# Posts

### August 01, 2015

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1:00 PM | Polynomials Explained in 5 Minutes

Polynomials Explained in 5 Minutes One of the simplest things you can do with a number is multiply it by itself. If x is the number, we have.. x*x Mathematicians use a shorthand for this. They write the number x with a small superscript 2 in the upper right corner like this.. x^2=x*x They describe this in several ways. Sometimes they say the number has been "squared", sometimes they say the number has been "raised to the power of 2". This notation immediately suggests x^3=x*x*x and x^4=x*x*x*x […]

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12:30 PM | Free GRIT Poster

I saw this GRIT poster on pinterest, and I decided I had to recreate it for my classroom this year. Here's my typed version:I've uploaded it here as an editable Publisher file and a non-editable PDF file. If you download the editable version, you will need these free fonts: HVD Comic Serif Pro and Caviar Dreams.I have formatted this to print on 18" X 24" paper. You can print this size of black and white poster at Staples for $1.99! Then, all you have to do is laminate it to have a […]

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12:00 PM | Blogging: One Year After

0. I have now eclipsed one year of blogging. 1. Before I started, I never thought I would have had time to write. I also never thought I would have enough to write about. 1. Dude. I was wrong. 2. … Continue reading →

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Dark Knowledge by Geoff Hinton Join the CompressiveSensing subreddit or the Google+ Community or the Facebook page and post there ! Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.
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9:00 AM | Saturday Morning Video: A Mouse Brain

From Science's An incredibly detailed tour through the mouse brain Join the CompressiveSensing subreddit or the Google+ Community or the Facebook page and post there ! Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix
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From Machine Learning & Computer Vision Talks , here is a series of videos on Reinforcement Learning, by David Silver from Google DeepMind:Lecture 10 | Reinforcement Learning : Classic Games (David Silver)Lecture 9 | Reinforcement Learning : Exploration and Exploitation (David Silver)Lecture 8 | Reinforcement Learning : Integrating Learning and Planning (David Silver)Lecture 7 | Reinforcement Learning: Policy Gradient Methods (David Silver)Lecture 6 | Reinforcement Learning
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8:05 AM | Ebola vaccine trial

You’ve probably heard that there are positive results from an Ebola vaccine trial (3News, Radio NZ, Stuff, Herald). The stories are all actually good. Here’s the (open-access) research paper The vaccine was genetically engineered: it’s a live virus for an animal disease that doesn’t spread in humans, modified to produce just one Ebola protein. Having […]

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7:30 AM | For Mathematics Teachers Only:

8/01/2015School is coming up soon and I have some tips that may eliminate some of the headaches you will get during the yearFirst, base your grading system on a million points instead of a hundred points. This will eliminate you discussion about being "only half a point away from passing". "But Bobby, you're over 5,000 points away from passing - I just can't curve your grade that much."Second, don't argue about whether students can use calculators on tests and quizzes. Just […]

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7:25 AM | Post-Modern Algebra

Originally posted on Math Online Tom Circle:Modern Algebra: Based on the 1931 influential book “Modern Algebra” written by Van de Waerden (the student of E. Noether). Pioneered by the 20th century german Göttingen school of mathematicians, it deals with…

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6:50 AM | August

This picture came about quite by chance. I had taken the picture from Hungerford Bridge on a misty morning, and the whole scene was in pale shades of gray. I decided to increase the contrast just a little; but, as … Continue reading →

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6:11 AM | A Good K To Try - a.k.

We have seen how the k means algorithm can classify a set of data into k subsets of mutually similar data with the simple iterative scheme of placing each datum into the cluster whose representative it is closest to and then replacing those representatives with the means of the data in each cluster. Whilst this has a reasonably intuitive implicit definition of similarity it also has the unfortunate problem that we need to know how many clusters there are in the data if we are to have any hope […]

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From the Fastml extra twitter feed here are the slides and videos of the Machine Learning Summer School Sydney 2015The program booklet can be downloaded here. The lab instructions are available here. Intro to Machine Learning (Webers) Lecture Slides: mlss2015-webers.pdf Video Recording: https://youtu.be/GtoD4l0sW2k Probabilistic Graphical Models (Domke) Lecture Slides: mlss2015-domke.pdf Video Recording: https://youtu.be/z3raBFHFVKk Optimization (Schmidt) Lecture Slides:
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4:39 AM | Linkage

