Last 5 posts from each of the top Math blogs
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emacs, vim, svn, doxygen, and friends - Stocking y ...
20 hours ago
by yNot
Charles Reid, a doctoral candidate at the University of Utah and a very good colleague of mine, has kindly agreed to post some lectures from his summer Scientific Computing Workshop on PMAN. Charles is not only knowledgeable in all Unix related stuff (Unix, Linux, OSX... and all things ending in x), but also a very rigorous researcher. You can find his original workshop series on his website, at the end of the internet: http://charles.endoftheinternet.org/.
and here's part 2
...
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LaTeX Symbols - Detexify
1 day ago
by yNot
say you're looking for some weird LaTeX symbol but you don't want to go through an exhausting list of possible candidates. You just want to draw that symbol and have someone tell you what the syntax for that is.
Well, Detexify does this exact thing!!! Go ahead and try it (and train it, and by all means donate for these guys).
This is by far one of the most useful things I found on the net (thanks to this article on fellow blog walking randomly).
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How to Add a Contact Me Page to your Blog or Websi ...
2 days ago
by yNot
Turn out to be quite simple using Google docs! Here are the steps:
Go to Google docs
Create a new form
Customize the form to your liking by filling it with required info (Name, email, website, message...)
To add new items use the Add item button on the upper left. Use this to add more entries. For the message, add a paragraph text.
Finally, here's how it could look like. Don't forget to name the form and put in a short description
Now, you can get the code to embed that form in your web ...
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How to Place Two Figures Side by Side in Latex Mul ...
3 days ago
by yNot
If you are using a multicolumn LaTeX class template, then placing two figures side by side so that they spawn the entire width of the page is done by simply using the {figure*} environment
egin{figure*}
subfigure{...}
subfigure{...}
end{figure*}Voila!
You may want to move the code for your figure around so that it doesn't show up on the last page. Also, try using [ht] for figure placement
egin{figure*}[ht]
subfigure{...}
subfigure{...}
end{figure*}This is a typical case with th ...
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Inexact Differentials
4 days ago
by yNot
In a previous post, I discussed the proper techniques to integrate an exact total differential. The major point to be drawn from exact differentials is that their parent function is independent of the path of integration. For example, the work done by gravity is independent of the path taken. It only depends on the end points of the path. This has to do with the fact that the gravitational force can be expressed as the gradient of a scalar. We call this type of force a conservative force field.
...
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Infinite Products, Part 2
20 hours ago
by John Armstrong
After all of yesterday’s definitions, we continue examining the countably infinite product of a sequence of totally finite measure spaces such that each . If and are positive integers with , it may happen that a non-empty subset is both a -cylinder and a -cylinder. By yesterday’s result, we find that we can write both [...]
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Infinite Products, Part 1
1 day ago
by John Armstrong
Because we know that product spaces are product objects in the category of measurable spaces — at least for totally measurable spaces — we know that the product functor is monoidal. That is, we can define -ary products unambiguously as iterated binary products. But things start to get more complicated as we pass to infinite [...]
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Fubini’s Theorem
2 days ago
by John Armstrong
We continue our assumptions that and are both -finite measure spaces, and we consider the product space . The first step towards the measure-theoretic version of Fubini’s theorem is a characterization of sets of measure zero. Given a subset , a necessary and sufficient condition for to have measure zero is that the -section have [...]
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Double and Iterated Integrals
3 days ago
by John Armstrong
Let and be two -finite measure spaces, and let be the product measure on . If is a function on so that its integral is defined — either is integrable, or its integral diverges definitely — then we write it as any of and call it the “double integral” of over . We can also [...]
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The Measures of Ordinate Sets
4 days ago
by John Armstrong
If is a -algebra and is a Borel-measurable function we defined the upper and lower ordinate sets and to be measurable subsets of . Now if we have a measure on and Lebesgue measure on the Borel sets, we can define the product measure on . Since we know and are both measurable, we can [...]
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Pythagorean triangles on a circle
18 hours ago
by Sol
If you’ve not yet discovered the Wolfram Demonstrations Project site you’re in for a great treat. The site has tons of interactive Math applications that you can run with the free Mathematica Player. In other words, you don’t need to own Mathematica to run the demonstration apps.
I find many of the apps to be very interesting. One I particularly like is “Enumerating Pythagorean Triangles.” It shows a nice relationship between Phythagorean Triples (positive integers ...
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A very clever calculator
2 days ago
by Sol
Below is an image from Wikipedia of a calculating device invented in 1891, Genaille’s rods. Each column in the image is a rod that can be placed wherever it’s needed in a calculation.
The image shows how to easily calculate 52749×4.
Can you figure out how this arithmetic tool works?
Making a set of these rods would be a great enrichment project. Here is a template (in different sizes) that you or your children or students can print and mount onto cardstock to make your own set ...
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Math Myths
3 days ago
by Sol
Don Cohen, AKA The Mathman, has been helping children of all ages to learn Math for 34 years. He has a CDROM book, Calculus By and For Young People, which he sells via his site.
I found these “Math Myths” from his site to be quite interesting:
You can’t take 7 from 3.
When you multiply, the answer is bigger.
You have to add from right to left.
When you subtract the result is smaller.
Fractions are small numbers.
There’s only one way to do something.
When you add t ...
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Rolling regular n-gons on catenary “roads”
5 days ago
by Sol
Here’s an interesting exploration, illustration courtesy of Mathematica:
There’s a nice animated illustration at Mathematica.
A particularly interesting case of a roulette is a regular n-gon rolling on a “road” composed of a sequence of truncated catenaries, as illustrated above. This motion is smooth in the sense that the geometric centroid follows a straight line, although in the case of the rolling equilateral triangle, a physical model would be impossible to constru ...
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Mental Floss brain game
6 days ago
by Sol
Mental Floss is one of my very favorite magazines. Here’s a simple (if you see it) puzzle from their web-site:
The answer is here.
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The Return of My Laptop
18 hours ago
So now I could blog again, as I have my home laptop back in my possession after to lending it to someone since Monday. I have a strict rule that my work laptop is for work only and for nothing non-work. (Both jobs count.)Anecdote from TuesdayGuy I know who appeared in Hard Problems: Can I borrow your laptop to read this paper [which he was reading on paper, dead-tree edition]? I can't find where [term] is defined, and I want to use find to search for it.Me: Sure. You can grab it from my ba ...
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More of the Same, Summer Job Style
4 days ago
Apparently a crew from South Korean television is coming to film us on Thursday.My principal minion fears that they will trounce him at Starcraft.I'm staying far away, as the crisis at my real job should hit emergency levels by Wednesday afternoon and will not be much better in time for Thursday morning's conference call.
