Mathematics

In this day and age of being green, some folks are looking at ways to save paper. Math worksheets are a great teaching resource since math is a practice subject. After much thought about expanding my worksheet library, I decided to work on a way to create online worksheets. I am proud to announce our new Math Worksheet Generator.Now visitors can create their own worksheets in seconds! Each worksheet is interactive, with a timer and instant scoring. These resources are intended for on-screen use, just like we also provided the option of printing the worksheet and the answer key. Many thanks to Noetic Learning for partnering with us on this venture.

Math Goodies Blog: Math Worksheet Generator

The academic year finished off with two rather different events: my LMS–Gresham lecture about the Mathematical Structures course, and marking the approximately 270 scripts. The LMS–Gresham Lecture Last week I gave the annual LMS–Gresham lecture. When they asked me to do it, a year ago, I was writing the course material for Mathematical Structures, and couldn’t think of anything else, so I said I would talk about that. In fact, I believe that a cohort of talented and passionate mathematicians is important – why else would I be doing this job? Anyway, the lecture went well. You can see the slides here; the slides don’t have all the ad libs, or the questions afterwards. After the lecture, we went for a pleasant meal in the nearby Indian restaurant. Incidentally, I went to the LMS–Gresham lecture last year to see how someone else (in this case Bernard Silverman) did it. But this year I have no idea who my successor is. Marking the exam The good news here is that the students seem to have done rather well in the exam. Of course there is lots of monitoring and standardization to be done yet, but it looks as if both the median and the average mark are just above the B/C borderline. The students have done me proud. (I did wish, though, that I had a little stamp saying “An example is not a proof!”) However, I noticed a couple of curious tendencies: Having given a counterexample to one statement, people tend to hunt for a different counterexample to the next, even if the same one works (for example, if the second statement is the contrapositive of the first). It’s as if the counterexample has exhausted its potency on one statement. When asked whether several properties hold (e.g. is a relation reflexive, symmetric, transitive?), there is a tendency to mention only the ones that do hold. We all have a mindset that inclines towards the positive, but to test a hypothesis you have to look at possible negatives. Here is a selection of things written by students which caught my eye. These are not in any sense a representative selection. Some of them show a lack of understanding which you might find worrying; I would excuse a lot of this on the grounds that in the stress of an exam you will almost certainly write things that with calm consideration you wouldn’t. Some contain good sense hidden under poor expression. Some show original and creative thought. Some of them show that the students have picked up my passion for mathematics! I have sometimes lightly edited these. √2 must be irrational since it falls between √1 and √3. “Clearly” cannot be used in a proof since nothing is clear without a proof of it. [This was a common reaction. One candidate said "You cannot be lazy and write "Clearly P(0) is true", you must prove it. It may be clear to you, not always clear to the reader". Bravo!] A set with no elements contains a single element which is the empty set. [After working out the cases n = 1,2,3] So it seems the formula is correct. However the above is not a proof. m2 is also even, since anything squared becomes even. If “less than” is related to ℕ, then ℕ is related to “less than”. Hence it is shown that P(n) is true for P(n+1). The proof does not include a conclusion box ☐ to indicate the end of proof [and is therefore invalid]. Therefore A is infinitely countable. [This quite common.] The relation “less than” on ℕ is not reflexive since a is not related to a for most natural numbers a. We need to prove by rejection. Suppose √2 is a rational number. Then it can be written in the form m/n. But we cannot write √2 in this form, so contradiction. The statement is not true as this cannot be proven. The contrapositive is not true as the statement is often true. Previous

