Mathematics

Jo Boaler has kindly asked me to spread the word about her free, upcoming course How to Learn Math. It sounds intriguing; in fact, I signed up and hope to be able to attend (to have the time).Here's her description of it:The course is a short intervention designed to change students' relationships with math. I have taught this intervention successfully in the past (in classrooms); it caused students to re-engage successfully with math, taking a new approach to the subject and their learning.In the 2013-2014 school year the course will be offered to learners of math but in July of 2013 I will release a version of the course designed for teachers and other helpers of math learners, such as parents. In the teacher/parent version I will share the ideas I will present to students and hold a conversation with teachers and parents about the ideas. There will also be sessions giving teachers/parents particular strategies for achieving changes in students and opportunities for participants to work together on ideas through the forum pages. Concepts1. Knocking down the myths about math.Math is not about speed, memorization or learning lots of rules. There is no such thing as “math people” and non-math people. Girls are equally capable of the highest achievement. This session will include interviews with students.2. Math and Mindset.Participants will be encouraged to develop a growth mindset, they will see evidence of how mindset changes students’ learning trajectories, and learn how it can be developed.3. Teaching Math for a Growth Mindset.This session will give strategies to teachers and parents for helping students develop a growth mindset and will include an interview with Carol Dweck.4. Mistakes, Challenges & Persistence.What is math persistence? Why are mistakes so important? How is math linked to creativity? This session will focus on the importance of mistakes, struggles and persistence.5. Conceptual Learning. Part I. Number Sense.Math is a conceptual subject– we will see evidence of the importance of conceptual thinking and participants will be given number problems that can be solved in many ways and represented visually.6. Conceptual Learning. Part II. Connections, Representations, Questions.In this session we will look at and solve math problems at many different grade levels and see the difference in approaching them procedurally and conceptually. Interviews with successful users of math in different, interesting jobs (film maker, inventor of self-driving cars etc) will show the importance of conceptual math.7. Appreciating Algebra.Participants will be asked to engage in problems illustrating the beautiful simplicity of a subject with which they may have had terrible experiences.8. Going From This Course to a New Mathematical Future.This session will review where you are, what you can do and the strategies you can use to be really successful.

(Click on the cartoon to see the full image.) (C)Copyright 2013, C. Burke.A big hit for the Ram-Ones about 34 years ago.

It’s that time of year again, and while I miss the buttercups in Reading, we had as usual a feast of interesting mathematics and a large and enthusiastic audience. It was a bit more tightly focussed than I would have liked. We had a lot of references to Szemerédi’s Regularity Lemma; even Ben Green was using a version of the Regularity Lemma for integers, proved by him and Terry Tao, in his talk. (Curiously, Szemerédi was giving a new proof of a known result, avoiding the use of the Regularity Lemma in order to obtain better bounds.) No finite geometry, no enumeration … I’ll just talk briefly about three of the highlights. An old result of Erdős asserts that, if A is any finite set of natural numbers of size n, then A contains a sum-free subset of size at least n/3. The proof is simple and beautiful, so here it is. Pick a random real number a from the uniform distribution on [0,1], and let Sa be the set of those n in A for which the fractional part of an is between 1/3 and 2/3. Clearly Sa is sum-free. The average size of Sa is obviously n/3. So there is some choice of a for which the size of Sa is at least n/3. Ben, with his students Sean Eberhard and Freddie Manners, has proved that the constant 1/3 here is best possible. He gave us a clear outline of the proof. It is necessary to avoid two kinds of “large” sum-free sets. These were very familiar to me from my own work on sum-free sets. The first are periodic sets, such as the set of odd numbers, the set of numbers congruent to 2 or 3 (mod 5), and so on, which occur with positive probability in the choice of a random sum-free set; the second consists of the interval [x, 2x) which comes up (along with the odd numbers) in the Cameron–Erdős conjecture (which was proved by Ben in his PhD thesis). He described the method of doing this in a couple of simplified cases. To me, it had an adèlic flavour about it; the real completion of the rationals is involved with avoiding the intervals, and the p-adic completions in avoiding the periodic sets. Gábor Kun, as usual, had a very interesting project to talk about. This is a “finitization” of the concept of amenability. A bit technical, so I won’t attempt a description; but it involved a conjecture of von Neumann, a conjecture of Thomassen, and an algorithmic the Lovász Local Lemma. The final talk on the second day, the Norman Biggs lecture, was given by Noga Alon, who always gives a good talk, and this was no exception. He was talking about random Cayley graphs, and asking in particular what can be said about the girth or the chromatic number of a random Cayley graph for a given group. He started off by asking: if the order of the group is 10^(10^(10^10)) (I won’t attempt that in HTML), and we choose a generating set of size 10^10, then the chromatic number is with high probability 2 if the group is an elementary abelian 2-group, 3 if it is cyclic of prime order, and bigger than 10 if it is PSL(2,p). There were lots of technical results, but there was only time to give us a brief taste of the methods used. Given that these techniques are now available, is it time to revisit Babai’s problem: Is it true that, if G is a group which is neither abelian nor generalized dicyclic, then a random Cayley graph for G has automorphism group precisely G with high probability?

