We prove that a 3--dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by its Gauss image.
We prove that a 3--dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by its Gauss image.
Ah, mathematics. That single word, mathematics, can divide - and strike fear in the hearts of - individuals like no other term.
The second way to teach quantum mechanics eschews a blow-by-blow account of its discovery, and instead starts directly from the conceptual core - namely, a certain generalization of the laws of probability to allow minu signs (and more generally, complex numbers). Once you understand that core, you can then sprinkle in physics to taste, and calculate the spectrum of whatever atom you want.He approaches the whole book by this philosophy. Every now and then he moves into technical details that are best skipped--either you already know it or will get lost trying to follow. But no problem, the story remains. You need to appreciate Scott's sense of humor and his philosophical tendencies, and he does get way too philosophical near the end, particularly a strange attack on Bayesian that involves God flipping a coin. At the end of the book Scott contemplates whether computer science should have been part of a physics department but after one reads this book the real question is whether physics should be part of a CS department.
A well written note by Frenkel that attempts to explain Deligne’s work that won him this year’s Abel Prize.
On Jeopardy recently the final Jeopardy question was as follows.
TOPIC: Island Countries.
ANSWER: No longer Western, this one-word nation has moved to the west side of the international Date Line to join Asia and Australia.
BILL: What is SAMOA!?Darling wondered how I know that:
DARLING: How did you know that? Is there a Ramsey Theorist in Samoa?
BILL: Not that I know if, but that's a good guess as to how I knew that. Actually Lance had a blog post Those Happy Samoans about Samoa going over the international dateline and losing the advantage of having more time to work on their conference submissions.
DARLING: Too bad there isn't a Ramsey Theorist there to take advantage of that!
The course is a short intervention designed to change students' relationships with math. I have taught this intervention successfully in the past (in classrooms); it caused students to re-engage successfully with math, taking a new approach to the subject and their learning.
In the 2013-2014 school year the course will be offered to learners of math but in July of 2013 I will release a version of the course designed for teachers and other helpers of math learners, such as parents. In the teacher/parent version I will share the ideas I will present to students and hold a conversation with teachers and parents about the ideas. There will also be sessions giving teachers/parents particular strategies for achieving changes in students and opportunities for participants to work together on ideas through the forum pages.
You probably already know about the two packages that you can use to typeset Fitch-style natural deducation proofs in LaTeX. Here's another, which you may be interested in if you use Barker-Plummer, Barwise, and Etchemendy's popular logic text Language, Proof, and Logic. It makes proofs like this:

I've taken Etch's original style file and Dave's documentation, put it together in standard docstrip format, cleaned up the code a bit and added a few features. You can download the beta from
https://github.com/rzach/lplfitch
I've also attached the documentation here.
Please file any problem reports on github, if you could, or email me directly. (The comment system here is unreliable.) I'm hoping to put it on CTAN in a month.
My solution: Take mom out to lunch the FOLLOWING week. Some of my friends tell me NO- you can't just MOVE Mothers day- what are you--- The Master of Space and Time? The key is that my mom AGREES with me and in fact raised me with these values: (1) Never do X when everyone else is doing X, its too crowed, and (2) Learn the polynomial VDW theorem.
While this solution may work for me, it may not work for everyone. Here are some options to alleviate the restaurant crunch:
However, the entire tradition of taking mom out to lunch on mothers day may fade. The origin is that mom cooks for the family most days, so this ONE day they take her out. Nice! But more and more households share responsibilities (NOTE- I have no facts or stats to back this up but it has a certain truthiness about it) hence the notion of taking mom out to lunch may seem more and more odd over time. Then again, its still nice being taken out to lunch.
Another report on how students don’t learn as well when they attempt to multi-task.
She's done these classes several times before (as you may know :) ), and my kids have really enjoyed them. She's warm and engaging - and knows her science. What number do you need to add to 3 to get a double fact?I had never heard the term double fact! I really didn't know and there was no way toderive it! I don't recall what my guess was but it was incorrect.See herefor what they are.
Is this a common term? If you Google
"Double fact" mathYou get roughly 6,000 hits. (Down from 17,000 a few months ago when I first sketched out this post.)Is that enough hits to be a real term? Is number-of-hits a good measure?
Are there other math terms that are being taught in elementaryschool that are not that well known to people like us? (Though if you have children perhaps you know them.)Note that no matter how much math you know, there may be terms you don't know and can't derive (though you can make an intelligent guess).
My name is Bill Gasarch, and I am NOT smarter than a fifth grader.
In 1972 I read that the four-color theorem was an open problem. From what I read it seemed like there was some progress on it (e.g., results like `if its false the graph has to be yah-big) but it seemed to be years away from being solved. I assumed that a new idea was needed to solve it.