The issue of random sampling in compressive sensing was made more clear, in my view, by the work of Ben Adcock and Anders Hansen ( see A Q&A with Ben Adcock and Anders Hansen: Infinite Dimensional Compressive Sensing, Generalized Sampling, Wavelet Crimes, Safe Zones and the Incoherence Barrier. ). In short, the whole random sampling story has some problems at low frequencies. In MRI, the field at the leading edge of compressive sensing, several sampling techniques have been evaluated to corner this issue down. What is most interesting in this whole story is the connection with the hardware: We are here seeing a direct connection between actual hardware constraints (sampling authorized by the hardware) and the mathematics of sampling. One needs to realize that this connection between those two fields is rare. Here is another example of the connection between mathematics of sampling and hardware constraints: Travelling salesman-based compressive sampling by Nicolas Chauffert, Philippe CIUCIU, Jonas Kahn, Pierre Weiss. The abstract reads: Compressed sensing theory indicates that selecting a few measurements independently at random is a near optimal strategy to sense sparse or compressible signals. This is infeasible in practice for many acquisition devices that acquire samples along \textit{continuous} trajectories. Examples include magnetic resonance imaging (MRI), radio-interferometry, mobile-robot sampling, ... In this paper, we propose to generate continuous sampling trajectories by drawing a small set of measurements independently and joining them using a travelling salesman problem solver. Our contribution lies in the theoretical derivation of the appropriate probability density of the initial drawings. Preliminary simulation results show that this strategy is as efficient as independent drawings while being implementable on real acquisition systems. If somebody were to explain to me why they have pi^2 as opposed to pi^(1/2), I'd really appreciate it. 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.

Algebra class E-course sign in.

Whoever ... proves his pointand demonstrates the prime truth geometricallyshould be believed by all the world,for there we are captured~Albrecht DurerThe 141st day of the year; 141 is the first non-trivial palindrome appearing in the decimal expansion of Pi, appearing immediately after the decimal point, 3.14159. Tanya Khovanova, Number Gossip EVENTS1819 the first bicycle in the U.S. was seen in New York City. Such bicycle velocipedes or "swift walkers" had been imported that same year. Shortly thereafter, on 19 Aug 1819, the city's Common Council passed a law to "prevent the use of velocipedes in the public places and on the sidewalks of the city of New York."**TIS (Skateborders take note, you are not the first to be banned from the sidewalks)1908 Glenn (Hammond) Curtiss was a pioneer in the development of U.S. aviation whose aircraft were widely used during World War I. That the Wrights made the first powered flights has generally been accepted, but the achievements of Curtiss spanned several decades and took the airplane from its wood, fabric and wire beginnings to the forerunners of modern transport aircraft. Curtiss made his first flight on his 30th birthday, 21 May 1908, in White Wing, a design of the Aerial Experiment Association, a group led by Alexander Graham Bell. White Wing was the first plane in America to be controlled by ailerons instead of the wing-warping used by the Wrights. It was also the first plane on wheels in the U.S. *TIS (See 1878 Birth below)1901 the first U.S. State motor car legislation was an act to regulate the speed of motor vehicle, passed in Connecticut. A limit was established of 12 mph within city limits and 15 mph outside, which were higher than the 8 mph city and 12mph country speeds in the bill as originally presented. Also, the car driver was required to reduce speed upon meeting or passing a horse-drawn vehicle, and if necessary, to stop to avoid frightening the horse.*TISThis last part about meeting (or passing) a horse, with or without cart, is still essentially the law in England and Ireland.In 1916, Daylight Saving Time was introduced in Britain as a war-time measure to save fuel. The idea began when a London builder, William Willett, presented a scheme of shifting the clock to better use the hours of daylight in summer. He campaigned and published a brochure on the subject in 1907 (in which his proposal was to adjust the clocks in four weekly adjustments of 10-mins). When Parliament did consider a Daylight Saving Bill, to implement a seasonal one-hour change, it failed for lack of support. However, a little more than a year after his death after his death, the idea was finally adopted during WW I for wartime fuel savings. Now most of the countries in the northern hemisphere use a form of daylight saving time. *TIS 1932 Amelia Earhart ?ew alone across the Atlantic, being the ?rst woman to do so. *VFR1952 IBM Announces Model 701, "Defense Calculator.": IBM announced its 701 machine and by doing so emphasized its commitment to innovation in electronic computing. The company's first computer designed for scientific computations. The IBM 701 had an electrostatic storage tube memory and kept information on magnetic tape. The company eventually sold 19 of the machines -- more than expected -- to the government and large companies and universities for complex research.*CHM BIRTHS429 B.C. Plato born in Athens. He died on the same date in 348 B.C. [Muller] [Should it be 427 B.C.?] *VFR 1471 Albrecht Durer, (21 May 1471 – 6 April 1528) German painter and engraver. Mathematicians are fond of his etching Melancholia for it contains the magic square. Oldstyle numerals are used in the two center squares to emphacize the year that this etching was done by Durer. There is still debate about the shape of the solid in the foreground of the picture. *TIS He also published a book on geometric constructions (1535) using a straight-edge and compass. Although designed to enable artists better represent a

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.