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Location, Location, Location
4 days ago
Google's search suggestions are location-dependent. How many letters do you need to type in before Google suggests that you're looking for Starcraft 2? And how high is it on the list?I must say that I know many, many, many people who are really bummed that they have a lot of work to do this week. I'm guessing that there are a lot of talks later this week that are going to suck because the authors were playing video games instead of preparing.(In other news, I'm lending my laptop to someone, so e ...
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Fun Times in Hot Weather
5 days ago
The sparse blogging may get even sparser. Things are getting stupid-crazy here at my summer job.And, then in added bonus fun, we have real excitement brewing at my regular job. So the system has been down for about a week, so no one could install anything that needed to be installed. At best, things can start being installed on Monday. There are things that I need to do before Thursday that rely on using things that are not yet installed.And then there is this whole east coast heat wave summer n ...
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I Just Realized that I'm Going to be One of Those ...
7 days ago
So since I still work for the university, I am still entitled to take classes for free, so I signed up to take another stats class in the fall.And today it dawned on me. I'm going to miss the week before Thanksgiving to go to a conference, and then I'm going to miss the entire week with Thanksgiving to go visit Germany.The class meets 28 times, and I am already planning on missing four of the last five days of class.Maybe I should switch my registration status to audit instead of for credit a ...
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Probability and Baby Blues
1 day ago
by Denise
[Photo by audi_insperation.] [In The Birthday Surprise, Alex discovered her family was expecting a new member...] What will the baby look like, Alex wondered. “Dad, is there any way to tell whether the baby will have blue eyes like I do, or brown like the rest of the family?” Dr. Jones shuffled the papers on [...]
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Alexandria Jones and the Birthday Surprise
3 days ago
by Denise
[Photo by D Sharon Pruitt.] [July 27th is Alex’s birthday, which she shares with Johann Bernoulli, an irascible mathematician from the late 17th century.] The guests had gone. Alex and her family sat around the table, sharing the last tidbits of birthday cake and ice cream. Alex smiled at her parents. “Thanks, Mom and Dad,” [...]
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Accidental Publication — Aargh!
4 days ago
by Denise
[Photo by striatic.] If you came to my blog looking for a math history post about the Bernoullis, I’m sorry! I retracted the post immediately, but Google Reader has a long memory. The real post will be coming soon, when I’m done polishing up the draft and putting in links. Note to self: Use the [...]
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Quotable: I Hate Fractions
8 days ago
by Denise
“I hate fractions.” “They probably hate you, too. The question is, which one of you will be master.” — Jonathan “I hate fractions” at jd2718
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Quotations XXIV: Probability
8 days ago
by Denise
[Photo by Micah Sittig.] I used to fill the margins of my math newsletter with quotations and tidbits of math history. Here are some quotes from the July/August 1999 issue on probability, along with a few others I’ve stumbled on while browsing the internet. No knowledge of probabilities helps us to know what conclusions are [...]
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Twitter Weekly Link Roundup for 2010-07-25
5 days ago
by Maria H. Andersen
Thankfully the column for MAA Focus is now written. I can enjoy the rest of the day and @kerisb's wedding! #
Wedding is over. Tomorrow? SMALLAB in Tempe and a few meetings, then redeye home. #fb #
Leaving Detroit to drive home. Stopping at TechSmith along the way. #
Home again. SMALLAB yesterday, TechSmith this morning and LIFT [...]
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Random But Organized Thoughts (7-25-2010)
5 days ago
by Maria H. Andersen
Great Links
The new xkcd cartoon about lack of innovation in TI-calculators [via Cameron Flint and Wade James]. Just for the record, I basically said the same thing on November 14, 2007 in my Calculator Rant.
Twitter Mood Maps reveal emotional states of America [via @hrheingold] – this reminds me of the website We Feel Fine, which explores human [...]
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Mathfaery: Elizabeth Hamman
7 days ago
by Maria H. Andersen
Elizabeth Hamman was a great math educator who will be truly missed in the International math community. She passed away very suddenly last week, at the age of 39, after suddenly developing a problem with blood clots in her lungs, which led to a bleed in her brain. Elizabeth started writing a blog [...]
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Twitter Weekly Link Roundup for 2010-07-18
> 10 days ago
by Maria H. Andersen
I don't think my body has recovered from a week of overdrive thinking. Got 8 hrs of sleep and feel like I could sleep ALL day. #fb #
Clearly, I need some coffee and a mental pep talk. #fb #
Say what you will about airlines, but I really like flying Delta (of course, I usually get [...]
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World Future Society Conference 2010
> 10 days ago
by Maria H. Andersen
This is the 3rd year I’ve attended the WFS Conference and it’s a difficult event to describe. You might imagine a collection of Nostradamus-like individuals, making predictions about the future, and I’ll admit it; this conference does have a larger proportion of older, bearded men than most conferences I attend. However, the vast majority of [...]
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Paranoia And Selling A Laptop
18 hours ago
by rjlipton
How do we erase a hard disk, for sure? Richard Nixon was not a theorist—of course. He was the President of the United States from 1969 until 1974, when he resigned in disgrace. He was also an “un-indicted co-conspirator” and probably one of the most paranoid presidents ever. Today I want to talk about paranoia. [...]
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Hedy Lamarr the Inventor
5 days ago
by rjlipton
The invention of spread spectrum and the role of amateurs in science and technology Hedy Lamarr was, of course, not a mathematician nor a complexity theorist. She was one of the great movie actresses of all time, and was once “voted” the most beautiful woman in the world. She was also an inventor. Today I [...]
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A New Million Dollar Prize?
9 days ago
by rjlipton
Possible new problems to add to the Clay list Grigori Perelman, the solver of the three-dimension Poincaré Conjecture, has declined to accept the first awarded Clay Prize. I may not understand him, but I think he is one of the most colorful mathematicians ever. Perhaps the award should have been offered to both him and [...]
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An Amazing Paper
> 10 days ago
by rjlipton
An amazing new set of conjectures and the jacobian conjecture Arno van den Essen is one of the world experts on the Jacobian Conjecture. He has written a book on the problem—really the book. Besides this he has made many contributions to the understanding of this great conjecture. Today I plan to talk about a [...]
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Making An Algorithm An Algorithm—BBP
> 10 days ago
by rjlipton
Finding the bits of in logspace Chee Yap is one of the top experts in various aspects of computational geometry. His has worked on problems as diverse as upper and lower bounds for comparison problems, to algorithms in geometric complexity, to methods to control rounding errors in geometric computations. One of his specialties is in [...]
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Passing Integrated Algebra apparently does not mea ...
8 days ago
by jd2718
Dan Koretz (Harvard) and Jennifer Jennings (NYU) (f/k/a Eduwonkette) looked a little at kids who take New York State exams. Turns out, the exams don’t predict much, or at least don’t predict what some people thought they did. Math A (now Integrated Algebra) are the graduation requirement in mathematics. And many kids passing the exam [...]
