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Archive of posts filed under the Resources category.

The Math Behind Gerrymandering and Wasted Votes — Quanta Magazine

The U.S. Supreme Court is currently considering a case about partisan gerrymandering in Wisconsin and Texas. One of the keys to the case is the “efficiency gap”, an attempt quantify the partisan bias in a given electoral map. For my latest article in Quanta Magazine, I explain and explore the efficiency gap using simple examples, and talk about some of the implications of this particular measurement.

Imagine fighting a war on 10 battlefields. You and your opponent each have 200 soldiers, and your aim is to win as many battles as possible. How would you deploy your troops? If you spread them out evenly, sending 20 to each battlefield, your opponent could concentrate their own troops and easily win a majority of the fights. You could try to overwhelm several locations yourself, but there’s no guarantee you’ll win, and you’ll leave the remaining battlefields poorly defended. Devising a winning strategy isn’t easy, but as long as neither side knows the other’s plan in advance, it’s a fair fight.

Now imagine your opponent has the power to deploy your troops as well as their own. Even if you get more troops, you can’t win.

The full article is freely available here.

Global Math Week Symposium

James Tanton is on a mission to bring joyous mathematics to the world.  His Global Math Project is about to launch Global Math Week:  during the week of October 9th, over 600,000 students from around the world will enjoy a shared mathematical experience based on Tanton’s Exploding Dots, a wonderful, surprising, and awe-inspiring take on place value.

James has been traveling the world for the past year spreading the good word about mathematics and his exploding dots.  If you haven’t yet signed up, I encourage you to do so.  The mathematics is wonderful, relevant, and inspired, and the Global Math Project has lots of resources at their homepage.

To kick off Global Math Week, the Global Math Project together with the Museum of Mathematics will be hosting a symposium at NYU’s Courant Institute.  Mathematical luminaries like Po-Shen Loh, Henry Segerman, and many others will be on hand to celebrate.  And I’m honored to be participating in a panel discussion on Uplifting Mathematics for All, where we will discuss how to make mathematics meaningful, fun, and coherent in and out of the classroom.

So get ready for Global Math Week!  Hopefully this is the first of many to come.

AMS — Math in the Media

The debut of my column in Quanta Magazine was recently featured by the American Mathematical Society’s Math in the Media!

In addition to a nice review of my first Quantized Academy column, “Symmetry, Algebra, and the Monster“, I was also interviewed by Math in the Media’s Rachel Crowell.  Here’s an excerpt:

AMS: What excites you most about Quanta’s addition of the Quantized Academy series?

PH: Quanta does a wonderful job showing how mathematics and science are vibrant, active endeavors.  The writers bring math and science alive, telling exciting stories of mathematicians, scientists and their work. Quantized Academy can help connect students, teachers, and other lifelong learners to those stories and the math behind them.

You can read the entire article here.  Thanks to the AMS, and to Rachel Crowell, for taking an interest and helping to spread the word!

Symmetry, Algebra and the Monster — Quanta Magazine

I’m excited to announce the launch of my column for Quanta Magazine!  In Quantized Academy I’ll be writing about the fundamental mathematical ideas that underlie Quanta’s stories on cutting edge science and research. Quanta consistently produces exciting, high-quality science journalism, and it’s a tremendous honor to be a part of it.

My debut column, Symmetry, Algebra and the Monster, uses the symmetries of the square to explore the basic group theory that connects algebra and geometry.

You could forgive mathematicians for being drawn to the monster group, an algebraic object so enormous and mysterious that it took them nearly a decade to prove it exists. Now, 30 years later, string theorists — physicists studying how all fundamental forces and particles might be explained by tiny strings vibrating in hidden dimensions — are looking to connect the monster to their physical questions. What is it about this collection of more than 10^53 elements that excites both mathematicians and physicists? 

The full article is freely available here.

STEM Grand Challenges

100Kin10I’m excited to be joining 100kin10 for their STEM Grand Challenges launch today in New York City.

Founded in 2011, the mission of 100kin10 is to recruit, train, and retain 100,000 excellent STEM teachers in 10 years.  To that end, they lead a coalition of nearly 300 public and private-sector organizations committed to supporting STEM education in the US.

Over the past two years, 100kin10 has been working to identify the key systemic problems in STEM education.  Today’s STEM Grand Challenges launch maps out the interconnected landscape of those problems and issues a series of challenges that address the problems identified as most pivotal among the network.

At the event, I’ll be speaking about my personal and professional experiences with some of the grand challenges, and I’m looking forward to hearing from a variety of different perspectives on how we can best improve STEM education.

You can learn more about 100kin10 here.