Last 5 posts from each of the top Math blogs
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Weyl Tube Formula
5 hours ago
by Walt
Simon Willerton has written an introduction to the Weyl tube formula.
More details can be found in this review of Alan Gray’s book on the subject.
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Applications of Fractional Derivatives
1 day ago
by Walt
In ordinary calculus, you define “integral derivatives” — the first derivative, second derivative, etcetera. If you think of differentiation as an operator D that takes functions to functions, then the higher-order derivatives are just Di for natural numbers i. As far back as Liouville, mathematicians have defined fractional derivatives, extensions of this definition [...]
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Magistra’s Mathematical Ghost
1 day ago
by Walt
I ran across this interesting post by a historian who was an undergraduate mathematics major. She found her old linear algebra notes, and was surprised to find how little of it she still understood:
It’s not just that I can’t answer this question now, it’s that I can barely comprehend even what it means. The [...]
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Class Notes in Probability, Statistics, and Operat ...
2 days ago
by Walt
Like many people, while a graduate student Roger L. Goodwin took a wide variety of courses in applied probability, statistics, and operations research. Unlike the others, though, he compiled lecture notes from all of his classes into one big book, available for download.
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Hilbert Space Methods for Differential Equations
4 days ago
by Walt
In addition to individual articles, the Electronic Journal of Differential Equations also publishes monographs in the area of differential equations. The first one was a book that I think I remember seeing on library bookshelves: Showalter’s Hilbert Space Methods for Differential Equations.
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Pedagogy
4 hours ago
Yes, it's true, I spent an hour making a worksheet and a quiz for the class that I am teaching that I will quite possibly never teach again. In fact, I have a worksheet leftover from last spring that I can recycle, and I don't really need to give a quiz, as the quiz-homework part of the grade is pretty much free points.Also true: I have not yet graded the previous quiz.Transitional: Possible collaborator for New Job is suggesting that I should do something with Alice. It is unclear to me if Al ...
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Fun with Data
1 day ago
Since I didn't feel like cleaning my house today I'm in the office playing with my dataset from the registrar's office.In all of our normal freshman-level classes, the mean math ACT score is over 1 point lower for female students than the mean for male students, with a tiny p-value. In these same courses, the success rate is higher for female students than for male students, with a modest p-value.
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Recent Adventures
2 days ago
Yesterday at check-in: I got to the Ithaca airport and checked in for my flight and they couldn't issue me a boarding pass, so they gave me some slip to let me through security without a boarding pass. Then at the gate they could issue me a boarding pass for my flight to Detroit but not for the leg from Detroit to home. I had to wait until I got to the gate in Detroit (and show ID again) in order to get my boarding pass for my flight from Detroit to home.Had a long conversation with the guy sitt ...
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Farewell, Ithaca!
3 days ago
Soon I will pack up the laptop and head towards the bus stop so that I can catch a bus to the airport and then fly back home so that I can attend a meeting tomorrow for New Job.In classic Ithaca style, right now I can see out the window of this cafe a Free Tibet march being led by several Buddhist monks carrying Tibetan flags. When I lived here, I didn't know that Namgyal was here. All I knew was that I saw a lot of monks on the bus.As expected, I didn't get as much done as I'd hoped to. I am st ...
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More from My Spring Break in Ithaca
4 days ago
Walked up the Buffalo St. hill. Once. Don't need to go up there again. Everything I might want at the top of the hill is also available at the bottom of the hill (except Korean food, which I have already dined on).The plot thickens with my new job. OK, probably my fault for not asking enough questions. (Some of them I know that I should have asked but don't care as much I am supposed to -- like which retirement plan the job has.) But some things just can not be anticipated. Lucky for me I work b ...
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Formspring
9 hours ago
by John Armstrong
For once I’m not the absolute last person on a fad. I’ve set up a page at Formspring. Any questions you have, you can ask there. No promises about answers, but it’s a nice anonymous feedback system.
Now to figure out how to add it to the sidebar…
[...]
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Root Systems Recap
1 day ago
by John Armstrong
Let’s look back over what we’ve done.
After laying down some definitions on reflections, we defined a root system as a collection of vectors with certain properties. Specifically, each vector is a point in a vector space, and it also gives us a reflection of the same vector space. Essentially, a root system [...]
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The Automorphism Group of a Root System
2 days ago
by John Armstrong
Finally, we’re able to determine the automorphism group of our root systems. That is, given an object in the category of root systems, the morphisms from that root system back to itself (as usual) form a group, and it’s interesting to study the structure of this group.
First of all, right when we first talked [...]
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Construction of E-Series Root Systems
3 days ago
by John Armstrong
Today we construct the last of our root systems, following our setup. These correspond to the Dynkin diagrams , , and . But there are transformations of Dynkin diagrams that send into , and on into . Thus all we really have to construct is , and then cut off [...]
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Construction of the F4 Root System
4 days ago
by John Armstrong
Today we construct the root system starting from our setup.
As we might see, this root system lives in four-dimensional space, and so we start with this space and its integer-component lattice . However, we now take another copy of and push it off by the vector . This set consists [...]
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Is this a LaTeX bug?
2 days ago
by David Speyer
I just discovered the following behavior, which seems counterintuitive to me. I’d like to claim I actually found a bug in LaTeX, but that seems unlikely. Still, I’m curious whether someone can explain the logic behind this.
Try to compile the following
egin{Theorem}[ cite[Theorem 1]{Gauss} ]
Every integer is the sum of three triangular numbers.
end{Theorem}
You’ll get
Runaway argument?
Theorem 1)
! [...]
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New arxiv interface for authors: go update your pa ...
2 days ago
by Scott Morrison
If you have any papers on the arxiv which have since been published, very likely you are amongst the many mathematicians who have neither added the journal reference to the arxiv article metadata, nor updated the arxiv copy to match the final (post-refereeing) version.
Go do this, right now.
The reason I’m so boldly telling you to [...]
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Google Public Data Explorer
5 days ago
by Scott Morrison
Google.org just announced their Public Data Explorer, with which you can very quickly and easily examine many interesting statistics. Here’s an example I cooked up in a less than a minute:
This shows the relationship between life expectancy and fertility rates; colours code regions, point sizes indicate infant mortality rates. If you follow this link, you [...]
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Draft piece on Math Overflow for the Notices
7 days ago
by Scott Morrison
Ravi Vakil, Anton Geraschenko and I are writing an opinion piece for the Notices about Math Overflow. Following in the fine tradition that John Baez started with his opinion piece about mathematical blogging, we’d like to post our draft here, and ask for suggestions and criticism!
Note that we’re working inside a fairly strict ~800 word [...]
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Knot polynomial identities and quantum group coinc ...
> 10 days ago
by Noah Snyder
Scott Morrison, Emily Peters and I have just uploaded to the arxiv our paper Knot polynomial identities and quantum group coincidences. In this paper we prove several new strange identities between certain specializations of colored Jones polynomials and other classical knot polynomials. For example, we prove that for any knot (but not for [...]
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My Prezi at ICTCM
1 day ago
by SplineGuy
I went out on a limb today. During my talk that I presented at the ICTCM 2010 conference in Chicago, instead of using a more traditional media supplement to my talk (such as overhead, powerpoint or PDFs), I used Prezi. Some of you may have heard of it, but most of you probably haven’t.
I discovered [...]
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Book Recommendation: The Housekeeper and the Profe ...
4 days ago
by SplineGuy
A couple of weeks ago, I finished reading a book that had been recommend in an article I was reading at the MAA website (Mathematical Association of America). The book was called “The Housekeeper and the Professor” by Yoko Ogawa.
I highly recommend this book as a quick read. It’s a heartwarming tale that wraps [...]
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ICTCM 2010: Twitter to the Rescue
6 days ago
by SplineGuy
Thank you Twitter!