W. T. Tutte's WWII cryptography work (G+)Cube into rhombic dodecahedron dissection video (G+)Calvin Seibert's geometric sand castles (G+)Paco Santos' Hirsch counterexample wins him the Fulkerson Prize (G+)Tessellating calligraphy (G+)MacTutor History of Mathematics website honored by the London Mathematical Society (G+)The backlash against using numerology to measure research quality gains strength (G+)Turns out that folded brain surfaces and crumpled paper balls obey the same scaling laws
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4:35 AM | NZ electoral demographics

Two more visualisations: Kieran Healy has graphs of the male:female ratio by age for each electorate. Here are the four with the highest female proportion, rather dramatically starting in the late teen years. Andrew Chen has a lovely interactive scatterplot of vote for each party against demographic characteristics. For example (via Harkanwal Singh), number of votes […]

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“No cubes were harmed during the making of this talk”

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4:05 AM | Calculus at Crisis IV: Best Practices

In my last three columns I explained the reasons that college calculus instruction is now at crisis:The need to teach ever more students, who often bring weaker preparation, using fewer resources.The fact that most Calculus I students have already studied calculus in high school (this past spring 424,000 students took an AP Calculus exam, an increase of 100,000 over the past five years).The pressures from the client disciplines to equip their students with the mathematical knowledge
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This month’s musings were inspired by the appearance of Greg Toppo’s excellent new book The Game Believes in You: How Digital Play Can Make Our Kids Smarter. In it, Toppo, who is USA Today's national K-12 education writer, does an excellent job of not only surveying the current scene in educational video games, he also exhibits a deep understanding of, and appreciation for, the educational potential of well designed video games. I have gone on record as saying it will likely turn […]

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By Kathleen Fowler, Associate Professor of Mathematics, Department of Mathematics and Computer Science, Clarkson University Since starting my career as a faculty member in 2003, I jumped right in to K-12 Outreach and have never looked back. I was motivated … Continue reading →

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3:54 AM | Day 0 – Room Setup

After two teaher workdays, I have my room set up. Students arrive on Monday. This is the view from the middle of my room: I really did take pictures of the rest of the room, but then I managed to delete them off of my phone before I got them to my laptop. But that’s cool; […]

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3:53 AM | Pyramid of Abstraction

I’ve been throwing around the term “pyramid of abstraction” recently, and there was some great pushback on Twitter this evening. This post is my attempt to clarify what I mean, and why I think it is a useful perspective to building students’ knowledge. Abstraction I’m defining abstraction very specifically. A student abstracts a concept, or […]

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Topology is all about squishing and stretching; distance shouldn't matter. But the infinite earring illustrates the delicate interplay between topology and geometry.
-- Read more on ScientificAmerican.com

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Does the sentence “intersections of subobjects are fiber products of the corresponding monics (which are ordinary products in the relevant overcategory)” look like a good explanation of the intuition that “intersections are a kind of product”? If so, yes.

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“Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it’s not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley” - Yōko Ogawa, The Housekeeper and the Professor.(via spring-of-mathematics)

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1:22 AM | The Slippery Eel of Probability

The Slippery Eel of Probability: Pradeep Mutalik:In school, we are trained to think that math problems always have one correct answer. But this is not necessarily true for problems dealing with probability, if the method used to reach the described situation is not fully specified. Surprisingly, the same problem can then have many different answers, all apparently equally valid. Take, for example, our new puzzle:

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1:00 AM | Heawood Graph

This is the Heawood graph. This graph can be drawn on a torus with no edges crossing in such a way that it divides the torus into 7 hexagons, each pair of which shares an edge. In 1890, Percy John Heawood proved that for any map drawn on a torus, it takes at most 7 colors to ensure that no two countries sharing a common boundary have the same color. The Heawood graph proves that the number 7 is optimal.

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12:00 AM | Simulating continuous Markov chains

In a blog post I wrote in 2013, I showed how to simulate a discrete Markov
chain.
In this post we’ll (written with a bit of help from Geraint
Palmer) show how to do the same with a continuous chain which can be
used to speedily obtain steady state distributions for models of queueing
processes for example.
A continuous Markov chain is defined by a transition rate matrix which shows
the rates at which transitions from 1 state to an other occur. Here is an
example of a continuous Markov […]

### July 31, 2015

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11:00 PM | On This Day in Math - August 1

Regarding all these basic topics in infinitesimal calculus which we teach today as canonical requisites ... the question is never raised, "Why so?" or "How does one arrive at them?" Yet all these matters must at one time have been goals of an urgent quest, answers to burning questions, at the time, namely, when they were created. If we were to go back to the origins of these ideas, they would lose that dead appearance of cut-and-dried facts and instead take on fresh and vibrant life again.Otto […]