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“I hate fractions”
9 days ago
by jd2718
… “They probably hate you, too. The question is, which one of you will be master.” Do you recognize the badly paraphrased literary reference? (inspired by this interesting post about teacher training, with interesting comments)
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Stop Resegregation in Wake County
> 10 days ago
by jd2718
I can’t go to the march, but I can spread the word. So can you. North Carolina NAACP calls march, July 20, (tomorrow, Tuesday) against the resegregation of schools in Wake County, North Carolina. (And before anyone in the north starts shaking a patronizing head over conditions in the south, let me point out that [...]
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AFT Convention in Seattle – Day 4
> 10 days ago
by jd2718
Day 4 of the Convention was the shortest. The morning session started a little after 9:30, and wrapped up near 1, and that was it. Credentials were updated (I think?) and election results announced. The Progressive Caucus swept. The opposition from Detroit got about 5%. Barbara Bowen (PSC) was the leading vote getter, followed by [...]
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AFT Convention in Seattle Day 1
> 10 days ago
by jd2718
Up to a point I’d been listening, fairly politely. Then Randi Weingarten read, from her prepared text: “Our vision is that every neighborhood school should be an excellent school that all families know they can count on, every year, for all of their children.” and that was too much. Neighborhood schools? When her legacy in [...]
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Knock-Knock Jokes Redux
21 hours ago
We've had a lot more fun with knock-knock jokes lately. I taught Vinny some pretty hilarious* jokes, including:A: Knock knock!B: Who's there?A: Boo.B: Boo who?A: Don't cry, it's just a joke!A: Knock knock!B: Who's there?A: Ach.B: Ach Who?A: Bless you!A: Knock knock!B: Who's there?A: Anita.B: Anita who?A: Anita tissue! Achoo!The entertainment value of that last joke has just been priceless. When I first told Vinny that joke, he then responded with the following joke:Vinny: Knock knock!Me: Who's ...
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Foods I Cannot Bear to Buy
6 days ago
If you come across any of the following foods in our pantry or refrigerator, it is not because I bought them:Honey. When I was a kid, we had a beehive in our back yard. Yes, in the city. I can't imagine that this would be legal today, but my dad kept bees in our backyard back in the day. Anyhow, the point is that honey from the beehive in your backyard is way better than anything you can buy on the shelf. And freshly harvested honey in the honeycombs... chewing on that is like eating a piec ...
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Adventures with Grandpa
> 10 days ago
We had a relaxing and enjoyable weekend with my dad. He came down for a visit on Friday night. Vinny and I went to the city pool with him for a couple of hours on Saturday. The pool was really nice -- very big, not too crowded (at least in part because it was overcast all day), and had a large section that was just the right depth for a three-year-old. Vinny had a blast playing with Grandpa and Mama in the pool, and was pretty disappointed at having to leave. But, he was exhausted, and when ...
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Adventures in the Mountains
> 10 days ago
On Saturday, we took a little road trip to see Fontana Lake, which is a human-made lake dammed by the largest concrete dam east of the Rockies. It is TVA's largest dam, and it was built to power the Manhattan Project. We plugged our destination into Gladys the Map (our friendly GPS), and off we went.What we didn't realize was that Gladys was sending us on US-129, an eleven-mile stretch of which is known as The Dragon, and quite popular with motorcyclists. There are supposedly 318 curves in th ...
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Hello, World!
> 10 days ago
Hi! Yes, I do have a blog, even though I don't seem to have enough time these days to write anything on it. Sorry about that. Things have been extra crazy here lately -- supervising three students is a lot of work. It could be a full-time job unto itself if you let it. In addition, I've suddenly been given another big task (supervising the hiring, care, and feeding of ten postdocs, most of whom have already been hired). It's an interesting task, and allows me to learn a lot of new things ab ...
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KenKen – Introduction and Strategy Tips to Solve ...
7 days ago
by Bill Lombard
Here is a four minute video that introduces the 4×4 KenKen. It can be played in HD (720p) for use in classrooms with projectors.
KenKen is a logic and mathematical puzzle which is similar to Sudoku. As a math teacher, I use KenKen to teach and reinforce logical, deductive reasoning and to help with number concepts [...]
Related posts:KenKen – a Video Introduction to the 3×3 Puzzle
KenKen for Teachers & Students – a Harvard Professor Speaks Up
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KenKen – a Video Introduction to the 3×3 Puzzle
8 days ago
by Bill Lombard
Here is a four minute video that introduces the 3×3 KenKen. It can be played in HD (720p) for use in classrooms with projectors.
KenKen is a logic and mathematical puzzle which is similar to Sudoku. As a math teacher, I use KenKen to teach and reinforce logical, deductive reasoning and to help with number concepts [...]
Related posts:KenKen for Teachers & Students – a Harvard Professor Speaks Up
No Child Left Behind and Global Competitiveness – a Video by Yong Zhao
Games ...
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Make Math a Fun Summer Activity – Guest Post by ...
> 10 days ago
by Bill Lombard
The following is a Guest Post from Alexis Montgomery, who is a content writer for Online Degree, where you can browse through various online degree programs to find a college that suits your needs.
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Some kids are born to do math. They see the numbers on a page or a blackboard and it’s like you’re suddenly [...]
Related posts:20 Free Resources for High School Math Teachers
20 Free Math Resources for Classroom Teachers
20 Free Online Math Games for Stu ...
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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.
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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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A proof length challenge
4 days ago
by David Speyer
Here is a question I thought of this morning, and have given no serious thought to — hence, perfect for a blog post. In any commutative ring, if and are matrices, and , then . For any fixed , there should be a proof of this by direct algebraic manipulation: Start with the equations saying [...]
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Bleg: Great combinatorial applications
> 10 days ago
by David Speyer
I am currently writing up a syllabus for a combinatorics course. I want to show the students that combinatorics is not just a collection of puzzles, but that it has connections to lots of interesting problems. Because the prerequisites for this course are fairly minimal (calculus and linear algebra), I think I’d do best to [...]
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“TeX, LaTeX and Friends” StackExchange site al ...
> 10 days ago
by Ben Webster
As those of you who follow StackExchange drama know (StackExchange is the platform that MathOverflow runs on), there was recently a change in how StackExchange sites are set up. Unlike the situation when MO was born, when anyone with a dream and willingness to pay cash could start a site, now they go through a [...]
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Statistics version of MathOverflow looking for bet ...
> 10 days ago
by David Speyer
Rob Hyndman is trying to start a question and answer site for people working in Statistics, running on the same software system that supports our beloved MathOverflow. Due to a change in the way StackExchange is licensing their platform, he can’t simply get up and start using it. Rather, he must first obtain a critical [...]