More specifically, I’m grateful to one of the co-chairs of the ICTCM conference for watching twitter and seeing my lament that I would not be able to attend the conference this year because I didn’t have the travel funds.
On February 11th, I posted:
Still trying to decide if ICTCM is in the cards [...]
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Student Writing in Differential Equations
8 days ago
by SplineGuy
As part of the group project that was assigned in my Differential Equations course, students were required to write a project report. I just wanted to post quickly today that I am significantly impressed with the performance of these students on the assignment provided.
In preparation for the writing portion of the project, I [...]
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A Kindle for all Seasons
> 10 days ago
by SplineGuy
About three weeks ago, I splurged and ordered myself a Kindle 2. I had bounced back and forth between wanting one and not but finally convinced myself that it was time to add another gadget to my repertoire. And let me say, I love it!! To alleviate any guilt over spending that kind of [...]
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Mathematweets
14 hours ago
by Maria H. Andersen
Whether you’re interested in using Twitter as a teaching tool or not, I think you’ll enjoy this very unique presentation, all built out of an illustration.
Mathematweets on Prezi
Possibly Related Posts:
Sorry … busy week
Teaching with Technology Discussion Panel
How to Study for a Math Test
India Travelogue
What have you learned from this blog?
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See ya at ICTCM
2 days ago
by Maria H. Andersen
This weekend I’ll be in Chicago at ICTCM. Here are my presentations and where you might be able to find me:
Thursday, March 11:
New Ideas for Online Resources (part of a short course) 1:30-2:15pm
Friday, March 12:
Wolfram Research Booth, 9:30-10am
Emerging Technologies Panel, 10:30am-12:15pm
Wolfram Research Booth, 12:30-1pm (I think someone better bring me lunch!)
Presentation: Mathematweets, 1:30-2:15pm
Tweetup (hotel bar): [...]
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Twitter Weekly Link Roundup for 2010-03-07
6 days ago
by Maria H. Andersen
Miscellaneous …
Do you think that Technology Skills should be a broad category on this list of transferable skills? http://bit.ly/Ljluw #
RT @Goamick: Webpage for the Emerging Digital Technologies Certificate program at Central Lakes College http://bit.ly/bafVaj #
Ultimate Rube Goldberg … This too shall pass http://www.youtube.com/watch?v=qybUFnY7Y8w #
All faculty meetings should be run in Pecha-Kucha format. 5 minutes, 20 [...]
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Playing to learn math?
9 days ago
by Maria H. Andersen
This presentation, built yesterday, is my philosophical argument for why we should be actively pursuing games as a way to teach algebra. In fact, you’ll find that many of the definitions of games and game design principles sound like they are describing algebra. Of course, the presentation misses something without my accompanying talk, [...]
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Twitter Weekly Link Roundup for 2010-02-28
> 10 days ago
by Maria H. Andersen
Led the choir this morning at #ITC10 … My first attempt at a flash mob! #
Syndication-oriented Architecture or Feed-frenzied Learning (using RSS to organize content) #
My ‘open-web’ MathET course from last semester: http://netvibes.com/mccmath105#ITC10 #
Will hace to check out NC State Twitter and UMW blogs later. #ITC10 #
RT @marcparry: For more info on some of the [...]
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NY State considers dumping most “Regents” Exam ...
6 days ago
by jd2718
They claim they could save $13.7 million.
Closing a budget gap is the wrong reason to dump the Regents. But there are lots of right reasons.
It’s in a memo from, Dr. John B. King, Jr., Senior Deputy Commissioner for P-12 Education. I like that. I mean “P-12.” I haven’t seen that designation before. Anyhow, he’s new. [...]
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Alice and Mathematics
6 days ago
by jd2718
In yesterday’s NY Times Melanie Bayley discusses some of the mathematical satire that Lewis Carroll created.
Tea party? T-party? With three elements, but time missing? She also hits continuity, logic, algebraic systems, even topology.
Here’s two paragraphs:
In the mid-19th century, mathematics was rapidly blossoming into what it is today: a finely honed language for describing the conceptual [...]
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Why don’t I like these logarithm questions?
8 days ago
by jd2718
I feel obliged to run my kids through exercises like these two, but I don’t like them. Speculate: Why do they rub me the wrong way? Am I right not to like these?
1.
,
.
Express in terms of x and y.
2. Write as a single log: 1 + log v – 3log w
What do you think? [...]
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New Action – not Unity, not ICE
9 days ago
by jd2718
To read it, click here.
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If Brownsville, Brooklyn was a city, what would it ...
> 10 days ago
by jd2718
Or Morrisania in the Bronx?
Central Falls, Rhode Island?
Not the same, but pretty close.
Look at the description drawn by Tom Hoffman of Tuttle SVC:
Central Falls is really unlike any other “city” you’ve ever seen. Just imagine carving out a one square mile chunk of the poorest immigrant neighborhood in the closest metropolitan area and calling it [...]
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Oh So Busy
2 days ago
Have I mentioned how busy I am lately?I mean, dang!You would think one little-old document wouldn't take that long to create. You would be wrong.
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HPC and the Future of Algorithms
5 days ago
As parallel computers get bigger and and more powerful, the way we use these machines has to change. The reason is that the machines are not just growing in clock speed, they're changing in architecture as well.Over the past decade, leadership high-performance computing resources have evolved from systems with thousands of CPUs to systems with hundreds of thousands of multicore CPUs. And in this time, the algorithms in the best science application programs have adapted to this change. Today, ...
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Weekend Fun
7 days ago
In a rare moment of convergence, both of my sisters and their sons will be at my dad and bonus mom's house on Sunday. This means that we'll be heading up there tomorrow and spending all day Sunday with them. There will be a cousin party. My sisters and I will have special sister time. I am bringing a cake baked by me and my favorite baking assistant, to celebrate my bonus mom's birthday (which was last month, but who's counting?!?!).I am looking forward to this little break from work. For m ...
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Today in +quot;Things You Learn As a Parent+quot;
> 10 days ago
Did you know that there are people who put videos of box fans and ceiling fans, complete with commentary about the quality of said fans, on YouTube? Neither did I.
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Running Like Mad
> 10 days ago
So, I learned from blogfriend PhizzleDizzle that until 1960, there were no women's summer Olympics events in which women ran 800 meters or more. And the women's marathon was not an event until 1984! (Here's her post -- warning for those sensitive to words of the four-letter variety: it is full of very descriptive and highly justified cursing!)Anyhow, this outraged me too after I learned about it. It's pretty sad that women couldn't participate in these sporting events because of erroneous bel ...
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Choosing the number of clusters II: Diminishing Re ...
18 hours ago
by Suresh
(this is part of an occasional series of essays on clustering: for all posts in this topic, click here)
In the last post, we looked at the elbow method for determining the right number of clusters in data. Today, we'll look at generalizations of the elbow method, all still based on the idea of examining the quality-compression tradeoff curve.
For the purpose of discussion, let's imagine that we have a plot in which the quality of the clustering (measured anyway you please, as long as 0 means ...
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Who pays for submissions ?
5 days ago
by Suresh
Writing a paper takes a tremendous amount of time. So, one of the frequent complaints that authors make is when PC members submit half-baked, clearly below-threshold reviews on a paper just to get the resume bullet and claim to have done their reviewing duties. Personally, I feel intense anger when receiving crappy reviews that come with not the slightest bit of insight, and then am expected to rebut them or accept them. Not to mention the long-term psychological damage incurred by having pape ...
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Choosing the number of clusters I: The Elbow Metho ...
5 days ago
by Suresh
(this is part of an occasional series of essays on clustering: for all posts in this topic, click here)
It's time to take a brief break from the different clustering paradigms, and ponder probably THE most vexing question in all of clustering.