Since the last Around the Blogs in 78 hours, we saw some announcements for GraphLab as a company, some calls for SPARC 2013 and GlobalSIP. All of these news in listed below. It even looks like some of you took advantage of the different groups set up for that purpose. Good! To recap, we now have the Google+ Community (384), the CompressiveSensing subreddit (115), the LinkedIn Compressive Sensing group (2273) or the Matrix Factorization (660). With these numbers, it would be a wise choice to directly pitch to these crowds when you want to talk about a new meeting, or a job or anything else for that matter. Laurent Gas chromatography and 2D-gas chromatography for petroleum industry: The race for selectivity Signal Processing for Chemical Sensing: ICASSP 2013 Special session Suresh Coding, Complexity and Sparsity 2013 (SPARC) 2013. On GPU algorithms Fabian Numerical optimizers for Logistic Regression Danny An Overview of Graph Processing Frameworks Kaggle Titanic Contest Funding for the next generation of GraphLab Bond Percolation in GraphLab Larry STEIN’S PARADOX Aaronson, COLT, Bayesians and Frequentists Dirk Open PhD position in applied analysis, mathematical imaging, inverse problems Existence of minimizers for the Horn-Schunck functional for optical flow Hein “Randomized Numerical Linear Algebra (RandNLA): Theory and Practice” Tianyi Our DMKD paper is selected as Top 5 Editor’s Choice Article for Free Reading Josh ITAR Craziness in the News Vladimir Gesture Recognition Startup Wins MIT $100K Entrepreneurship Competition Andrew SPARC 2013 Christian i-like workshop [talk] i-like[d the] workshop John Efficiency vs. Robustness Machine Learning Noisy Time Series V: Mean Reverting Processes Sebastien The aftermath of ORF523 and the final ORF523: Optimization with bandit feedback ORF523: Acceleration by randomization for a sum of smooth and strongly convex functions Anand CFP : GlobalSIP 2013 Deadline Extended to June 15 Cam 21st Century Problems Multi-Armed Bandits Machine Learning counter-examples How to solve the Price is Right's Showdown An algorithm to sort "Top" Comments Brian Seeing the potential in 3D While on Nuit Blanche, we had: Ghost Imaging does 3D and multispectral Imaging Sparse FFT implementations Another day at the Big Data: Theoretical and Practical Challenges Workshop A day at the Big Data: Theoretical and Practical Challenges Workshop Please take the time to nominate somebody or something today Sunday Morning Insight: Computational Cooking, you won't see food the same way anymore. The OSTP is seeking an Outstanding “Open Science” Champion of Change Saturday Morning Videos (part II) Saturday Morning Videos Credit: ESA/NASA Join the CompressiveSensing subreddit or the Google+ Community 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.

I will attend tomorrow MVA in Kyoto, a major conference on machine vision and applications. Here are the slides.

My 20th Harvard reunion book is in hand, offering a social snapshot of a certain educationally (and mostly financially) elite slice of the US population. Here is what Harvard alums name their kids.  These are chosen by alphabetical order of surname from one segment of the book.  Most of these children are born between 2003 and the present.  They are grouped by family. Molly, Danielle Zachary, Zoe, Alex Elias, Ella, Irena Sawyer, Luke Peyton, Aiden Richard, Sonya Grayson, Parker, Saya Yoomi, Dae-il Io, Pico, Daphne Lucine, Mayri Matthew, Christopher Richard, Annalise, Ryan Jackson Christopher, Sarah, Zachary, Claire Shaiann, Zaccary Alexandra, Victoria, Arianna, Madeline Samara Grace, Luke, Anna William, Cecilia, Maya Bode, Tyler Daniel, Catherine Alex, Gretchen Nathan, Spencer, Benjamin Ezekiel, Jesse Matthew, Lauren, Ava, Nathan Samuel, Katherine, Peter, Sophia Ameri, Charles Sebastian Andrew, Zachary, Nathan Alexander, Gabriella Liam Andrew, Nadia Caroline, Elizabeth Paul, Andrew Shania, Tell, Delia Saxon, Beatrix Benjamin Nathan, Lukas, Jacob Noah, Haydn, Ellyson Freddie Leonidas, Cyrus Isabelle, Emma Joseph, Theodore Asha, Sophie, Tejas Gabriela, Carlos, Sebastian Brendan, Katherine Rayne James, Seeger, Arden Helena, Freya Alexandra, Matthew George If you saw these names, would you be able to guess roughly what part of the culture they were drawn from?  Are there ways in which the distribution is plainly different from “standard” US naming practice?

