Image of the Week #153

A triple cubic Julia set, zoomed into an interesting region.

IOTW

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Karen Keskulla Uhlenbeck Wins the Abel Prize!

herselfOccupy Math is delighted to report that Professor Karen Uhlenbeck will, on May 21st, 2019, be awarded the Abel Prize for her work in geometric analysis and gauge theory by the King of Norway in a ceremony in Oslo. The prize is awarded at the discretion of the Norwegian Academy of Science and Letters and was established to serve as the “Nobel Prize” of Mathematics. Professor Uhlenbeck is currently at the Institute for Advanced Study in Princeton, New Jersey. She holds a permanent faculty position at the University of Texas at Austin. Dr. Uhlenbeck is the first woman to be awarded the Abel Prize, which Occupy Math takes as evidence that the world is continuing to become a more reasonable place, in some ways.

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Sure Bets are Losing Bets

topA bet is a situation in which you risk something of value which you may lose or, if your bet works out, you may make a gain, possibly a substantial one. Figuring out how gambling works was a massive spur to the development of mathematics. Blaise Pascal, a seventeenth century French mathematician, used mathematical analysis to spot a defect in the national lottery and make money. Pascal’s work is foundational to probability theory, something Occupy Math has talked about before. In this weeks post, Occupy Math will discuss a type of betting: funding research in science, technology, engineering, and mathematics (STEM) disciplines.

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Image of the Week #150

This week we take a Newton’s method fractal, with fifteen roots, and show how it forms in an animation.  Sorry for the small size — animation uses multiple pictures so it makes big images.

IOTW

What do mathematicians do all day? Part III

topThis week, Occupy Math continues the series What do mathematicians do all day? This post is Part III, which means there must have been a Part II. This week we report on some research on drawing maps with evolution, something Occupy Math did a couple posts ago. This week’s post uses a completely different technology and produces a very different type of map. An example appears at the top of the post. The red room is where the whole thing starts, the blue bars are corridors. Evolution is trying to lay down a lot of rooms — optional extras like doors and monsters are added later. The interesting thing about this post is that the evolved object can generate arbitrarily large maps.

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Students of the world! You have nothing to lose but your illusion of control!

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The Illusion of Control is the natural tendency of people to overestimate how much control they have over a situation. When you are in control, it increases your confidence and decreases your fear, so people like to feel in control. In this post Occupy Math will discuss an instance of the illusion of control that decreases students’ grades on a math test. This post raises and discusses a point about how to teach effectively and Occupy Math’s position on the issue is debatable and disliked by many of his students. Interested? Read on!

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