How do we choose k, the number of clusters ?This topic is so annoying, that I'm going to devote more than one post to it. While choosing k has been the excuse for some of the most violent hacks in clustering, there are at least a few principled directions ...
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Guest Post: Update from the CRA Career Mentoring W ...
> 10 days ago
by Suresh
(ed note: Jeff Phillips is at the CRA Career Mentoring Workshop. His Day 1 dispatch is here)
It is day two at the CRA Career Mentoring Workshop.
Today was all about funding, with speakers from NIH (Terry Yoo), DARPA (Peter Lee), Laboratory for Telecommunications Science (Mark Segal), and NSF (Jan Cuny). Jeanette Wing, the assistant director at NSF CISE also made an appearance at reception yesterday.
(ed. note: I just heard that Jeannette Wing is leaving CISE in July. This is sad news - she ...
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Guest Post: Update from the CRA Career Mentoring W ...
> 10 days ago
by Suresh
(ed note: Jeff Phillips is at the CRA Career Mentoring Workshop today and tomorrow, and filed this dispatch from Day 1.)
I am reporting from the CRA Career Mentoring Workshop. So far it has been excellent.
Frankly, I would not have even thought of coming (I did not even know about it), but it was highly recommended for all CI Fellows. But, having been here the first day, I would now recommend it to postdocs, early faculty, and senior graduate students set on a career in academics. Someo ...
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Have You Noticed?
2 days ago
by Denise
[Photo by apbeatty.]
Have you ever clicked a link from the Blog Parties for Teachers section of my sidebar? If not, you may be missing a lot of wonderful resources. Blog carnivals are a great way to keep up with the best of a particular teaching or homeschooling blog niche. I just updated all the links [...]
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Game: Target Number (or 24)
5 days ago
by Denise
[Photo by stevendepolo.]
Math concepts: addition, subtraction, multiplication, division, powers and roots, factorial, mental math, multi-step thinking
Number of players: any number
Equipment: deck of math cards, pencils and scratch paper, timer (optional)
Set Up
All players must agree on a Target Number for the game. Try to choose a number that has several factors, which means there will be [...]
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Can You Solve This?
9 days ago
by Denise
[Click on the image to see the equation more clearly.]
This equation resulted from my playing around with one of the submissions for this month’s Math Teachers at Play blog carnival. Remember, you can still join in the carnival by sending me a blog post through this handy submission form.
Meanwhile, be sure to visit the Carnival [...]
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Quotable: Make Them Laugh
> 10 days ago
by Denise
You have to make them laugh. You must never underestimate the power of laughing in a maths classroom.
— Carol Roberts
quoted in Laughing lesson Adult learning
Or, as Donald O’Conner put it:
I think this is my biggest failing as a teacher: I am too much the straight man.
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World Maths Day
> 10 days ago
by Denise
Parents of K-12 students: Act quickly if you want your student to participate in the (free!) World Maths Day. More than 2 million students from over 200 countries will join together in the annual quest to set a world record in answering math questions — a fun way to improve mental arithmetic skills. Students age [...]
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A type diagram for function spaces
2 days ago
by Terence Tao
In harmonic analysis and PDE, one often wants to place a function on some domain (let’s take a Euclidean space for simplicity) in one or more function spaces in order to quantify its “size” in some sense. Examples include
The Lebesgue spaces of functions whose norm is finite, as well as [...]
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Course announcement: 254B, Higher order Fourier an ...
3 days ago
by Terence Tao
Starting on Monday, March 29, I will begin my graduate class for the winter quarter, entitled “Higher order Fourier analysis“. While classical Fourier analysis is concerned with correlations with linear phases such as (where ), quadratic and higher order Fourier analysis is concerned with quadratic and higher order phases such as , , etc.
In [...]
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254A, Notes 7: The least singular value
8 days ago
by Terence Tao
Now we turn attention to another important spectral statistic, the least singular value of an matrix (or, more generally, the least non-trivial singular value of a matrix with ). This quantity controls the invertibility of . Indeed, is invertible precisely when is non-zero, and the operator norm [...]
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The Littlewood-Offord problem in high dimensions a ...
> 10 days ago
by Terence Tao
Van Vu and I have just uploaded to the arXiv our joint paper “The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi“. In this short paper we give a different proof of a high-dimensional Littlewood-Offord result of Frankl and Füredi, and in the process also affirmatively answer one of their [...]
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254A, Notes 6: Gaussian ensembles
> 10 days ago
by Terence Tao
Our study of random matrices, to date, has focused on somewhat general ensembles, such as iid random matrices or Wigner random matrices, in which the distribution of the individual entries of the matrices was essentially arbitrary (as long as certain moments, such as the mean and variance, were normalised). In these notes, we now [...]
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Algebra problem: two speeds
2 days ago
Photo courtesy of Ben CooperThe speed of a freight train is 14km/h slower than the speed of a passenger train. The freight train travels 330 km, in the same time that it takes a passenger train to travel 360 km. Find the speed of each train.Again, an algebra problem about speeds. Again, we will make a simple table about the two trains. The table will have columns for speed, distance, and time. | distance | speed | time-----------------------------------------------Freight train ...
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Heads up for Pi day (3/14)
2 days ago
Pi day is upon us in a few days... 3/14. I'll refer you to my earlier post about Pi day for some resources and ideas.
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Subitizing - a video review
4 days ago
What is subitizing ? It's probably a new word for most. It basically means being able to recognize instantly how many objects you see, without counting.We all do that with the dots on the face of a dice. People who play dominoes with the larger set also learn to do that with the dots on the dominoes (they can go up to 18).But why would such be important? It is for children, because it promotes number sense, and also ties in with the concepts of addition, subtraction, and even place value.Look a ...
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New Math Mammoth books
> 10 days ago
There are now three new books available in the Blue Series. They are all for grades 5-6. The material for these books came from the Light Blue 5th and 6th grade curricula. Please click on the links to learn more and see samples.Math Mammoth The Four Operations(with a Touch of Algebra)The main topics studied in this book are simple equations, expressions that involve a variable, the order of operations, long multiplication, long division, and graphing simple linear functions. The idea is not to p ...
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Dividing decimals by decimals
> 10 days ago
When dividing decimals by decimals, such as 45.89 ÷ 0.006, we are told to move the decimal point in both the dividend and the divisor so many steps that the divisor becomes a whole number. Then, you use long division. But why?Schoolbooks often don't tell us the why , just the how .This video explores this concept.Divide decimals - why do we move the decimal point?It has to do with the fact that when we move the decimal point, we are multiplying both numbers by 10, 100, 1000, or some other pow ...
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Doug’s “Top 10 MATLAB code practices that make ...
2 days ago
by Loren
Doug's Top 10 MATLAB code practices that make me cry
This week, Doug's blog focuses on what he considers to be some poor programming practices he's seen in MATLAB code.
I agree with much of his list, including, despite the comments, the nix on global [...]
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Nichomachus’s Theorem
9 days ago
by Loren
Ned Gulley is stepping in as guest blogger this week. You may remember an earlier guest entry from him on calendars and leap years. Ned has been working at MathWorks almost as long as I have, and as we were chatting the other day, he reminded [...]
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Ensuring Positive Values - Part 2
> 10 days ago
by Loren
My last post started the discussion about how to ensure data values met certain constraints. The solutions I talked about were ones where
you checked at certain places during a calculation, but the constraints were not continuously enforced. [...]
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Ensuring Positive Values - Part 1
> 10 days ago
by Loren
Do you sometimes need to be sure an array has only bounded, positive values? At least one customer asked about this recently
and noted that it could be quite involved. Depending on the duration for which [...]
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Constrained Sorting of Arrays
> 10 days ago
by Loren
In a variety of applications, customers have requested a way to sort arrays subject to some constraints. One use case is when a row in an array represents a data record. Clearly,
to sensibly sort data [...]