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Some questions about motives
> 10 days ago
by David Speyer
As I tried to read up on motives in preparation for my last post, I thought of some questions that seemed natural to me, but weren’t addressed in the sources I was reading. So here they are, in the hope that experts will find them obvious. One set of questions concerns motives for nonproper varieties, [...]
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Launch Day Hiccups
> 10 days ago
by Will
As some of you noticed, we launched the new version of MaplePrimes today. Unfortunately, we have ran into server problems with the new site, and have switched back to the old version of the site.
We are working on figuring out what the cause of the problem is, and will be re-launching the new site soon.
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MapleSim Blog Post
> 10 days ago
by bthur
I thought that some of you would be interested in Tom Lee's latest blog post at Maplesoft.com regarding MapleSim 4, and what it means to both Tom and Maplesoft. As always, your comments and thoughts are greatly appreciated.
You can read his post here.
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New Primes coming soon, just not this week.
> 10 days ago
by Will
Last week, I announced that the new MaplePrimes was going to be launched this week. Unfortunately, that won't be the case.
The reason is that we will be powering the search on new Primes with our Google Mini. Unfortunately, the influx of all of the new Primes content and online help content caused us to fill up the hard drive on the server that Maplesoft currently owns.
read more
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Maple 14 and MaplePrimes bug reports
> 10 days ago
by eithne
The MaplePrimes community continues to provide very helpful feedback about how well the product is working (and how well it isn’t!). Thank-you. We always appreciate your taking the time to report these problems so we can make our products better. Maple 14 includes several fixes that were made specifically in response to reports made from MaplePrimes, including improvements in:
• Polygon plots
• StringTools
• fsolve
• Density plots
• Operator overl ...
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The New MaplePrimes is Coming Next Week
> 10 days ago
by Will
We've been working hard on the brand new version of MaplePrimes over the last few months. I am glad to announce that the new version will be launching publicly next week. The new site fixes many of the requests we've received from MaplePrimes users over the years, and adds new features that we think will make the new site easier to use, and a better way to get and share information about Maple and MapleSim.
read more
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Bitwise Operators and Negative Numbers
6 days ago
by sput
When representing integers using a fixed number of bits, negative numbers are typically represented using two’s complement. If using n bit numbers, the two’s complement of a number x with 0 ≤ x < 2n is (-x) mod 2n = 2n - x. But what do you do if you want to work with unbounded/multiple-precision [...]
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Release: Sputsoft Numbers 0.2 (formerly SputArithm ...
> 10 days ago
by sput
I am very excited about this release. The library has been redesigned and almost everything has been rewritten. Even the name has changed, it is now called Sputsoft Numbers (instead of SputArithmetic). Features include: A generic, portable backend that should make compilation possible on practically every modern C++ compiler and architecture. Compilation against a GMP [...]
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Book Review: The Book of Numbers
> 10 days ago
by sput
The Book of Numbers is a wonderful book about, well, numbers. And lots of them. From ancient ways of writing numbers to Gaussian integers to surreal numbers. The authors are some tough mathematicians, too. John H. Conway is Professor of Mathematics at Princeton University, an authority in game theory and group theory, and the inventor [...]
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Arithmetic by Geometry
> 10 days ago
by sput
Today real numbers are most often represented visually by applying (elementary) functions to (decimal) integers. Throughout history, though, arithmetic and propositions involving (positive) real numbers were often considered from a purely geometrical point of view. Real numbers were identified by the length of some line segment and, e.g., the product of two numbers was identified [...]
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Line-line Intersection in the Plane
> 10 days ago
by sput
How do you calculate the point where two lines in the plane intersect? It is not very hard to do, but the formula can look quite complicated, depending on how you write it up. This article is a reminder that it can be expressed in a simple manner.
We start out by not restricting ourselves to [...]
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More cookies
3 days ago
by Brent
I recently received the following interesting problem from Shadowcat, which is a generalization of the cookie problem I’ve written about previously. We again want to count the ways to distribute identical cookies to non-identical students, with the twist that we impose an upper bound on the number of cookies received by each student (quite [...]
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Right answers for the wrong reasons
> 10 days ago
by Brent
Here’s a recent xkcd which as a math educator I found particularly funny. Some questions for my readers:
What numbers besides 3 and 9 would “work” here?
Do you have any particularly funny or interesting stories of students getting something right for the wrong reason? Post them in a comment (or, better yet, on your [...]
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Optimal change-carrying
> 10 days ago
by Brent
Recently Michael left the following challenge in a comment:
I’ve been trying to optimize my change-carrying habits. What is the smallest amount of quarters, dimes, nickels and pennies one can carry while still being able to give perfect change (two decimals)?
It’s not 100% clear what Michael meant by “give perfect change”, but let’s assume the goal [...]
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Manufactoria
> 10 days ago
by Brent
A friend of mine just pointed me to a most excellent puzzle game, Manufactoria, wherein you build little machines to test robots. For now I won’t give away the secret of what real math/computer science topic the game teaches you, but I’ll write more about it later. For now, just have fun playing [...]
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The broken weight problem: solutions and further e ...
> 10 days ago
by Brent
First of all, let me say to all my readers how fantastic it felt to post a puzzle, after not posting anything for two months, and get eighteen thoughtful, insightful comments in just three days; it’s every blogger’s dream. You all are fantastic and make this a lot of fun — thanks for reading!
I [...]
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Graphical Display Techniques - Part 1
8 days ago
by Loren
I've recently been working with some customers who need to display extra information on top of a plot. Steve showed some examples for superimposing lines on images in such a way so they are visible despite what's going on in the picture. Today I'll [...]
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Scalar Roulette
> 10 days ago
by Loren
A while ago, Steve posted an article entitled Functional Design Clunkers on his blog. Well, I have a confession to make too. Have you ever been bitten by the ambiguity in the contour function?
[...]
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Vuvuzela Denoising with Parametric Equalizers
> 10 days ago
by Loren
Today I’d like to introduce a guest blogger, Charu, who is a Technical Marketing Manager at The MathWorks. Charu regularly
presents webinars on signal processing topics, and most recently presented a webinar highlighting R2010a capabilities in the [...]
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What Data Is Available?
> 10 days ago
by Loren
Yes, I know, data are, but the title just sounded terrible that way.
Ever wonder what data you have stored in some files, particularly MATLAB MAT-files? Sometimes I'd like to know what's there
[...]
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World Cup Soccer and the Vuvuzela
> 10 days ago
by Loren
Anyone been watching soccer lately? If so, you may have noticed a buzz in the background, created by many people playing
the vuvuzela. This contribution on the File Exchange by Choqueuse Vincent might help you filter the [...]
