Useless Numerology for 2016: Part 1

The following entertaining (but useless) facts about the number 2,016 appeared in a recent Facebook post (and subsequent comments) by the American Mathematical Monthly.

$2016 = 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3$

$2016 = 2^{10} + 2^9 + 2^8 + 2^7 + 2^6 + 2^5$

$2016 = 1+2+3 + \dots + 62 + 63$

$2016 = \displaystyle \sum_{n=0}^{63} (-1)^{n+1} n^2$

$2016 = (1+2+...+8+9)^2 - (1+2)^2$

$(2 + 0 + 1)! = 6$

$2016 = 2^{11} - 2^5$

$2016 = 2016 \times 1$

The last tongue-in-check equation is my favorite.

In this series, I’ll explain why these different expressions for $2016$ have to be equal to each other. I’ll begin with tomorrow’s post.

The Wrong Door, Or Why Math Gets a Bad Rap

I really enjoyed this news article on how to motivate young students to enjoy mathematics. Surprise, surprise: it isn’t by doing a whole bunch of rote arithmetic or algebra problems.

http://www.maa.org/news/the-wrong-door-or-why-math-gets-a-bad-rap

Deciphering recommendation engines

From the video’s description: “Data scientist Cathy O’Neil provides a glimpse of the methods that Netflix, Google, and others apply to recommend or offer to users selections based on their apparent interests.” This is a non-intuitive but real application of linear algebra.

Simpson’s Rule and Sums of Powers

Source: https://www.facebook.com/AmerMathMonthly/photos/a.250425975006394.53155.241224542593204/737391462976507/?type=1&theater

Preparation for Industrial Careers in the Mathematical Sciences: Improving Market Strategies

The Mathematical Association of America recently published a number of promotional videos showing various mathematics can be used in “the real world.” Here’s the fourth pair of videos describing how mathematics is used in the world of finance. From the YouTube descriptions:

Dr. Jonathan Adler (winner of King of the Nerds Season 3) talks about his career path and about a specific research problem that he has worked on. Using text analytics he was able to help an online company distinguish between its business customers and its private consumers from gift card messages.

Prof. Talithia Williams of Harvey Mudd College explains the statistical techniques that can be used to classify customers of a company using the messages on their gift cards.

Arrangements of Stars on the American Flag

Reasonable star patterns on the American flag correspond to special factorizations; the density of such factorizations is less than the density of values in a multiplication table; Paul Erdös showed this density asymptotically approaches zero by considering the average number of prime factors of an integer. – See more at: http://www.maa.org/programs/maa-awards/writing-awards/lester-r-ford-awards/arrangements-of-stars-on-the-american-flag#sthash.e9PHpilF.dpuf

Read the article here: http://www.maa.org/programs/maa-awards/writing-awards/lester-r-ford-awards/arrangements-of-stars-on-the-american-flag

Preparation for Industrial Careers in the Mathematical Sciences: Finding the Safest Place to Store Nuclear Waste

The Mathematical Association of America recently published a number of promotional videos showing various mathematics can be used in “the real world.” Here’s the first pair of videos describing the process of mathematical modeling. From the YouTube descriptions:

Dr. Genetha Gray talks about her path and about a research problem that she worked on at Sandia National Laboratories. Using quite limited geological data, they had to create a groundwater flow computational model, with parameters to be determined, so that they could study the feasibility and safety of prospective subsurface nuclear waste storage sites.

Prof. Gwen Spencer of Smith College introduces the mathematics behind optimization, calibration, and the quantification of uncertainty in models and in the results that they give.

Preparation for Industrial Careers in the Mathematical Sciences: Creating More Realistic Animation for Movies

The Mathematical Association of America recently published a number of promotional videos showing various mathematics can be used in “the real world.” Here’s the first pair of videos describing how mathematics is used for computer animation. From the YouTube descriptions:

Dr. Alex McAdams, Senior Software Engineer at Walt Disney Animation Studios, talks about how mathematics is used to make realistic, yet art directable, animations.

Prof. Joseph Teran of the Department of Mathematics at UCLA gives an overview of the numerical linear algebra and iterative method techniques that are used to simulate physical phenomena such as water, fire, smoke, and elastic deformations in the movie and gaming industries.

Mirror Image Symmetry from Different Viewpoints

From the YouTube description:

Erica Flapan (Pomona College) explains why it is important to determine whether a molecule has mirror image symmetry, and discusses the differences between a geometric, chemical, and topological approach to understanding mirror image symmetry.

Your Humble Servant, Isaac Newton

From the YouTube description:

Almost fifty years ago, Cambridge University Press published the correspondence of Isaac Newton, a seven-volume, 3000-page collection of letters that provides insight into this great, if difficult, genius. William Dunham shares his favorite examples of Newton as correspondent. He ends with Newton’s most-quoted line about standing on the shoulders of giants and how his search for its place of origin led him, improbably, to a library in Philadelphia.