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More MATLAB statistics toolbox licensing woes (and ...
8 days ago
by Mike Croucher
A little while ago I was having a nice tea break when all hell broke loose. Complaint after complaint started rolling in about lack of network licenses for the MATLAB statistics toolbox and everyone was wondering what I intended to do about it. A quick look at our license server indicated that someone had started [...]
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The Inverse Graphing calculator
9 days ago
by Mike Croucher
According to a new website, if you plot the following equation
then you’ll get the following graph
Head over to the Inverse Graphing Calculator to generate your own. It would be interesting to solve these equations and see if the website is correct.
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If you could have one MATLAB toolbox for free then ...
> 10 days ago
by Mike Croucher
One of MATLAB’s strengths is that it has a toolbox for almost everything. One of it’s weaknesses is that you have to pay separately for them all! Basic MATLAB is cheaper for most people than basic Mathematica but, in my experience at least, many people need access to statistics, optimization,symbolics, curve fitting and (increasingly) parallel [...]
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An alternative to binopdf using the NAG toolbox fo ...
> 10 days ago
by Mike Croucher
The Problem
A MATLAB user came to me with a complaint recently. He had a piece of code that made use of the MATLAB Statistics toolbox but couldn’t get reliable access to a stats toolbox license from my employer’s server. You see, although we have hundreds of licenses for MATLAB itself, we only have a few [...]
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Command line Mathematica on Mac OS X
> 10 days ago
by Mike Croucher
On a Linux machine with a normal install of Mathematica you can usually get access to a command line version of Mathematica by typing
math
at the command line. Command line Mathematica is useful for situations where you want to do batch processing, perhaps as part of a Condor pool or something, but I’ll not write about [...]
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Netflix Challenge 2 Canceled
1 day ago
by jl
The second Netflix prize is canceled due to privacy problems. I continue to believe my original assessment of this paper, that the privacy break was somewhat overstated. I still haven’t seen any serious privacy failures on the scale of the AOL search log release.
I expect privacy concerns to continue to be a big [...]
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Yahoo! ML events
> 10 days ago
by jl
Yahoo! is sponsoring two machine learning events that might interest people.
The Key Scientific Challenges program (due March 5) for Machine Learning and Statistics offers $5K (plus bonuses) for graduate students working on a core problem of interest to Y! If you are already working on one of these problems, there is no [...]
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Specializations of the Master Problem
> 10 days ago
by jl
One thing which is clear on a little reflection is that there exists a single master learning problem capable of encoding essentially all learning problems. This problem is of course a very general sort of reinforcement learning where the world interacts with an agent as:
The world announces an observation x.
The agent makes a choice [...]
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Deadline Season, 2010
> 10 days ago
by jl
Many conference deadlines are coming soon.
Deadline
Double Blind / Author Feedback
Time/Place
ICML
January 18((workshops) / February 1 (Papers) / February 13 (Tutorials)
Y/Y
Haifa, Israel, June 21-25
KDD
February 1(Workshops) / February 2&5 (Papers) / February 26 (Tutorials & Panels)) / April 17 (Demos)
N/S
Washington DC, July 25-28
COLT
January 18 (Workshops) / February 19 (Papers)
N/S
Haifa, Israel, June 25-29
UAI
March 11 (Papers)
N?/Y
Catalina Island, California, July 8- ...
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Sam Roweis died
> 10 days ago
by jl
and I can’t help but remember him.
I first met Sam as an undergraduate at Caltech where he was TA for Hopfield’s class, and again when I visited Gatsby, when he invited me to visit Toronto, and at too many conferences to recount. His personality was a combination of enthusiastic and thoughtful, with a great [...]
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Counting, Multiplication Principle, Pigeonhole Pri ...
4 days ago
by Dave Marain
The following video is available on my new MathNotations Videos Channel.
This particular video is a 10 minute discussion of developing the Multiplication Principle of Counting. It is designed more for the instructor than the student although it may be helpful in clarifying this important concept. The focus is on using multiple representations to reach the widest variety of learning styles. It is appropriate for any teacher of mathematics but particularly for the middle school teacher or those ...
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Another Algebra Problem for the +quot;Ages!+quot;
> 10 days ago
by Dave Marain
Forgive the lame attempt at punnery in the title but I hope you will see the many layers in the following discussion about a 'typical' word problem involving people's ages. Perhaps, not so typical but I hope it will be topical!
Please bear in mind that this blog is geared essentially toward the K-12 math teacher. Most of the problems I write are not intended to stump people. Rather they are vehicles to engage a discussion of instructional practice as we move toward a leaner, deeper and more c ...
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Does Learning/Playing Chess Develop The 'Mathemati ...
> 10 days ago
by Dave Marain
Nothing revolutionary about this question but it's been on my mind for some time and, now, that I have a six-year old grandson who seems to be analytical like me (we speak the same language!), I've decided to introduce him to chess via chess puzzles.
I'm not writing this because I believe one should develop a math curriculum around chess! I'm simply suggesting that any activity which requires problem-solving, analysis and creativity develops the mind. Chess is only one of many such vehicles whi ...
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Odds and Ends -- Week of 2-15-10
> 10 days ago
by Dave Marain
Catchup time...
So where are the answers and followup discussion to the previous two problems I posted? They're coming. I plan to make a video of the investigation in the 143 problem.
I think it would be so useful to post videos of actual lessons that demonstrate how some teachers implement explorations in the classroom at all levels from K-12. I'm sure there are some of these already online but they seem to be few and far between and I'm really referring to best practices here to serve as ...
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Can Your Students Find At Least Three Methods? Odd ...
> 10 days ago
by Dave Marain
I've been working on a new website which I will share with you when ready but I haven't forgotten my faithful readers who may have forgotten me!
There are so many issues in mathematics education that it would take forever to update you on all of them, however, I know that you are already aware of most of these.
Some Significant Current Issues in Math Ed
Moving Inexorably Towards Common Standards in Math
Teachers Need a Clear Curriculum Map/Content Guide rather than Standards!
Rapid Push Towa ...
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Products, Limits and Parametric Polymorphism
6 days ago
> {-# LANGUAGE RankNTypes #-}When I wrote about memoizing polymorphic types I mentioned that you can think of forall a. F(a) as the product over all types a of F(a), where F is some type level function. For example F might be a type constructor like []. That's not completely accurate, as I hope to now explain. Along the way we should get some insight into the meaning of the limit of a functor in a category.Suppose we have two types, A and B. We can form their product (A, B). We have the two p ...
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The Categorification of the Naturals
> 10 days ago
A heavyweight looking title, but this post is really about nothing more than doing arithmetic.Peano ArithmeticI've seen many articles on type level arithmetic. They all seem to share the idea that the Haskell type system can be made to perform computations by treating types as symbols that can be manipulated according to rules. But every article I have seen seems to miss the important idea that the naturals don't have to simply be empty symbols - that they are perfectly good types with elements ...
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Tagging Monad Transformer Layers
> 10 days ago
A quick post extracted from some code I was writing at the weekend.> {-# OPTIONS_GHC -fglasgow-exts #-}> {-# LANGUAGE ScopedTypeVariables, OverlappingInstances #-}> import Control.Monad.Trans> import Control.Monad.State> import Control.Monad.Writer> import Control.Monad.IdentityMonad transformers can get a little ugly. Here's a toy example that looks pretty bad:> test1 :: StateT Int (StateT Int (StateT Int (WriterT String Identity))) Int> test1 = do> put 1> li ...
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Target Enumeration with the Euler Characteristic. ...
> 10 days ago
Part 1> import Data.CharA Statement of the ProblemThe problem I ultimately want to solve, and its solution, is described in the paper Target Enumeration via Euler Characteristic Integrals. My goal here is to show how to implement that solution on a computer and make it accessible to a wider audience.Suppose we have a set of targets we want to count. This could be anything from enemy tanks rolling over the plains to electronically tagged wildlife roaming the countryside. Each target has a regi ...
