about the site.

And here.

I was also reading a New York Times article today about the web sites Course Hero and Cramster.

The future of education will, I believe, move in a direction that makes use of these tools, but still challenges students to learn and solve difficult multi-step problems.

I was saying to one of my students today that in difficult multi-step problems, knowing the answer is generally not all that helpful – it’s making sense of the answer that is important.

Some skills never go out of style – for instance, just because we have cars, that doesn’t mean we shouldn’t learn to walk!

Even though simple calculators are ubiquitous, we should still develop number sense and learn to calculate and work with whole numbers, fractions, decimals and percentages by hand.

The same goes for elementary algebra – once hand-held computer algebra systems become common, I believe that we should still learn the basics of elementary algebra – for the same reason we should learn to compute without a calculator – critical thinking.

We can’t think critically about something we don’t understand.

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I went to Lincoln City this past weekend for the ORMATYC Conference.  ORMATYC is the Oregon Mathematical Association of Two Year Colleges and is a part of the larger group AMATYC, the American Mathematical Association of Two Year Colleges.

Just about every year, we have a conference in Lincoln City – this is the fifth one I’ve attended.  It’s a great experience to get together with other community college math instructors from Oregon to talk about math and math education.  It’s a valuable forum to find out what other schools are doing in their math classes and how we compare with those other schools.

In attending this conference every year, I have learned more about both math and math education.  In some cases it was about how to present a particular topic in class, while in other cases it was something that provided additional background information about the topics I teach so that I can share these ideas with my students.

In addition to being exposed to new ideas about math and math education, another positive aspect of this conference is being part of a community.  After 5 years, I have gotten to know some of the other instructors and have a better idea about which talks to attend while I’m there.

This year, I saw Jim Ballard of OIT Klamath Falls give a talk on the mathematics of finance.  There was a lot of discussion about the current economic situation and he didn’t really get a chance to talk about the Black-Scholes equations which are somewhat controversial, but have been used in mathematical finance for over 20 years.  I wrote about math and finance in an earlier post.

I also attended a session with Ron Wallace of Blue Mountain CC about deciding which topics to teach and which to leave out in the math curriculum.  He asked if anyone there had used the quadratic formula in their lives outside of teaching in the past five years.  I was the only one to raise my hand.

I did use the quadratic formula a few years ago when my Mom asked me about the cost of Medicare Part D programs.  The formula for pricing in Medicare Part D is quadratic in that it initially becomes more expensive the longer you wait to enroll, but the money you save by not enrolling right away can offset the higher premiums you end up paying.

On Friday afternoon I went to a presentation by Art Peck of Lane CC.  I had seen his talk last year about the connection between the Fibonacci Sequence and the Mandelbrot Set, which was excellent.  This year, he talked about applications of mathematics to environmental problems, including alternative energy.  There is a lot of mathematics involved in scientific research that is focused on the environment.  For particular examples, he mentioned a textbook and companion website that have been developed and have some great application questions.

This is an important time for alternative energy generation and research directed at the environment in general.  I wrote an earlier post about the Solar Tres project.  The development of electric car motors and batteries has reached a point that production of “all-electric” car models is happening now.  One of my calculus textbooks has a cover page addressed to the instructor saying “The first person to invent a car that runs on water may be sitting right in your classroom.”

On Saturday morning, I saw a presentation by Geza Laszlo called “Rational Approximations of Roots of Polynomials.”  This is a very interesting topic.  It has connections to some of the material we cover in MTH 111 about roots of polynomials, but it is more closely related to the ideas we discuss in MTH 116 about using Newton’s method to approximate a square root.

Newton’s method uses calculus, but the method itself was known to the Greeks, even though they did not have formal knowledge of the methods of calculus.  The idea of approximating irrational numbers with rational numbers is also of great importance in constructing a musical scale.  Attempting to approximate (log3)/(log2) with a rational number determines how an octave will be separated into notes and how accurate the scale will be.

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