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Where in the World is MathNotations?
19 hours ago
by Dave Marain
Have you been wondering about the question in the title or just assuming that I'm on hiatus?
No videos?
No provocative comments about standardized curriculum?
No interviews with the movers and shakers in math education on the national front?
Most importantly, no anecdotes from my 3-yr old grandson? Is the world coming to an end?
Seriously, I suspect the world is still spinning on its axis, perhaps just a tad more tilted. And my faithful readers/subscribers have far more important concerns i ...
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Happy 4th! SAT Problems on Twitter, SAT Math Quiz ...
> 10 days ago
by Dave Marain
Well, let's see...
I haven't posted in almost a month, I haven't been promoting our wonderful Math Carnivals, I haven't brought you any updates or controversial material, I haven't produced any new and exciting videos,...
So what have I been doing? Enjoying the heat wave here in the Northeast?
1. Finishing up my SAT Math Quiz Book Volume One which will hopefully be done before the world ends in 2012. I haven't decided yet how I will make these available to my readers or schools or students or ...
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SAT Videos: Twitter Problems of the Day 6-9 and 6- ...
> 10 days ago
by Dave Marain
As we wind down toward the summer my SAT Problems and Videos continue to pick up steam! Below is the latest video from you YouTube channel, MathNotationsVids. I want to thank those who voted in my survey of these videos. I am gratified but I really need more specific suggestions on how to improve these. Your comments on YouTube or here are welcome!
Note: Because I am explaining two problems on one video, I am omitting details and multiple solution paths. Therefore these videos may be useful for ...
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Video Solutions to Two Twitter SAT Problems of the ...
> 10 days ago
by Dave Marain
Please vote in the poll at the right. Be candid in your opinion of these videos. It will guide me in the future to improve. Don't hesitate to share your opinions on MathNotationsVids and rate each video there as well. If you subscribe to my feed, please vote directly on the site. Only a few days left...
The title says it all so here is the video as promised:
I could have said so much more about each of these problems but I decided to show one method for each without embellishment. This ena ...
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A Little Birdie Tweeting the SAT Blues, Carnivals ...
> 10 days ago
by Dave Marain
Well, today's SAT Tweet comes too late for many students taking SATs this morning (unless you're in a much later time zone) but I posted it anyway since it can certainly be used to review for final exams in Algebra 2 or whatever ∫ -ated name you have for it in your district!
As you can see if you visit this site (rather than get the RSS feed), I'm now posting the Twitter Problems of the Day in the right sidebar. I'm new at this, don't have too many Twitter followers yet and I am learning t ...
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ICS 2011: A Question
9 days ago
There has been a lot of discussions about ICS --- Innovations in (Theoretical?) Computer Science --- conference, some pre-conference aspirations, post mortem analyses and the buzz of the sequel.I noticed from CFP of ICS 2010 that There will be printed proceedings, distributed at the conference, and thereafter available for purchase from Tsinghua University Press. The proceedings don't seem to have an ISBN or equivalent, papers are not yet indexed by DBLP or equivalent, and how long will this ...
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Internet Ads Update
> 10 days ago
Some updates:[Tutorial] While teaching a course on Internet Ad Systems in Spring (followup to this), I realized that while Algorithmers and Economists have connected with problems in that area, the database and data mining community has focused more on the interface between IR and ads, and less on some of the core data mining problems that arise directly in these systems. So, I decided to spend time abstracting such problems and will give a tutorial at VLDB 2010. [FOCS Result] Renato Paes Leme ...
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Music in Tel Aviv and NY
> 10 days ago
In Tel Aviv, my visit, happened to coincide with the White Night, an annual celebration that keeps the city open all night. Rothschild Boulevard, a boulevard of modernist buildings from Bauhaus to soon a Richard Meier tower, was lit with music from around the world and wandering crowd. Observation: Trying to dress well and look good in Tel Aviv is like going to FOCS and STOC and trying to look smart. You can try it, but everyone around you is smart, and you look silly.Back at home. The city le ...
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Small Food
> 10 days ago
I am away for a few days in Israel. Here are two disconnected thoughts.Do animals (not humans) have the concept of a dessert? I can imagine a Tiger after some nice rare meat but before some water, smacking its lips and looking around for something sweet and small.What does sushi look like that will fit into a toddler's palm?
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Distractions: cartoon, map and video
> 10 days ago
I am coming out of a hectic season of refereeing. So, I need some distraction:Cartoon on the left. Thank you NYer.Interactive map of population migration in US. Thank you, Forbes. Guggenheim Museum solicits creative videos. Deadline July 31. Thank you, YouTube.
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On hiatus II
8 days ago
by Terence Tao
I’ll be taking a break from blogging and other work for a few weeks. Filed under: admin
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The Golden-Thompson inequality
> 10 days ago
by Terence Tao
Let be two Hermitian matrices. When and commute, we have the identity When and do not commute, the situation is more complicated; we have the Baker-Campbell-Hausdorff formula where the infinite product here is explicit but very messy. On the other hand, taking determinants we still have the identity Recently I learned (from Emmanuel Candes, who [...]
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Cayley graphs and the geometry of groups
> 10 days ago
by Terence Tao
In most undergraduate courses, groups are first introduced as a primarily algebraic concept – a set equipped with a number of algebraic operations (group multiplication, multiplicative inverse, and multiplicative identity) and obeying a number of rules of algebra (most notably the associative law). It is only somewhat later that one learns that groups are not [...]
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Mini-polymath2 discussion thread
> 10 days ago
by Terence Tao
I’ve just opened the Mini-polymath2 project over at the polymath blog. I decided to use Q5 from the 2010 IMO in the end, rather than Q6, as it seems to be a little bit more challenging and interesting. This post will serve as the discussion thread of the project, intended to focus all the non-research [...]
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Finitary consequences of the invariant subspace pr ...
> 10 days ago
by Terence Tao
One of the most notorious open problems in functional analysis is the invariant subspace problem for Hilbert spaces, which I will state here as a conjecture: Conjecture 1 (Invariant Subspace Problem, ISP0) Let be an infinite dimensional complex Hilbert space, and let be a bounded linear operator. Then contains a proper closed invariant subspace (thus [...]
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Numb3rs Canceled
8 days ago
by Walt
I was never a big fan, so I just heard that Numb3rs was canceled for the fall. I guess the law will have to go back to fighting crime the old-fashioned way: calling in Batman to help.
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Teaching Calculus in Haiti
> 10 days ago
by Walt
Eugene Lim went to Haiti after the earthquake to teach calculus after the earthquake. He has posted a first-hand account at Cosmic Variance.
