Image of the Week #70

Image of the week! A cheerfully shaded wedge-convergence Mandelbrot subset.
IOTW

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Announcing a Calculus Book by Occupy Math

textFor the past three years Occupy Math has been working on a calculus text for the integrated first-year math and physics course he co-designed. The regular books did not have the right topics in the correct order. This post announces that the book is ready. It is the second edition (now with far fewer errors!) We used the book last year and found a need to revise and extend.  The book is not a standard calculus book and the rest of the post is about that. The big points are: we got the cost down to less than half that of the book it replaces. It covers all the topics of a standard first year calculus course for science majors. The presentation is different based on decades of experience with what does and does not work.

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Image of the Week #69

This is what happens when you use quadrant convergence on a Newton’s method fractal with a tiny rotation added into the iterator.  This one is for z^6-1=0 with a rotation of about 0.2 radians.

IOTW

Logic in Discourse: Tools for Reducing Asshattery

Humans have a natural ability to do logic predicated on learning rules from their environment. Training in mathematics improves your logic — and makes you more effective in an argument (at least the polite sort). It’s often humorous when somebody does not follow those rules. In the show Parks and Recreation, actress Amy Poehler plays the director of the Parks and Recreation department in a small town in Indiana. At one point a citizen, at a town meeting, says this. “I found a sandwich on a bench in one of your parks! (pause) Why wasn’t there any mayonnaise on it?” Something that sounds like a complaint about littering turns in a completely unexpected direction. Occupy Math starts with this because the fact that this condiment twist in the citizen’s complaint was funny means that there is hope in a moderately awful situation.

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Image of the week #68

This is another fourth-power Mandelbrot set — at the looks-like-chocolate level of zoom.  It is rich in oddly-polygonal looking basins of attraction.  Star lake on Chocolate island.IOTWb.png

Business thinking gutted my university — is your education in danger?

devos

This week’s Occupy Math is venturing again into the sociology and politics of education in the service of addressing a pressing problem. There are places where Occupy Math managed to wedge in a little math — and there are tips on self-defense for those of you who might pay for educational opportunities. The basic thesis of this post is that trying to run education like a business degrades education and also fails at the normal goals of business. The basis of the problem is that education is critical, people really want it, which means the demand for it is inelastic (doesn’t change much with price), which in turn means price can get totally out of control. This also makes education a fertile ground for con-artists, who are always willing to exploit people who really want something.

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Problem Factories

factory

One of the things a math teacher needs is a supply of good problems. Occupy Math and his collaborator Andrew McEachern have coined a new term in connection with this need: Problem Factories. A problem factory has two parts. The first is a basic understanding of a mathematical fact, the second is a general type of problem or puzzle based on that fact. Ideally the understanding of the math will specify which versions of the problem can be done and give an idea of how hard they are. From this point, the way forward lies in an example.

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Fractal Lenses

Lens

Occupy Math has already taken a shot at explaining what fractals are. He has tried to supply engaging holiday fractals. On of the least popular posts is on the incredible complexity of the Mandelbrot Set and there is a post on making family trees of fractals (and other things). What’s left? This week Occupy Math is going to turn up the weird to eleven and use fractal algorithms as lenses — a different type of lens from the one shown at the top of the post. The only thing you really need to know about fractals to get a sense of what is going on is that a fractal is based on an algorithm that moves a point around in a complex way until it is captured. The details of the algorithm and the conditions for “capture” give you the shape and then you also need a coloring algorithm. Today’s post is all about a really odd way to color fractals.

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