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Counting Targets using the Euler Characteristic, P ...
> 10 days ago
Using LaTeX was so much easier than HTML that I'm doing it again. The PDF is here and the literate Haskell source is here.AbstractThe problem I ultimately want to solve, and its solution, is described in the paper Target Enumeration via Euler Characteristic Integrals by Baryshnikov and Ghrist. My goal here is to show how to implement that solution on a computer, and by doing so make it accessible to a wider audience.Thanks to @alpheccar for tweeting about the original paper.
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An Open Letter to Wayne Bishop (and the MC/HOLD po ...
3 days ago
Responding to some positive remarks about progressive mathematics education, Wayne Bishop (seen above), a founding member of the anti-progressive reform group Mathematically Correct wrote: Such speculation sounds beautiful, of course, but I have yet to meetany mathematician who was taught in a full-blown discovery environment.This prompted me to write the following open letter:Dear Wayne and Posse: Reading your comment about what sort of mathematicians you've never met, I must point out that I' ...
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Keith Devlin - Extended
> 10 days ago
Yes, the debate about multiplication-as-repeated-addition debate is still raging. It popped up again recently on math-teach thanks to a post by the always-thoughtful Jonathan Groves on February 16th, 2010, and has already engendered some fifty-five responses (whether the growth of the thread is additive, multiplicative, or exponential is left as an exercise for the student).Interested readers are urged to check both the discussion on math-teach (see the link above) and to go to the columns Mr. G ...
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Elitism and mathematics education: Why tracking is ...
> 10 days ago
As I survey the many pressing issues facing US education in general and mathematics education in particular, one that never goes away is tracking (or streaming or whatever euphemism is being served up by its advocates these days). To me, it is anathema. Not that I see no reasons to mix things up within classrooms frequently so that there are occasionally homogeneous as well as heterogeneous groupings along various constructs, including ability, gender, ethnicity, and others). But I will never ...
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Good Tests, Bad Tests: Can The Testing Fanatics Te ...
> 10 days ago
And do they really care?Consider the following problem:=====================================3, 4, 6, 7, 10, 12The number n is to be added to the list above. If n is an integer, which of the following could be the median of the new list of seven numbers?I. 6II. 6 1/2III. 7(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III==============================================In considering your evaluation of the question, you may wish to know the following facts: this is the 13th of ...
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You Want Proof? I'll GIVE You Proof!
> 10 days ago
Once again, the fires of discord are raging on math-teach@mathforum.org. One of the threads I've been embroiled in revolves on several axes: one is about teaching pure mathematics in K-12. Another is about visual proofs. The one I wish to specifically deal with here is the one that links the two: what comprises the nature of proof in elementary school mathematics classrooms and how do we get students in those grades to develop their notions of what a mathematical proof actually is?The problems i ...
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Grandiose Crankery: Cantor, Godel, Church, Turing, ...
4 days ago
A bunch of people have been asking me to take a look at yet another piece of Cantor crankery
recently posted to Arxiv. In general, I'm sick and tired of Cantor crankery -
it's been occupying much too much space on this blog lately. But this one is a
real prize. It's an approach that I've never seen before: instead of the usual
weaseling around, this one goes straight for Cantor's proof.
But it does much, much more than that. In terms of ambition, this thing
really takes the cake. According to ...
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Animal Experimentation and Simulation
> 10 days ago
In my post yesterday, I briefly mentioned the problem with simulations
as a replacement for animal testing. But I've gotten a couple of self-righteous
emails from people criticizing that: they've all argued that given the
quantity of computational resources available to us today, of course
we can do all of our research using simulations. I'll quote a typical example
from the one person who actually posted a comment along these lines:
This doesn't in any way reduce the importance of informin ...
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Scumbag Animal Rights Villains Harass Children for ...
> 10 days ago
This post is off-topic for this blog, but there are some things that
I just can't keep quiet about.
Via my friend and fellow ScienceBlogger Janet over at Adventures in
Ethics and Science, I've heard about some absolutely disgraceful
antics by an animal rights group. To be clear, in what follows, I'm not saying that all animal rights folks are scumbags: I'm pointing out that there's a specific group of animal rights folks who are sickening monsters for what they're doing.
The background: Th ...
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Friday Random Ten, 2/19/2010
> 10 days ago
Transatlantic, The Whirlwind (Part 4) - A Man Can Feel :
a track from the new Transatlantic album. Transatlantic is
a supergroup: it's made of members of Marillion (Pete Trevawas on
bass), the Flower Kings (Roine Stolte, guitar), Spock's Beard (Neil
Morse, vocals and keyboards), and Dream Theater (Mike Portnoy, drums).
In general, I don't like supergroups; they're usually more of a
commercial stunt than anything else. But I love Transatlantic;
and this album is fantastic - it's ...
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Disco Strikes Out Again: Casey Luskin, Kitzmiller, ...
> 10 days ago
For a lot of people, I seem to have become the go-to blogger for
information theory stuff. I really don't deserve it: Jeff Shallit at
Recursivity knows a whole lot more than I do. But I do my best.
Anyway, several people pointed out that over at the Disco Institute,
resident Legal Eagle Casey Luskin has started posting an eight-part
series on how the Kitzmiller case (the legal case concerning the teaching of
intelligent design in Dover PA) was decided wrong. In Kitzmiller, the
intelligent de ...
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Rhythm, Rhyme, Results: rapping about Math for Pi ...
1 day ago
by Sol
[ Editor’s Note:
Taunia from “Rhythm, Rhyme, Results” wrote to me asking if I’d blog about her education site. The site sells fun educational music and, in particular, has some Math songs in their Pi Day Collection. I wrote back letting Taunia know that I rarely plug commercial sites but I liked what her company was doing (luring students to Math with rap music) so I’d give her a plug on two conditions:
She sends me a couple of sample songs so that I feel good abo ...
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Review: Manga Guide to Statistics
> 10 days ago
by Sol
The Manga Guide to Statistics is a cartoon book in the same style as the publisher’s Manga Guide to Calculus, which I reviewed a while back. It’s been close to thirty years since I studied statistics (in High School) and reading this book brought back memories.
For the same reasons that I liked Manga’s Calculus book, I enjoyed this one. It tells a story. It has pictures, so it engages the visual sense as well as the “word processing” sense. It takes a subject that ...
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Slide rules rule
> 10 days ago
by Sol
The March/April 2009 issue of the Stanford Magazine had this delightful letter to the editor.
GOLDEN RULES
The article on Tom Wyman and his slide rule collection (“Calculating Collector,” Red All Over, January/February) takes me back to 1972, when Hewlett Packard introduced the HP-35, its first pocket scientific calculator, priced at $395. I was living in Palo Alto then, so I went to the Stanford Bookstore to see it. I found a gentleman standing at the counter, experimenting with the displa ...
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An information theory puzzle
> 10 days ago
by Sol
My brother shared this puzzle with me this morning. He heard it on the radio but no solution was offered. Neither of us know what the answer is so I’m looking forward to one of you posting the answer in the comments. Here’s the puzzle:
Bob and Alice are both millionaires. They’re both curious to know who is richer but they don’t want to tell the other one how much money they have. Without engaging a trusted third party, how can they both know who is richer?
I wonder if ...
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Nonplussed! Review
> 10 days ago
by Sol
“Nonplus” is not a particularly common English word so I looked it up on dictionary.com.
–verb (used with object)
1. to render utterly perplexed; puzzle completely.
–noun
2. a state of utter perplexity.
“Nonplussed” is a book full of perplexing facts, and solid Math to explain the perplexities. In other words, this book is about mathematically provable facts that don’t actually seem to be true.