Then, in 1976, it was SOLVED by Appel-Haken. From what I read it wasn't so much a new idea but very clever use of old ideas and a computer program. I also heard that it was just at the brink of what computers could do at the time, and that it would have taken 1200 grad student hours. (There is a good description of the proof on Wikipedia here.)
At the time I heard there were objections to the proof. Later when I read some of them they didn't seem like real objections. They boiled down to either
In 1996 Robertson, Sanders, Seymour, Thomas was obtained a simpler proof. In 2005 Werner and Gontheir formalized the proof inside Coq- a proof assistant. To quote Wikipedia This removed the need to trust the various computer programs used to verify particular cases;it is only necessary to trust the Coq Kernel At this point I doubt anyone seriously doubts that the theorem has been proven.
There have been more computer-assisted proofs since then. See here for a list of some of them. That article also claims that such proofs are controversial and not always accepted. Is this really true? I thought the controversy was gone except for the topic of the next paragraph.
A famous computer assisted proof (or perhaps ``proof'') is the Kepler Conjecture. In 1998 Thomas Hale claims to have proven it. The proof involved rather complex computer calculations. The referees say they are 99% sure its true. Here's hoping an easier proof is found.
Computer assisted proofs may become more common. I just hope we still know WHY things are true.
Was Appel-Haken the first use of computer assisted proofs? I doubt it, but it was likely the first one to have an impact. It was important to know that this kind of proof could be done.
Is there a much shorter proof? A combinatorist once told me that since the function
f(n) = max size of proofs of statements of length n
30 Apr 2013
In this Newsletter:
1. Math resource: MathGraph32
2. Prime numbered cicadas
3. Relieving test anxiety
4. Math puzzle
5. IntMath Poll
6. Final thought:
Once again I apologize for the long gap since the last IntMath Newsletter. I’m involved in several large projects (including developing online modules for a math course and 2 academic integrity courses). Once those are done, hopefully I’ll be able to get back to a regular schedule of writing.
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MathGraph32 is a great free tool for exploring 2D and 3D math concepts. |
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The 17-year cicada is due to emerge in north-eastern parts of USA in Spring 2013. What is their connection to prime numbers? |
Annie Murphy Paul writes the Brilliant Report for Time magazine, It’s an interesting collection of research about the brain and how to squeeze more out of it.
A recent article, How to Eliminate Test Anxiety gives some good pointers, which as she says, are reasonably simple, inexpensive and, as recent studies show, effective."
Here’s some short quotes from her list of suggestions:
1. Unload on paper. Spend ten minutes writing about your thoughts and feelings immediately before taking a test.
The practice, called "expressive writing," is used by psychologists to reduce negative thoughts in people with depression. They tried the intervention on college students placed in a testing situation in Beilock’s lab, and in an actual Chicago school, where ninth-grade students engaged in the writing exercise before their first high school final. In both cases, students’ test scores “significantly improved,” according to an article they published last year in the journal Science.
2. Affirm your values. Apprehension over tests can be especially common among minority and female students. That’s because the prospect of evaluation poses for them what psychologists call "stereotype threat"—the possibility that a poor performance will confirm negative assumptions about the group to which they belong ([this posits] that girls can’t excel in math and science; blacks and Latinos aren’t college material).
3. Engage in relaxation exercises. Younger kids aren’t immune from test anxiety. As early as first and second grade, researchers see evidence of anxiety about testing. Their worries tend to manifest in non-verbal signs that adults may miss, [like] stomachaches, difficulty sleeping, and a persistent urge to leave the classroom to go to the bathroom.
See more details on these anxiety-reduction techniques here:
From The Brilliant Report: How To Eliminate Test Anxiety
The puzzle in the last IntMath Newsletter was about expressing the number one using nines, a minus sign and dots.
Correct answers were given by dalcde, Christopher, Bonnie, Andrzej, Dineth, Nicos and Thomas.
Math symbols were a challenge: I knew it was going to be tricky to type in the answers for this puzzle. I started to write some pointers about how to do it and stopped, because that would have given the answers away! (There is a "Preview" button on the response box for the blog. You can use it to make sure your math looks OK before posting.)
9<sup>9-9</sup> = 1
It will look like this:
99-9 = 1
0.\dot{9} = 1
At the bottom of the equation editor page there is an "embed" box with code. Copy that code into the "respond" box in most blogs and it will look like:
Note 1: I included the "0" before the decimal point in my answer above. A lot of people don’t notice the dot, and misread decimal numbers. (Yes, I know the question specified "one nine" only, but it’s worth mentioning.)
