Graduate School

Last year, I finished my bachelor’s degree in mathematics at the University of Reno, Nevada. Since then, I completed my student teaching, and have been working as a substitute when work is available. I had been hoping to find a full-time teaching position, but the school district is currently under major budgetary constraints, and has not been hiring very many new teachers. The lack of consistent work and the tightness of our own budget has made this a long and frustrating year.

And then I got some good news.

Last week, the math and stats department at UNR accepted me into the master’s program in mathematics, and offered me a very generous teaching assistantship. There are some amazing faculty at UNR, and I am looking forward to working with them over the next couple of years. I am also looking forward to the teaching assistantship which, in addition to helping me cover the costs of graduate school, should offer me a great opportunity to hone my skills as an instructor.

I can’t express how excited I am.

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The Mandelbrot Set—Part V: Coloring the Mandelbrot Set

The Mandelbrot Set Series:

This post is the fifth in a series on the Mandelbrot set. Thus far, we have managed to define the Mandelbrot set as a collection of points or numbers on the complex plane. Every point is either in the set or not in the set, thus the images of the Mandelbrot set that we have created have all been in black and white. Fortunately for all of us who like a little bit of color, there are ways to add a splash of color in a way that are mathematically informative. This post covers one such method.

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Monday Mandelbrot Madness IX

Ganglia - click to enlarge.

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Monday Mandelbrot Madness VIII

Harvest Festival - click to enlarge.

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The Mandelbrot Set—Part IV: Defining the Mandelbrot Set

The Mandelbrot Set Series:

This post is the fourth in a series on the Mandelbrot set. In previous posts, we have discussed what fractals are, given a hint as to the complexity of the Mandelbrot set, and laid some groundwork on the complex plane. Now we are finally ready to actually define the Mandelbrot set.

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Simplicity

Today I taught a pre-algebra lesson on ordering real numbers. In discussing this topic, we determined that in order to compare or order numbers, it is helpful to format them in a similar fashion. For instance, it is difficult to compare a fraction to a decimal without first representing the fraction as a decimal, or the decimal as a fraction.

I told the students that they could could compare decimals to decimals, fractions to fractions, or percentages to percentages, just so long as they used the same form for all of their numbers. I then recommended that they change everything to a decimal representation, because it was the easiest form to work with.

Much to my surprise, the students seemed almost offended that I was trying to make math easier for them. They thought that I was cheating them by not showing them how to change everything to fractions, then compare those fractions 1NB: Both of these topics have been presented to these students before, though not together. Changing numbers to fractions was part of last week’s material, while comparing fractions using a common denominator was covered earlier in the year (as well as in lower grades).. I was, quite frankly, shocked that they would feel this way. I loved it when teachers showed me short cuts, or tried to make things easier.

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Monday Mandelbrot Madness VII

Snowflake - click to enlarge.

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Nature by Numbers

Today, I would like to share one of my favorite things: a short film by the very talented Cristóbal Vila called Nature by Numbers. The film melds the beautiful composition “Often a Bird” by minimalist composer Wim Mertens with some wonderfully imaged examples of mathematics in the natural world. I highly recommend that you watch the film in HD—it is utterly worth it.

As a work of art, I think that the film stands very well on its own. Even to a person who knows nothing about mathematics, the link between mathematics and nature is made very clear, even if the mathematics itself is obscure to the viewer. That being said, I think that there is value in going a step deeper. In the interests of fostering that deeper understanding, I would like to examine some of the mathematics on display in the film.

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Irrational Numbers

About 2,500 years ago, mathematics was dominated by the Greek mathematician and philosopher Pythagoras. Pythagoras and his followers formed an almost religious group, complete with secret symbols, mysticism, and a dogmatic approach to mathematics. One of the important aspects of Pythagorean mathematics was the idea that, in essence, any distance could be measured with a kind of universal measuring stick.

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Monday Mandelbrot Madness VI

Lightning - click to enlarge.

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