Here is a great example of the state of being nonplussed and my ...
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More Indoor Tennis in D/FW Area
> 10 days ago
by algorithmist
Do you play tennis in the D/FW area and live relatively close to the airport? Bummed out by the bad weather this winter? Well, the Hilton D/FW Lakes has the solution for you. They have reopened indoor courts. The court area alternates between meeting space and tennis, so it’s important [...]
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Black History Month Robert Walter Johnson
> 10 days ago
by algorithmist
Over the past two years, I profiled several black mathematicians, many of which had an indirect influence on my own career. I’ve been very busy taking care of family issues as of late, so blogging has gone off my personal radar. Even so, I recently realized I have yet to profile a single black contributor [...]
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Who Dat?
> 10 days ago
by algorithmist
Just a quick shout out to friends and business associates from N.O., including Chris Giordano (director of tennis and sports club at the Hilton D/FW Lakes). Congratulations on the superbowl win!
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Aussie Open Wrapup
> 10 days ago
by algorithmist
Well, this was a really good tournament. On the mens side, I’m always pleased with a Federer win. Last year, he seemed to be weighted down with the effort to match Sampras’ slam record. Running into an inspired performance by Nadal, his serve broke down in the crucial fifth set. This year, he seemed very [...]
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Trigonometric Parameter Model
> 10 days ago
by algorithmist
The question that generated this topic was very similar to a problem I worked on recently. It deals with the trend of the last few posts on creating simple models that fit data. Suppose we have a parameter, z. It does not make any difference what z is; it could be depth [...]
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Rhombic Flowers
> 10 days ago
by Eric Gjerde
Hi everyone,
I#8217;m getting all packed and ready to head off to Japan tomorrow for the JOAS convention this weekend in Tokyo! They#8217;ve honored me quite a bit by inviting me there as a guest, and I hope to make it a very tessellation-centric time :) I#8217;m looking forward to meeting lots of new friends!
I thought [...]
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Mother and Child
> 10 days ago
by origomi
Mother and Child, originally uploaded by cedison.
Christine Edison posted photos of this absolutely stunning piece. I am always impressed by her ability to take ideas and use them in new ways, creating completely unique and fascinating works.
She#8217;s been making quite a few beautiful organic pieces as of late - pop over to her Flickr stream [...]
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Origami Tessellations Calendar
> 10 days ago
by Eric Gjerde
We just published a 17-month academic year calendar full of beautiful images of origami artwork from my book, #8220;Origami Tessellations: Awe-Inspiring Geometric Designs#8220;.
Available now for ordering - it#8217;s being printed on-demand by HP#8217;s MagCloud, which prints out some extremely nice product.
Speaking of items on the calendar: The 2009 Origami USA convention is coming very [...]
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OMG NYC meeting, April 2009
> 10 days ago
by origomi
20090418_1325, originally uploaded by one97tom.
I visited the great people at OMG NYC (Origami Meetup Group NYC) last April, and taught some tessellation basics and a few models while I was there.
My friends Christine Edison and Adrienne Sack were also in town, and they came along - note Christine here on the left, no doubt explaining [...]
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Which School? Help!
> 10 days ago
by Eric Gjerde
I#8217;m writing today to ask for your advice.
Over the last five years, I have come quite far - rediscovering and developing an art form which is fairly unique, meeting many like-minded and gifted artists, and making friends all over the world through our shared love of paper arts. This has been a wonderful journey and [...]
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Under the Ruler Faster than the Ruler
> 10 days ago
by Kenny
I was just talking to Michael Weisberg, who is also visiting ANU currently, and he pointed me to this video showing a counterintuitive physics demonstration. I had seen the video before, so we started discussing how it might work. He pointed me to the explanation videos that the author of that video made, [...]
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A Stronger Two-Envelope Paradox
> 10 days ago
by Kenny
Consider the standard two-envelope paradox – there are two envelopes in front of you, and all you know is that one of them has twice as much money as the other. It seems that you should be indifferent to which envelope you choose to take. However, once you’ve taken an envelope and opened [...]
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Probabilistic Proofs of Undecidable Sentences?
> 10 days ago
by Kenny
As I suggested (though perhaps not made as clear as I would have liked) in my forthcoming paper “Probabilistic Proofs and Transferability”, I think that probabilistic proofs can be used to provide knowledge of mathematical facts, even though there are reasons why we might think they should remain unacceptable as part of mathematical practice. [...]
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The Strong Free Will Theorem
> 10 days ago
by Kenny
Wow, it’s been about four months since I’ve posted here! Anyway, I’ll try not to continue that pattern in the future.
In the February issue of the Notices of the American Mathematical Society, John Conway and Simon Kochen have a paper explaining their “free will theorem”, which I believe strengthens it slightly from earlier versions. [...]
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Guessing the result of infinitely many coin tosses
> 10 days ago
by Kenny
I’ve stolen the title of a very interesting post by Andrew Bacon over at Possibly Philosophy. He considers a situation where there will be infinitely many coin flips occurring between noon and 1 pm, but instead of getting faster and faster, they’re getting slower and slower. In particular, one coin flip occurs at [...]
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GeoGebra has just received the prestigious Tech Aw ...
> 10 days ago
by Bill Lombard
More kudos for GeoGebra; I continue to share this wonderful open-source software program with others and watch them experience the joy as they see mathematics come alive with power and creativity. My students experience this on a regular basis.
From the Tech Awards website: http://techawards.org/
“The Tech Awards program inspires global engagement in applying technology to humanity’s [...]
Related posts:First North American GeoGebra Conference – Ithaca, New YorkGeoGebra Has N ...
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20 Free Resources for High School Math Teachers
> 10 days ago
by Bill Lombard
The following is a Guest Post from education writer Karen Schweitzer. Karen is the About.com Guide to Business School. She also writes about online colleges for OnlineColleges.net.
++++++++++++++++++++++++++++++++++++++
Are you looking for new ways to present advanced mathematical concepts to your high school students? The Internet offers many free online resources for lessons, games, activities, and [...]
Related posts:20 Free Math Resources for Classroom TeachersFree Online Math Courses fo ...
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Games and Puzzles that Reach the Kids and Teach th ...
> 10 days ago
by Bill Lombard
The title of this post is from a conference session at the California Math Council conference at Asilomar in December, 2009. You may download the handout through the following link:
Games and Puzzles that Reach the Kids and Teach the Standards
Puzzles and Games are a great way to build enthusiasm, excitement, and skills in a math [...]
Related posts:Algebra Activities that Reach the Kids and Teach the StandardsKenKen Activity Masters from the New York Times Teach Your Students Numerical Reason ...
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Algebra Activities that Reach the Kids and Teach t ...
> 10 days ago
by Bill Lombard
I will be presenting a session at the California Math Council’s conference in southern California on 7 November, 2009 with the title of this blog article. I’ve included a link below to the conference presentation.
This session will cover several pedagogical topics that have made my students successful learners, including Conceptual Layering, as well as snippets [...]
Related posts:CMC-S (Palm Springs) and CMC-N (Asilomar) GeoGebra UpdatesFirst North American GeoGebra Conference ...
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George Polya, Master Problem Solver – a Model fo ...
> 10 days ago
by Bill Lombard
George Polya was a master of problem solving, and his effect on other teachers has been extraordinary. His most popular book, How to Solve It, has sold over a million copies. As is the case with many great books, Polya had been turned down by three publishers before finding one to publish the English version [...]
Related posts:20 Free Math Resources for Classroom TeachersWhy Study Math? We Have Some Great News for Math Teachers!Free Online Math Courses for TeachersMath Students Tackle Cryptog ...