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Less good and bath math at ScienceBlogs
> 10 days ago
by Walt
Mark Chu-Carroll, the math blogger at ScienceBlogs, has quit the site, after ScienceBlogs made the bizarre decision to host a blog sponsored by Pepsi. The ensuing blow-up has caused ScienceBlogs to pull the Pepsi blog, Food Frontiers, but a version of it lives on at Pepsi’s own site.
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Introduction to Grothendieck Categories
> 10 days ago
by Walt
Grothendieck categories are a generalization of categories of modules. Sheaves of abelian groups over a topological space also form a Grothendieck category. Grothendieck categories are a special case of abelian categories, but the extra structure allows additional theorems to be proved.
Grigory Garkusha has a thorough introduction to the subject on arXiv.
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snarXiv is a site the generates parody abstracts f ...
> 10 days ago
by Walt
snarXiv is a site the generates parody abstracts for high-energy physics theory papers, a la arXiv. While the abstracts don’t quite make sense, they eerily resemble the real thing.
snarXiv versus arXiv is another site that gives you a random snarXiv and arXiv paper title, and asks you to tell the fake from the real [...]
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a new work, and Ohio
> 10 days ago
by origomi
a new work, originally uploaded by EricGjerde.
I recently finished this piece and sent it off for a show in Ohio (The FAVA Folding Festival, organized by James Peake and Ray Schamp). I think it’s making it’s way from there to another show later on in the year at the Sandusky Cultural Center, also in Ohio. [...]
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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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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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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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Goodbye, Scienceblogs
> 10 days ago
So my decision is made. I'm closing up around here. I'm in the process of working out exactly where I'm going to go. With any luck, Seed will leave this blog here long enough for me to post an update with the new location. But I'm through with Seed and ScienceBlogs.
Read the comments on this post...
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Seed, Conflicts of Interest, and Sleaze
> 10 days ago
As my friend Pal wrote about, Seed Media Group, the corporate overlords of the ScienceBlogs network that this blog belongs to, have apparently decided that blog space in these parts is now up for sale to advertisers.
We've been advertiser supported since I joined up with SB. I've never minded that before. Providing a platform and bandwidth takes money, which has to come from somewhere. The way that ads have been handled before has been no problem: the ads are clearly distinguished from the co ...
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Searching for Topics
> 10 days ago
As regular readers have no doubt noticed by now, posting on the blog
has been slow lately. I've been trying to come back up to speed, but so
far, that's been mainly in the form of bad math posts. I'd like to get
back to the good stuff. Unfortunately, the chaos theory stuff that I was
posting just isn't good for my schedule right now. Once you get past
the definitions of chaos, and understanding what it means, actually
analyzing chaotic systems is something that doesn't come easily t ...
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Saturday Recipe: Ginger Scallion Sauce
> 10 days ago
Today's recipe is something I made this week for the first time, and trying
it was like a revelation. It's simple to make, it's got an absolutely
spectacularly wonderful flavor - light and fresh - and it's incredibly
versatile. It's damned near perfect. It's scallion ginger sauce, and once you
try it, it will become a staple. To quote David Chang, whose cookbook
I learned this from: if you've got ginger scallion sauce in the fridge, you'll
never be hungry.
There are two main variations of thi ...
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The Surprises Never Eend: The Ulam Spiral of Prime ...
> 10 days ago
One of the things that's endlessly fascinating to me about math and
science is the way that, no matter how much we know, we're constantly
discovering more things that we don't know. Even in simple, fundamental
areas, there's always a surprise waiting just around the corner.
A great example of this is something called the Ulam spiral,
named after Stanislaw Ulam, who first noticed it. Take a sheet of graph paper.
Put 1 in some square. Then, spiral out from there, putting one number in
each sq ...
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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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Kenken game for summer fun
> 10 days ago
As most of you are taking a break from math or school work, here's a little (addictive) math game to play online or as printed version: Kenken.In it, you have to place the numbers in the grid kind of like in Sudoku so that no number appears twice in the same row or column, BUT there's an additional twist: it gives you cages , and the numbers within a particular cage have to work to a given answer with a given math operation (either addition, subtraction, multiplication, or division).KenKen prac ...
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My favorite music
> 10 days ago
This is a bit different entry from the norm, and if you're not interested in music (or oldies music), just ignore it. (I realize people's musical tastes vary tremendously.) I just wanted to share a bit of news of my favorite, 24K Gold Music Shows, and their new YouTube channel. They mainly play music from 50s and 60s; that is, oldies music.(Well, I do also like classical music pretty well -- I played piano in my youth for 13 years, and still occasionally do at home.) You can now see 24K Gold mus ...
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Math Jokes 4 Math Folks book
> 10 days ago
I recently received Math Jokes 4 Mathy Folks from the author, Patrick Vennebush. This is a very comprehensive collection of math-related jokes that all mathy people will definitely enjoy, and math teachers could use this book to enliven their lessons.I have seen several of the jokes on the Internet, but never such a large collection.The jokes are categories into chapters such asOne-Liners, ( A hungry clock goes back four seconds. )Graphic Jokes, (For example, Cube Roots picture you see on th ...
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Algebra 1 curriculum advice
> 10 days ago
I have just finished writing a LONG article on homeschool algebra 1 recommendations and advice. It took me quite many hours to write and research.Questions about what to do for algebra 1 have become one of the frequently asked questions , so I decided to write down something that I can refer people to, from now on.I realize you may have different opinions and even suggestions for algebra curriculum in homeschool, so if you let me know, I'm willing to look into other possibilities not mentioned ...
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Common Core State Standards released
> 10 days ago
Common Core State Standards is a state-led initiative (not by the government) and designed by a diverse group of teachers, experts, parents, and school administrators.They hope these standards will be adopted by various states. We shall see! It would definitely help if the math standards didn't vary so much among the various states. In some states, there are SO many standards and objectives per grade that it seems impossible students could learn it all well.You can view the mathematics standards ...
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7 TeV collisions tonight…
> 10 days ago
by Jim Pivarski
… if all goes well. The LHC has been circulating two 3.5 TeV beams off and on for the past week, and tonight they plan to turn off the separators keeping them apart. We should then see the first 7 TeV collisions ever produced in a laboratory. If there are any undiscovered particles with [...]
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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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RAII vs finally
> 10 days ago
Since I'm pretty new to C++, I wasn't too deeply familiar with RAII; like most Schemers I just thought of it as C++'s version of dynamic-wind. This week I learned an important distinction between C++ destructors and Java's finally. The latter, of course, unilaterally executes when the body terminates, regardless of how or when it terminates. The thing that gives destructors more expressiveness for dealing with cleanup is that they only execute for the objects that have been initialized. This me ...