Note 2: I was aware the question was somewhat country-specific. The Europeans write a decimal number using a comma, not a dot.
And as Andrzej pointed out in his response regarding the recurring part:
There are three symbols for recurring fractions: dash, dot (UK and USA) and () in Poland. So the solution is slightly tricky; it depends on nationality.
It would be really nice if we had consistent math notation around the world, especially when for something as simple as writing numbers!
New puzzle: 216 cubes of side length 1 cm are arranged to make a cube with side length 6 cm.
A sphere of diameter 6 cm is inscribed in the large cube such that the center of the sphere is the center of the cube. How many complete unit cubes is contained in the sphere?
You can leave your responses here.
Donald Trump is a real estate millionaire who became quite famous as a result of his role in the TV series The Apprentice. He once said:
Work hard. Someone’s always watching.
Until next time, enjoy whatever you learn.
The post IntMath Newsletter: Prime cicadas appeared first on squareCircleZ.
MathGraph32 is a great free tool for exploring 2D and 3D math concepts.
(It’s been around for a while, but I only recently discovered it.)
There is a download version as well as an online Java-based version.
According to the site, MathGraph32 is an:
Open source cross-platform software of geometry, analysis and simulation.
It was developed by French-speaking mathematician, Yves Biton. Some of the examples are in French, but it’s quite easy to see what is going on. (There is an English version of the program).
Here are some examples from MathGraph32 (images by them).




You can explore several examples (some for “teaching purposes”), and there are tutorials that help explain the use of the applet.
It’s well worth checking out!
The link again: MathGraph32
The post MathGraph32 appeared first on squareCircleZ.
Maria,
I just have to thank you for your wonderful math program. I emailed you late last summer about my 6th grade daughter who was terribly behind in math. You suggested I start her back in the grade 1 book to give her a fresh and solid start. I did and she has done great! She has completed both first grade books, both second grade books and has now started the multiplication "theme" books (I decided to just do multiplication because most of the other things in the 3rd grade book she already knows). I can't believe she's flown through 2 grade levels and is starting a third in less than one school year. She still does not love math, but she is doing well and has built some confidence. Your method for learning multiplication tables is terrific. She's learned 2, 4, 3, 5, 10, 11 in about 3 weeks!
I love that you focus, not just on learning the facts, but on understanding the concepts. Not just "this works", but "this is why this works". Many programs don't do that; it's just rote memorization which is partly why Grace got so behind. She never understood why she was carrying (for instance), she just did it. Now that it makes sense, it's really sticking with her.
I'm using your program with my other younger children, too, and am just as happy. Also, it's so easy for me to use. Almost no prep time and free worksheets when they need a little extra help or some review!
Thank you again and again for your wonderful program!
Blessings,
Lisa
If you're in Austin, you probably know this already. If you're not, it's probably too late. But this is what I'll be doing this weekend:
Friday, 26 April 2012
Thomas Uebel, University of Manchester, “The Logic of Science and the Pragmatics of Science: The Challenge of Complementarity.”
Christopher French, University of British Columbia, “Carnap, Jeffrey and Explication of Radical Probabilism.”
Sebastian Lutz, Ludwig-Maximilians-Universität München, “The Criteria for the Empirical Significance of Terms.”
Saturday, 27 April 2012
Sahotra Sarkar, University of Texas, “Nagel on Reduction.”
Michael Stoeltzner, University of South Carolina, “Could Mathematical Physics serve as a Model for Formal Epistemology?”
Flavia Padovani, Drexel University, “Reichenbach On Causality in 1923: One Word, Many Concepts”
Richard Zach, University of Calgary, “Carnap on Logic.”
Thanks to Sahotra Sarkar for putting this together!

"Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning."You can generate worksheets for this exact standard! They can look like this:
Today is the official publication date of my first book The Golden Ticket: P, NP and the Search for the Impossible by Princeton University Press, though the book has been available on Amazon and in some bookstores for a couple of weeks now. This book takes a non-technical tour of our favorite open question through a series of stories and examples, covering P, NP, NP-complete, the "beautiful world" if P = NP, and how to deal with hard problems since we surely don't live in that world and a bit of history, cryptography and quantum. How "non-technical": I never actually define P and NP and avoid formulas and terminology except as needed to describe circuits and Cook's theorem.
Google's logo for today (interactive, by the way) is a tribute to Leonhard Euler -- a very famous mathematician from the 1700s. Today is the 306th anniversary of his birth (he was born on April 15, 1707).
Then, if you study graph theory, you'll immediately encounter the famous problem about the Seven Bridges of Königsberg. Euler solved that, as well.