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Summer camps
> 10 days ago
We didn't really have summer camps when I was growing up. At least not thematic ones. We'd go to the seaside with teachers, but I don't recall doing any work. Today is my last day in math camp and in Portland, OR. I'm teaching a class on Banach Tarski paradox (take an orange, cut it up into finitely many pieces, rearrange them and make two oranges of sizes equal to the original one; or if you'd like do the same to pea and rearrange the pieces to make a ball size of the sun). Anyhow, with years I ...
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Craziness
> 10 days ago
Mark sent me an email: This is a school in the same county as the one we grew up in. Go to the one about Mount Vernon Teacher could be Fired . I tried looking for a written story, and couldn't find it. Apparently, people watch newspapers these days. So I googled it: Columbus DispatchLife Site News?!?There are loads of others. Now, what sort of a teacher must this guy be if a LOCAL SCHOOL BOARD votes unanimously to fire him?
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Left to write right :)
> 10 days ago
I'm afraid I may have hyped up this post too much, but here it is. I've heard many times people talk how students interpret equal sign as a signal to do something. While I certainly noticed that, I still think it would be unfair to say that the students do not understand the actual meaning of equal sign: the two quantities/objects separated by an equal sign are the same quantity/object. However, this understanding is somewhat fragile, and to me very surprising. This is where my left to right com ...
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Catch up
> 10 days ago
The semester is over, and I enjoyed my last week immensely. I wish I could take more time off (although there was some work involved I mostly played), but no such luck. My 1010 class is over. I take it the people in charge believe I did a good job because I get another one in the fall: 180 enrollment cap. I myself doubt this is even possible. ... There was a week long intermission here. I went to Berkeley for a conference on teaching algebra. I had fairly interesting couple of days, although in ...
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More about me
> 10 days ago
Got tagged by Jonathan (who is a math teacher) The rules: 1. The rules of the game get posted at the beginning. 2. Each player answers the questions about themselves. 3. At the end of the post, the player then tags 5-6 people and posts their names, then goes to their blogs and leaves them a comment, letting them know they’ve been tagged and asking them to read your blog. 4. Let the person who tagged you know when you’ve posted your answer.Here we go.1) What was I d ...
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Amdahl's Law
> 10 days ago
by dohashi
Amdahl's Law is a formula for determining the theoretical speed up when parallelizing a function. For example, imagine we wanted to parallelize a function that spends 90% of its time in one algorithm. If there is a parallel version of that algorithm, how much faster would the entire function run with 2, 4 or more cores?
read more
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Sparse Polynomial Arithmetic 3: Multiplication and ...
> 10 days ago
by roman_pearce
In our previous article we described a packed representation for sparse polynomials is designed for scalability and high performance. The expand and divide commands in Maple 14 use this representation internally to multiply and divide polynomials with integer coefficients, converting to and from Maple's generic data structure described here. In this post I want to show you how these algorithms work and why they are fast. It's a critical stepping stone for our next topic, which is parallelization ...
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MaplePrimes v2 Community Beta
> 10 days ago
by bthur
Back in September, I posted an announcement about our plans for the new version of MaplePrimes. Well a few months and many, many hours of development later, we are approaching the end point!
read more
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Canadian Flag
> 10 days ago
by alex_01
In the book Introduction to Maple by Andre Heck books.google.co.uk/books the author manage to plot the canadian flag
in maple by using the following code:
read more
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Rossler System, Further investigation: chaos
> 10 days ago
by longrob
This is an update to my earlier post on the Rossler system, one of the simplest examples of a dynamical system in 3 dimensions that can exhibit deterministic chaos.
restart;
interface(displayprecision=10):
PDEtools:-declare(prime=t,quiet):
ross_x:=diff(x(t),t)=-y(t)-z(t):
ross_y:=diff(y(t),t)=x(t)+a*y(t):
ross_z:=diff(z(t),t)=b+x(t)*z(t)-c*z(t):
rossler_sys:=ross_x,ross_y,ross_z;
#Find fixed points:
read more
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Quaternion Julia Set Fractals
> 10 days ago
by admin
The taffy-like quaternion Julia sets are similar to complex Julia sets, except that they exist in four dimensions rather than just two. They aren’t really useful or significant; but, like other fractals, they tend to look pretty.
A Quick Review
Before getting into quaternion Julia sets, here is a short review of how complex Julia sets [...]
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Complex Julia Set Fractals
> 10 days ago
by admin
Complex Julia Sets
A Julia set, named after French mathematician Gaston Julia, is a type of fractal defined by an iterative function over the complex numbers. The study of fractals has applications in complex dynamics, partial differential equations, statistics, etc, but most people like them because they produce pretty images. The following is an [...]
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4D Art and Visualizing Higher Dimensions
> 10 days ago
by admin
I began to show the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by 3; and how a Line of three inches, moving parallel to itself through a length of three inches, makes a Square of three inches every way, which [...]
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Triangular Numbers and the Devil
> 10 days ago
by Brian
Recently, an inquiring reader asked about Triangular Numbers:
Hello,
My son is currently working his way through The Number Devil (by Hans Magnus Enzenberger) and is enjoying it thoroughly. He was particularly happy about the triangular numbers in Chapter 5 because I had just coincidentally given him a worksheet which involved calculating how many blocks [...]
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The Parallax View
> 10 days ago
by Brian
Only having one method to accomplish anything handicaps you. Having a second method does not degrade the first. It enhances it. It makes each part greater, and it makes the whole greater than the sum of the parts. [...]
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Math Mojo vrs. Anti-intellectualism
> 10 days ago
by Brian
Knowledge isn't something to be afraid of, nor is it something to be proud of. It is just something to be curious about. Curiosity ends when you think you know the answer, but you don't care why it is true - you just know [...]
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Occam’s Razor – A Tenet of Math Mojo
> 10 days ago
by Brian
Occam's Razor is generally seen as The simplest explanation is generally the best one. This is true, but the phrasing is dangerous ... I think it should be The simplest explanation that makes sense and does not contradict other known facts is generally the best one. Of course that is more like what William of Occam meant, but unfortunately it is not how many people [...]
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Math Mojo and Financial Insights
> 10 days ago
by Brian
Getting out of but the teacher said we have to do it this way way of thinking is about the best thing you can do for your mental development. Yeah, maybe you have to do it that way in school, to get a grade, but please realize that grading is a way for schools to keep you obedient, not make you enlightened. [...]
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Particle body-count 2
> 10 days ago
by Jim Pivarski
As a result of today’s talks, here’s the updated body-count (all four experiments with a lot of overlap):
Particle
Original discovery
Method of observation in the LHC experiments
Electron/positron
1896 (e-), 1932 (e+)
Peak at 1.0 in calorimeter energy to track momentum ratio, also observed in pairs from photon conversions in matter (X γ → X e+e- where X is a [...]
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The particle body-count
> 10 days ago
by Jim Pivarski
Earlier today, the LHC finished its 2009 run. They did everything they said they were going to do: provide physics-quality 900 GeV collisions and break the world record by colliding protons with a combined energy of 2.36 TeV (that happened Monday), as well as many other studies to make sure that everything will work for [...]
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Erratum: no high-energy collisions yet
> 10 days ago
by Jim Pivarski
Yesterday, when I said,
The LHC has officially become the world’s highest-energy collider, by colliding protons at 2.36 TeV (above the Fermilab Tevatron’s record of 1.96 TeV),
I misunderstood a point in the press release that wasn’t heavily stressed. The LHC has become the world’s highest-energy accelerator, reaching counter-rotating energies of 1.18 TeV each, but the beams [...]
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Rediscovering the Standard Model
> 10 days ago
by Jim Pivarski
In the past week, three milestones have been passed:
the first π0 particles have been reconstructed from their decay products, shown at the public LHC week 1 conference (by CMS and LHCb);
the LHC has officially become the world’s highest-energy collider, by colliding protons at 2.36 TeV (above the Fermilab Tevatron’s record of 1.96 TeV);
the first paper [...]