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A Theory of Typed Hygienic Macros
> 10 days ago
A Theory of Typed Hygienic MacrosPhD Dissertation, 2010We present the λm-calculus, a semantics for a language of hygienic macros with a non-trivial theory. Unlike Scheme, where programs must be macro-expanded to be analyzed, our semantics admits reasoning about programs as they appear to programmers. Our contributions include a semantics of hygienic macro expansion, a formal definition of α-equivalence that is independent of expansion, and a proof that expansion preserves α-equivalence. The k ...
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Effective ML
> 10 days ago
Yaron Minsky has giving great advice on effective ML lately. For my money, the single most important lesson is #3: make illegal states unrepresentable. There are so many benefits-- and I've seen the awful drawbacks of not following it.
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Cyclic reference graphs FTW
> 10 days ago
I've just created my new Mozilla-hosted blog! I don't have intention of stopping this one here, but I'm moving my Mozilla-related (and consequently ECMAScript-related) thoughts to that space.Also, um, I should hopefully have some pretty good news in a couple weeks.
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Single-frame continuations for Harmony, ctd
> 10 days ago
Continuing last week's series of posts on single-frame continuations for ECMAScript Harmony:The inimitable Waldemar Horwat points out the flaw in my strawman proposal (strawman strawman?):Since in the final expression you have A(... A(x)), you'll just end up executing the same finally block twice under certain circumstances.This program demonstrates the bug:function captured() { try { handler->(); throw throw ; } finally { alert( finally! ); }}function handler(k) { k ...
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ICML +amp; COLT 2010
> 10 days ago
by jl
The papers which interested me most at ICML and COLT 2010 were:
Thomas Walsh, Kaushik Subramanian, Michael Littman and Carlos Diuk Generalizing Apprenticeship Learning across Hypothesis Classes. This paper formalizes and provides algorithms with guarantees for mixed-mode apprenticeship and traditional reinforcement learning algorithms, allowing RL algorithms that perform better than for either setting alone.
István Szita [...]
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MetaOptimize
> 10 days ago
by jl
Joseph Turian creates MetaOptimize for discussion of NLP and ML on big datasets. This includes a blog, but perhaps more importantly a question and answer section. I’m hopeful it will take off.
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2010 ICML discussion site
> 10 days ago
by jl
A substantial difficulty with the 2009 and 2008 ICML discussion system was a communication vacuum, where authors were not informed of comments, and commenters were not informed of responses to their comments without explicit monitoring. Mark Reid has setup a new discussion system for 2010 with the goal of addressing this.
Mark didn’t want to [...]
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The Good News on Exploration and Learning
> 10 days ago
by jl
Consider the contextual bandit setting where, repeatedly:
A context x is observed.
An action a is taken given the context x.
A reward r is observed, dependent on x and a.
Where the goal of a learning agent is to find a policy for step 2 achieving a large expected reward.
This setting is of obvious importance, [...]
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Google Predict
> 10 days ago
by jl
Slashdot points out Google Predict. I’m not privy to the details, but this has the potential to be extremely useful, as in many applications simply having an easy mechanism to apply existing learning algorithms can be extremely helpful. This differs goalwise from MLcomp—instead of public comparisons for research purposes, it’s about private utilization [...]
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TheoryOverflow: An Update
> 10 days ago
by Suresh
Now that I'm done with SODA (any word on number of actual submissions?), I thought I'd do a brief update on the proposed theoryCS Q&A site (currently laboring under the inelegant name of TheoryOverflow). I've had various questions from people, and have wondered about others. So rather than force you all to trawl meta.stackoverflow.com for answers, I thought I'd dish them out here.
I want my TO site ! When is it coming ?
The site is going through what is called a 'commit' stage. The StackE ...
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Tools every modern conference needs
> 10 days ago
by Suresh
(while I procrastinate on my SODA edits)
Crowdvine: an all-encompassing social network solution for conferences that includes schedule planning, networking, activity monitors (who's coming to my talk) etc
A paper discussion site (could be within crowdvine, or even something like Mark Reid's ICML discussion site)
A good paper submission/review manager like HotCRP (not CMT !)
Videolectures.net
Facebook/twitter/blog for official announcements.
At the very least, a website with all the papers for ...
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TheoryCS discussion site: A call for help.
> 10 days ago
by Suresh
Many of you are familiar with Mathoverflow.net (MO), the discussion site where (mostly) professional mathematicians come to discuss research problems, get questions answered by experts in the area, and have very enlightening discussions on a host of topics in mathematics.
The conversation is at a very high level. The moderators (and the community at large) do an excellent job of pruning out the posters fishing for homework answers, the vague questions with answers that any google search could r ...
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Metrics via pullbacks
> 10 days ago
by Suresh
One of the things I end up having to do a lot of is ponder distance metrics. Not the nicely behaved norm-induced ones, but more bizarre entities. metrics over shapes, metrics on lattices, metrics on distributions, and the like.
There are many constructions for building metric structures on spaces for which it's not clear how to do so. One of the neatest methods is via pullbacks, exploiting the algebraic and continuous duals for vector spaces.
The basic idea is as follows: You want to build a m ...
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And for some Sunday entertainment
> 10 days ago
by Suresh
(dare I say XKCD-style) Flowcharts for the life of the tenured and untenured professor. A collaborative School of Computing effort between my colleagues John Regehr, Matthew Might and myself (who says professors can't collaborate inside a department!).
Incidentally, we also make up the vast majority of our department's blogging presence.
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A particularly lousy version of academic dishonest ...
> 10 days ago
by Jim Stankewicz
Last semester, a number of emails like this circulated: Subject: Math Requirements From: FirstnameLastname@yahoo.com To: jstankewatbutIdon’twantspammath.uga.edu Dear James Stankewicz, My name is Firstname Lastname and I am a graduate student at the University of Prestigious Institution studying for my ph d in math. I am taking a class and we are studying Field and Galois Theory and [...]
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A new crank! And a call for examples
> 10 days ago
by Charles Siegel
While I somehow never get emails from cranks, I tend to find them at the slightest provocation on the internet. Here’s a new one: Miles Mathis, who I’ve not run into before. He’s also a physics crank (multidisciplinary research!) so for the more mathematically minded, just jump down to Section 2, where he has some [...]
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ICTP Day 15 – The End
> 10 days ago
by Charles Siegel
Today the conference ended, and I’ve got an early plane to catch. I’ll be away from the blog for a bit. Here’s the notes from the last day, which, I admit, are a bit sketchier than most of the others, but they’re what I have: 1. Cattani – Mixed Hard Lefschetz and Mixed Hodge-Riemann Bilinear [...]
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The Schottky Problem (ICTP)
> 10 days ago
by Charles Siegel
These are my notes, and are only a rough approximation of the actual talk: 1. General Torelli and Schottky Problems Take a class of smooth projective varieties with the same Hodge numbers. We can immediately ask two questions about the map from the set of these objects to the period domain: Torelli: Is the map [...]