Miller also made significant contributions to the theory of isomorphism testing—the problem of telling whether two structures are the same except for the labeling of their components. He showed the equivalence of many different isomorphism problems to the still-open problem of graph isomorphism, and identified many special cases that could be solved efficiently. These included the problem of testing isomorphism for a special case known as bounded-genus graphs, a result he obtained with John Reif in 1980. In 1985, in another collaboration with Reif, Miller invented the concept of "parallel tree contraction." This is one of the most fundamental primitives in parallel algorithm design with wide applications to graph theoretical and algebraic problems.
In 1984, Miller moved into the area of scientific computing. He set up the theoretical foundations for mesh generation, and was the first to design meshing algorithms with near-optimal runtime guarantees. His subsequent research led to his breakthrough 2010 results with Ioannis Koutis and Richard Peng that currently provide the fastest algorithms—in theory and practice—for solving "symmetric diagonally dominant" linear systems. These systems have important applications in image processing, network algorithms, engineering, and physical simulations.

In the 1950's, a Hungarian sociologist Sandor Szalai studied friendship relationships between children. He observed that in any group of around 20 children he was able to find four children who were mutual friends, or four children such that no two of them were friends. Before drawing any sociological conclusions, Szalai consulted three eminent mathematicians in Hungary at that time: Paul Erdos, Paul Turan, and Vera Sos. A brief discussion revealed that indeed this is a mathematical phenomenon rather than a sociological one. (Namely R(4)=18&leq20.)
I'm having difficulty in solving this question which involves calculating fractions - this question relates to finding an arc length.
140 divided by 360, multiplied by 2, multiplied by 22 divided by 7, multiplied by 12:
140
360× 2 × 22
7× 12
| 7 18 | × | 2 | × | 22 7 | × | 12 |
| 1 18 | × | 2 | × | 22 1 | × | 12 |
| 1 2 × 9 | × | 2 | × | 2 × 11 1 | × | 12 |
| 1 9 | × | 2 | × | 11 1 | × | 12 |
| 1 3 | × | 2 | × | 11 1 | × | 4 |
| 1 3 | × | 2 | × | 11 1 | × | 4 | = | 88 3 |
AP press 2050: The new pope was elected in just 2 hours using EasyPope, the software based on EasyChair, software designed to deciding which papers get into a conference. The new Pope was quoted as saying How did they manage in the old days actually Flying to Vatican to elect someone. This just seems silly.
As a society we are gaining efficiency but loosing connectivity
Working together, they pioneered the field of provable security, which laid the mathematical foundations that made modern cryptography possible. By formalizing the concept that cryptographic security had to be computational rather than absolute, they created mathematical structures that turned cryptography from an art into a science. Their work addresses important practical problems such as the protection of data from being viewed or modified, providing a secure means of communications and transactions over the Internet. Their advances led to the notion of interactive and probabalistic proofs and had a profound impact on computational complexity, an area that focuses on classifying computational problems according to their inherent difficulty.Shafi and Silvio's paper Probabilistic Encrytion really did set the stage for modern cryptography. Their paper with Charlie Rackoff, The Knowledge Complexity of Interactive Proof Systems started my own research in that area. When I did my graduate work at MIT, I had many great discussions with Shafi and Silvio about cryptography and proof systems and I owe them much for my own research career.
If you are wondering how well your homeschool math program is working, pay attention to your children.If so, then be assured: your children are already miles ahead of most of their peers. Their foundations are solid, and the details will eventually fall into place as you continue to play with mathematical ideas together.
- Do they understand that common sense applies to math?
- Can they give logical reasons for their answers?
- Even when they get confused, do they know that math is nothing to fear?
I’ve been off Being Human (the original UK version) for a while now. I stopped watching after the first episode of season 3, in part because the American version came out and I got into that before it started circling the drain, and in part because Mitchell gets on my damned last nerve.
Now I’m back to watching it after I discovered all the original cast members leave by the end of the show. I’m so looking forward to seeing emo-goth pretty boy Mitchell get dusted— or maybe they’ll dial up his already epic levels of self-pity, narcicissm, and angst to the point that he combusts— that this was just what I needed to get back in the game.
Too bad that means Lenora Crichlow and Russell Tovey will be leaving eventually too. Their acting is the strongest reason I watch this show: when they cry, I cry. When Lenora gives her monologues, I cry a little. When Russell opens up about his feelings, I ball. It’s pathetic, I know, but the point is that they’re very good at getting across the underlying message of the show: that even monsters can be human, because humanity is about our relationships.
Anyhooo, now I’m back to watching Robson Green play a homeless(?) drifter werewolf dad forced into underground supernatural cage fights.
Math Teachers at Play blog carnival #59 is posted at Learners in Bloom. Looks good, as usual!