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Protons have *collided* in the LHC
> 10 days ago
by Jim Pivarski
At least it looks like it from this CMS event display:
See the CMS e-commentary for hourly updates and more information. (That’s how I know which results are public. )
The yellow boxes are silicon strips that detected the passage of particles (most likely pions in this case) and the green lines radiating from the center [...]
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Generalizing Javadot
> 10 days ago
The idea of Javadot is to allow the rich lexical syntax of Lisp and Scheme with the elegance of the dot-notation from the C tradition by simply allowing scope to trump lexical splitting: if foo.bar is in scope as an identifier, then it parses as a variable reference; otherwise it parses as foo . bar . It's a simple compromise, it's easy to understand, it plays well with lexical scope, and (in an infix language) you can always circumvent it with whitespace. (I don't think it needs to complic ...
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Eich's Law
> 10 days ago
Found this gem in a C++ comment while digging in the SpiderMonkey codebase:After much testing, it's clear that Postel's advice to protocol designers ( be liberal in what you accept, and conservative in what you send ) invites a natural-law repercussion for JS as protocol : If you are liberal in what you accept, others will utterly fail to be conservative in what they send. The comment is unsigned, but it sounds like Brendan.
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Wading into the C
> 10 days ago
No time for deep thoughts these days; too much hacking, dissertating, designing, and committeefying going on. Just a couple notes based on recent experiences hacking in C/C++:1. Not being able to rely on recursion makes me sad.2. Downwards macro-args in C:#define MY_ENUM_LIST(m) m(RED, 0), m(GREEN, 1), m(BLUE, 2)#define DEF_ENUM_ENTRY(c, v) c = v#define QUOTE_ENUM_ENTRY(c, v) #ctypedef enum rgb { MY_ENUM_LIST(DEF_ENUM_ENTRY)} rgb;const char *rgb_names[] = { MY_ENUM_LIST(QUOTE_ENUM ...
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Computer Science Education Week
> 10 days ago
In honor of Computer Science Education Week, I'll just cite a passage I find inspirational about the role of computer science education: Yet programming is more than just a vocational skill. Indeed, good programming is a fun activity, a creative outlet, and a way to express abstract ideas in a tangible form. And designing programs teaches a variety of skills that are important in all kinds of professions: critical reading, analytical thinking, creative synthesis, and attention to detail. We the ...
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Ezra: Function calls are not stack frames
> 10 days ago
I don't have much to add to this but 's saying :It's worth reading . I especially appreciate his point about confusing semantics with cost model.
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Penn Alexander math club: map coloring
> 10 days ago
by Brent
Today in math club I had the students explore map coloring. I tried to leave it as open-ended as possible to start—I just said that we were going to draw maps with countries, and try to give each country a color, so that no two adjacent countries have the same color. I was [...]
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Irrationality of pi: the integral that wasn’t
> 10 days ago
by Brent
And now for the punchline! Today we’ll show that, for large enough values of ,
completing the proof of the irrationality of .
First, let’s show that is positive when . We know that is positive for . But I claim that is too. Remember that
and are clearly positive [...]
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Irrationality of pi: the impossible integral
> 10 days ago
by Brent
We’re getting close! Last time, we defined a new function and showed that and are both integers, and that . So, consider the following:
The first step uses the product rule for differentiation (recalling that and ); the last step is what we showed last time. Now we see [...]
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Dimensions
> 10 days ago
by Brent
I’ve only watched the trailer so far, but this looks extremely cool! Some beautiful, fascinating videos about math, with lots of extra accompanying material and explanations on the website.
Hat tip to Phil Wadler.
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Divisor nim
> 10 days ago
by Brent
Yesterday in math club I had the students play a game which I dimly remember seeing somewhere but forget where. Since I don’t know what it is really called, I’m calling it “divisor nim”. Here’s how it works:
The players pick a positive integer.
The two players work together to write down all the divisors [...]
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Monodromy and Moduli
> 10 days ago
by Charles Siegel
Today, we’re going to prove a BIG theorem, but only in the characteristic zero case (we’ll be working over as usual). The theorem is rather tough, and to do it in positive characteristics it’s best done through stacks. Specifically, we’ll be proving the irreducibility of the moduli space of curves of genus .
For a [...]
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Monodromy Representations
> 10 days ago
by Charles Siegel
A departure from directly working with varieties, we’re going to do something that’s strictly topological (at first glance) but which really has deep and important connections with Hodge theory. We’re going to talk about monodromy and monodromy representations.
Let be a fiber bundle. Though we don’t really NEED any hypotheses, as far as I’m aware, [...]
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Beauville makes a list
> 10 days ago
by Charles Siegel
If you like Hyperkähler manifolds (and who doesn’t?) go check out Beauville’s new preprint: Holomorphic symplectic geometry: a problem list. It’s nice and short survey of the basic facts of hyperkähler manifolds, including a bunch of conjectures and open problems in the area.
Filed under: Algebraic Geometry, Open Problems
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The Hodge Theorem
> 10 days ago
by Charles Siegel
Previously, we talked a bit about the category of Hodge structures, and did some basic constructions. However, I’d claimed that this was algebraic geometry (at least, in the categories on the post) so today, we’ll talk about a LOT of Hodge structure that arise in nature. Everything I say is true in more generality (for [...]
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Algebraic Geometry Belongs to Sheaves
> 10 days ago
by Charles Siegel
Over at the n-Category Cafe, Tom Leinster has written an excellent post pointing out that sheaf theory is NOT a subfield of algebraic geometry. I feel I have a few things to add, not enough for a long post, but enough that I’d rather post here than fill up their comment thread (plus, the blatant [...]
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The blog is dead .... long live the blog!
> 10 days ago
After almost 500 posts, this will be the last post here ........ but for good or ill, I'll be continuing at my website http://www.logicmatters.net (and the posts here at blogspot have been imported to that new blog, though the aesthetics are at the moment a bit primitive).Geeky explanation: At very long last, I'm joining the cool kids and and using the Wordpress platform on a hosted site. That's not in fact to make blogging easier, but because Wordpress works as a nice content management system ...
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Gödel Without Tears -- 5
> 10 days ago
Here now is on the idea of a primitive recursive function. The preamble explains why this matters and where this is going. [As always, I'll be very glad to hear about typos/thinkos.]The previous episodes are available:
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Ruse gets a beta minus.
> 10 days ago
Philosophers don't get asked often enough to write for the newspapers and weeklies: so it is really annoying when an opportunity is wasted on second-rate maunderings. on whether there is an atheist schism . And he immediately kicks off on the wrong foot.Eh? Where on earth has that or meaning come from? In what coherent sense of meaning does an atheist have to deny meaning?It gets worse. Eventually a lot worse.That is so mind-bogglingly inept it is difficult to believe that Ruse means it ser ...
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The Autonomy of Mathematical Knowledge -- Chap. 2, ...
> 10 days ago
To return for a moment the question we left hanging: what is the shape of Hilbert's naturalism according to Franks? Well, Franks in §2.3 thinks that Hilbert's position can be contrasted with a Wittgensteinian naturalism that forecloses global questions of the justification of a framework by rejecting them as meaningless. According to Hilbert … mathematics is justified in application (p. 44), and for him the skeptic's path leads to the death of all science . Really? But, to repeat, if ...
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The Autonomy of Mathematical Knowledge -- Chap. 2, ...
> 10 days ago
Hilbert in the 1920s seems pretty confident that classical analysis is in good order. Mathematicians have pursued to the uttermost the modes of inference that rest on the concept of sets of numbers, and not even the shadow of an inconsistency has appeared .... [D]espite the application of the boldest and most manifold combinations of the subtlest techiniques, a complete security of inference and a clear unanimity of results reigns in analysis. (p. 41 -- as before, references are to passages ...