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ICTP Day 14 – Doomsday
> 10 days ago
by Charles Siegel
I gave my talk today. It seems to have gone over well, though I’m not entirely happy with it…but then, as with many people, I’m my own harshest critic. Here’s the notes from other talks, the notes from mine will follow in a separate post. 1. Doran – Normal forms for lattice polarized K3 surfaces [...]
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Death to Hydrae (or the operational semantics of o ...
> 10 days ago
Unprovable PropositionsAmong other things,
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Constructing Intermediate Values
> 10 days ago
IntroductionThe Intermediate Value Theorem, as it is usually told, tells us that if we have a continuous real-valued function f on the closed interval [0,1], with f(0)<0 and f(1)>0 then there is a point x in (0,1) such that f(x)=0. Here's a sketch of a proof:Define three sequences li, ui, xi recursively as follows:xi+1 = (li+ui)/2(li+1, ui+1) = (li, xi+1) if f(xi+1)>0(li+1, ui+1) = (xi+1, ui) otherwiseSet l0=0, u0=1.The xi+1 are bracketed by the li and ui, and |ui-li|=2-i so the xi form ...
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Optimising pointer subtraction with 2-adic integer ...
> 10 days ago
IntroductionHere is a simple C type and a function definition:struct A{ char x[7];};int diff(struct A *a, struct A *b){ return a-b;}It doesn't seem like there could be much to say about that. The A structure is 7 bytes long so the subtraction implicitly divides by 7. That's about it. But take a look at the assembly language generated when it's compiled with gcc:movl 4(%esp), %eaxsubl 8(%esp), %eaximull $-1227133513, %eax, %eaxretWhere is the division by 7? Instead we see multiplication by ...
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On representing some real numbers exactly
> 10 days ago
There are uncountably many real numbers, and only countably many finite strings of symbols, so we know for sure that there is no scheme to represent all real numbers as finite strings of symbols in such a way that different reals get different representations. However, there are useful subsets of the real numbers that *are* equipped with finite encoding schemes. I hope to give some examples of such sets, including one, the set of periods, that isn't currently well known outside the mathematical ...
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A Partial Ordering of some Category Theory applied ...
> 10 days ago
I've had a few requests from people wanting to teach themselves applications of Category Theory to Haskell based on posts I've made. I've made things difficult by posting stuff at random levels of difficulty and without any kind of organising thread through them. So here's an attempt to list a bunch of posts related to aspects of category theory. I've grouped them by themes and within each theme I've tried to list the articles in order of difficulty. Unfortunately there can be big gaps between o ...
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My Favorite Week: Math Circle Summer Teacher Train ...
> 10 days ago
Ellen and Bob Kaplan, Jordan Hall, University of Notre Dame, 7/7/10I just got back from Notre Dame, and boy, is my brain tired! Well, actually not. Despite a lot of walking for this out-of-shape math educator and a lot of strenuous mathematical thinking, I'm exhilarated after my first Math Circle Summer Teacher Training Institute with the wonderful Bob and Ellen Kaplan. This was the third such institute held at the University of Notre Dame, a campus that seems as isolated from time as a medieval ...
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Who Was George Polya's Intended Audience? (Or More ...
> 10 days ago
George Polya, c. 1973One of the more difficult aspects of wars, even ones where the main ammunition is words, is separating lies from facts. Every side in a war has a proclivity for propaganda. Inconvenient facts are brushed aside. Inaccuracies, petty or gross, become the coin of the realm. The Big Lie rules. Of course, sometimes, it is possible to sort through the fog of war to arrive at what appears to be incontrovertible truth. It may take years, even decades, to find the facts, even when the ...
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I Saw Mathematics Education Future and Its Name Is ...
> 10 days ago
Dan MeyerSome thinkers/innovators and their ideas are simply too good for even the media to miss. Dan Meyer is one such thinker. He happens to be, amongst other things, a high school mathematics teacher in Felton, CA, barely a stone's throw from Santa Cruz. He teaches geometry to kids he describes in ways that makes them sound like non-enthusiasts in mathematics, at least when they enter his classes in the fall. Dan blogs at dy/dan on a variety of issues related to teaching mathematics, but his ...
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What Time Is It?
> 10 days ago
Lillian R. LieberAlways fascinating to find out that it's 1959. POSTULATES are, as you know,the RULES for playing some game .Surely anyone in his right mindwould not even try toplay a game without knowing itsBASIC RULES!And yet,some people, young and old,try to play the games ofarithmetic and algebra WITHOUT EVER realizingthat these HAVE basic rules!Now, mind youit is NOT BECAUSE these rulesare difficult,NOT BECAUSE there are too many of them!On the contrary, they are very simpleand very few,as ...
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Going by the book? Why math texts are resources, n ...
> 10 days ago
I have addressed the issue of how to view mathematics textbooks in K-12 several times before ( Changing order of topics: an example from practice , and The Book Gods amongst others, but it seems to rear its unlovely head periodically amongst real teachers and mathematics educators. A recent post to a math teacher list I read posed the following:I know this question might sound silly, but I need to know what you think. Do you believe it is counterproductive to literally teach math by the book ...
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Chasing Rabbits in Stat Class
> 10 days ago
by SplineGuy
"Whoa! Dr. Franklin, that was fast."
One of my students made such a comment on the speed with which I entered numerical data into a spreadsheet using the 10-key number pad. Being well into a 3 hour class, I decided it was a good time to give a bit of a break to the stats [...]
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10 Tips for Living
> 10 days ago
by SplineGuy
From The Happiness Project by GretchenRubin
Just came across these in reading random blogs and thought they were very good. My favorite is #7.
Here are ten tips from Pope John XXIII about how to live a better life, day to day:
1. Only for today, I will seek to live the livelong day positively without wishing to solve the problems [...]
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ScribTEX moves my LaTEX editing online
> 10 days ago
by SplineGuy
Thanks to a comment in an earlier post on MonkeyTex, I was introduced to an online tool for editing and compiling LaTEX documents and projects.
For those that don’t know, LaTEX is a tool used by mathematicians, scientists, and engineers to typeset their print or electronic documents. In order to render the symbolic notation [...]
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Fibonacci and Our Number System
> 10 days ago
by SplineGuy
I just started reading “The Unfinished Game” by Keith Devlin which documents a correspondence between Fermat and Pascal that literally changed the course of mathematics and even, some would argue, of history in general. The correspondence laid the foundations for probability theory.
What I just learned was something I’d never heard before:
“The modern, so-called Hindu-Arabic [...]
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My Prezi at ICTCM
> 10 days 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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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 ...
