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Mathematics and History

I had a limited understanding of what I could do with math when I was in school, which was as much my fault for being narrow-minded as anyone else’s fault for not showing me the incredible breadth of mathematical applications. This ultimately contributed to an unsatisfying experience in graduate school and a departure from math, which I talked about in this story.

So as a teacher I make sure students know that math will always create options for them. I tell them that whatever they decide to study — science, humanities, the arts — they should keep taking math classes as long as they enjoy them. There are quantitative aspects to every discipline, and knowing math will always set them apart and give them an edge in their field.

Recently a student asked me about how mathematics could be applied to the study of history. She is passionate about studying both, but sees them as disconnected and unrelated. I had a few answers for her, but I was looking to provide her with more. So I put out a request on Twitter.

The response was remarkable. I learned a lot, and so did my student! Here is a brief summary of the great resources, links, and ideas that were offered.

There were many more responses, and I recommend looking through the Twitter thread. Thanks to everyone for contributing, and for helping to keep one more student studying math.

By MrHonner, ago

The (Imaginary) Numbers at the Edge of Reality — Quanta Magazine

My latest column for Quanta Magazine connects the complex numbers from high school math classrooms to the quaternions and octonions, numbers systems currently being used in cutting-edge math and science research.

Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What could be less practical than a number described as imaginary?

But imaginary numbers, and the complex numbers they help define, turn out to be incredibly useful. They have a far-reaching impact in physics, engineering, number theory and geometry. And they are the first step into a world of strange number systems, some of which are being proposed as models of the mysterious relationships underlying our physical world.

Some physicists currently believe that the octonions, an eight-dimensional number system with non-commutative, non-associative multiplication and seven square roots of -1, may be the key to understanding the fundamental interactions between particles and forces. Learn more about their connections to “imaginary” numbers in the full article, which is freely available here.

By MrHonner, ago

How Network Math Can Help You Make Friends — Quanta Magazine

My latest column for Quanta magazine introduces network science, an area of mathematics that has developed rapidly over the past 30 years and has impacted fields like computer science, biology, and economics.

In my column, I use friendships to develop the basic concepts of networks and explore different structures.

When you start at a new school or job, or move to a new city, how do you go about making new friends? You could take an active approach, forging strategic connections with the popular kids and the movers and shakers. Or you could leave things to chance, relying on random groupings and associations. Whatever your approach, understanding the structure of existing friendships in your new community can help you make the best connections, which will ultimately define your circle of friends.

One particular network structure, the so-called scale-free network, has emerged as a useful model in a wide variety of fields. But recent research suggests that these scale-free networks may not be as ubiquitous as we might have thought. You can learn more by reading my column here.

By MrHonner, ago

NYSMTP Summer Conference

Next week I’ll be attending and presenting at the New York State Master Teacher Program’s annual Summer Conference at SUNY Cortland.

The NYSMTP summer conference brings together Master Teachers from around New York state for two days of professional learning and networking. The theme of this year’s conference is “Convergence”, and features presentations from Dr. C. Alex Young from NASA, mathematician Steven Strogatz from Cornell, and New York’s Education Commissioner MaryEllen Elia.

I’ll be presenting Scratch Across the Math Curriculum with Dan Anderson, a Master Teacher from New York’s Central Region. Dan and I will be sharing our work bringing computer science into math class using the Scratch programming language. This is a continuation of the work I’ve been sharing at workshops and conferences across the country the past several years.

I’m proud to be a part of the NYS Master Teacher program through Math for America, the NYC-based organization that served as a model for the state program, and I’m grateful to MfA for their support in participating in events like the NYSMTP’s summer conference.

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By MrHonner, ago

Story Collider Podcast

I performed at a Story Collider event earlier this year and now my story is featured on their podcast!

The mission of the Story Collider is to share true, personal stories about science. Their latest podcast is titled Loneliness: Stories About Finding Friends, and it features my story about how my relationship with math has changed over the course of my life and career. It also includes a poignant story from physicist Cindy Joe about her experience working at Fermilab and her pet snail.

You can find the podcast, and the transcript of my story here, and you can see a video of my talk here.

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By MrHonner, ago
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