Mathematicians are like Frenchmen:whatever you say to themthey translate into their own language and forthwith it is something entirely different.-- Johann Wolfgang von Goethe (Maxims and Reflexions, 1829)The 140th day of the year; 140 is the sum of the squares of the first seven positive integers. 12 + 22 + 32 + 42 + 52 + 62 + 72 = 140. *Prime CuriosEVENTS 1663 Robert Hooke was one of 98 persons who were declared members at a meeting of the Royal Society. He was admitted to society on 3 Jun 1663, and was peculiarly exempted of all payments. Before the Royal Society had been establish in 1660, Hooke was already distinguished for the invention of various astronomical instruments, and the air-pump he contrived for Charles Boyle (whom he had assisted for several years with chemical experiments at the Philosophical Society, Oxford). He invented a balance or pendulum spring (1656-58), one of the greatest improvements in the construction of timepieces. By 1662, he had been appointed curator of experiments to the Royal Society, and on 11 Jan 1664, awarded a salary of £30 per annum for life for that position.*TIS 1665 Newton's earliest use of dots, "pricked letters," to indicate velocities or fluxions is found on a leaf dated May 20, 1665; no facsimile reproduction of it has ever been made.' The earliest printed account of Newton's fluxional notation appeared from his pen in the Latin edition of Wallis' Algebra [Cajori, History of Mathematical Notations, vol. 2, p. 197] *VFR1715 In a letter written to Leibniz, May 20, 1716, John Bernoulli discussed the equation:d2y/dx2 = 2y/x2where the general solution when written in the formy = x2/a + b2/3xinvolves three cases: When b approaches zero the curves are parabolas; when a approaches infinity, they are hyperbolas; otherwise, they are of the third order. *John E. Sasser, HISTORY OF ORDINARY DIFFERENTIAL EQUATIONS THE FIRST HUNDRED YEARS 1875 The International Bureau of Weights and Measures established by the International Metric Convention, Sevres, France. The bureau is the repository for the “International Prototype Meter” and the “International Prototype Kilogram.” *SAU= St. Andrews Univ And for your (in case you thought that 3D movie technology was new, file)In 1901, Claude Grivolas, one of Pathe's main shareholders in Paris, France, invented a projector that produced three-dimensional pictures.*TIS1927 At 7:40 a.m., Charles Lindbergh took off from Roosevelt Field in Long Island, N.Y., aboard the "Spirit of St. Louis" monoplane on his historic first solo flight across the Atlantic Ocean. He arrived in France thirty-three and one-half hours later. *TIS1930 The Institute for Advanced Study incorporated. Two and a half years later Albert Einstein and Oswald Veblen were appointed the ?rst professors. [Goldstein, The Computer from Pascal to von Neumann, p. 77]*VFRIn 1956, the first hydrogen fusion bomb (H-bomb) to be dropped from an airplane exploded over Namu Atoll at the northwest edge of the Bikini Atoll. The fireball was four miles in diameter. It was designated as "Cherokee," as part of "Operation Redwing."*TIS1961 France issued a stamp honoring Charles Coulomb (1736–1806) [Scott #B 352]. 1968 A team of six high school students from Upstate New York went to London to participate in the Fourth British Mathematical Olympiad. This was the ?rst time a team from the U.S. participated in an international mathematical competition. [The College Mathematics Journal, 16 (1985), p. 331] *VFRIn 1975 Norway issued a stamp for the centenary of the International Meter Convention in Paris. It pictures Ole Jacob Broch (1818– 1889), the ?rst director of the International Bureau of Weights and Measures. [Scott #655] *VFR At least ten other countries issued stamps to commemorate the same event, including Bulgaria, Romania, France, the Soviet Union..... but not the USA. (see 1975 below for another)1975 Sweden issued a stamp picturing a metric tape measure to honor the centenary of the International Meter Co

The last post, entitled To the brainy, the spoils, linked to an Economist article about management consulting. It would appear that in the public sector, the highest paid employees tend to work in a tax-exempt sports-entertainment complex that is, for strange historical reasons, hosted by the higher education system. (Via UOMatters)

Exciting news in academic publishing! There’s a startup company in the UK, called Flooved, who are on a mission to revolutionize scientific publishing. What sets them apart from many similar-sounding initiatives is that they seem to have a solid business model and they seem to be doing all of the right things, therefore my bet is that they are going to succeed. What they do is to compile existing lecture notes, handouts and study-guides, and along the lines of the Open Access movement, to make them freely available online. The advantage to students is clear. The advantage to instructors is that more people read and use the material. The advantage to publishers who contribute content (are you listening, big publishing companies?) is that they get precise and useful information on how the students are using their content, and this helps them make informed decisions to put them ahead of the competition. Beyond this, the Flooved model makes education available to people worldwide, including to people who don’t have access to universities. Now, if only they could also provide assessment and accreditation…