"Whenever you have a physical object to be reconfigured, geometric folding often comes into play. This class is about algorithms for analyzing and designing such folds."

Great answer on quora. "Over on Google+, Timothy Gowers liked this comment so much he wished it were published someplace like the Notices of the American Mathematical Society."

Although it didn't catch up there are some interesting (advanced) materials. "This is an attempt to give a quick guide to the top few levels of the Tricki. It may cease to be feasible when the Tricki gets bigger, but we might perhaps be able to automate additions to it. Clicking on arrows just to the right of the name of an article reveals its subarticles. If you want to hide the subarticles again, then you should click to the right of them rather than clicking on the name of one of the subarticles themselves, since otherwise you will follow a link to that subarticle."

Good lecturer.

"Today I want to talk about why some proofs are hard to understand, not hard to discover." Discussion in the comments section is interesting.

Blog on mathematics. "My name is Akhil Mathew. I’m a rising sophomore at Harvard studying mathematics. I blog about the subject here, at Climbing Mount Bourbaki. / For me, blogging is a useful way for me to better understand the subject; I’ve long enjoyed writing notes to myself, and the internet medium allows me to communicate mathematics with others. It also gives me additional motivation to check for errors. / My interests are rather amorphous and frequently change. The varying topics discussed here will reflect that. Right now, however, they are centered on algebraic geometry."

"A remarkable transformation is now underway in how scientists make discoveries. Mass online collaborations are being used to prove mathematical theorems; online markets are allowing scientific problems to be outsourced; and online citizen science projects are enabling amateurs to make scientific discoveries. These and other projects show how we can use online tools to amplify our collective intelligence, and so extend our scientific problem-solving ability. This promise is only part of the story, however, for today there are many cultural barriers inhibiting scientists from using online tools to their full potential. I will discuss these cultural barriers, and how they can be overcome."

"This is the first of what I hope will be a long series of posts aimed at providing back-up to first-year Cambridge mathematicians. This may seem a strange thing to do, since the Cambridge system of supervisions (classes taught on a one-to-two basis, usually discussing questions set by lecturers) already provides an excellent back-up to lectures. Do Cambridge undergraduates, who already have closer attention than in any other university I know about, really need even more help?"

Good resources in the first comment.

"I've been fascinated by the phenomenon the question addresses for a long time. We have complex minds evolved over many millions of years, with many modules always at work. A lot we don't habitually verbalize, and some of it is very challenging to verbalize or to communicate in any medium. Whether for this or other reasons, I'm under the impression that mathematicians often have unspoken thought processes guiding their work which may be difficult to explain, or they feel too inhibited to try."

"Click on the links below to download PDF files containing double-sided flash cards suitable for printing on common business card printer paper. If you don't have or don't want to buy special business card paper, I have also included versions which include a grid. You can use scissors or a paper cutter to create your cards." + LaTeX source files.

Genius and Biographers: The Fictionalization of Evariste Galois

Seems like a good book.

Another essay on teachings of mathematics.

"Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields." // Benedict Gross seems like a great lecturer! Course uses Artin's book "Algebra".

"Beautiful Young Minds was a documentary first shown at the BritDoc Festival on 26 July 2007 [1][2] and first broadcast on BBC 2 on 14 October 2007.[3] The programme follows the selection process and training for the British team to compete in the 2006 International Mathematical Olympiad (IMO), as well as the actual event. It was directed and shot by Morgan Matthews, edited by Joby Gee, and featured music by Sam Hooper. It was also screened at the Bath Film Festival in October 2007."

"MathJax is an open source JavaScript display engine for mathematics that works in all modern browsers."

"A reading protocol is a set of strategies that a reader must use in order to benefit fully from reading the text. Poetry calls for a different set of strategies than fiction, and fiction a different set than non-fiction. It would be ridiculous to read fiction and ask oneself what is the author's source for the assertion that the hero is blond and tanned; it would be wrong to read non-fiction and not ask such a question. This reading protocol extends to a viewing or listening protocol in art and music. Indeed, much of the introductory course material in literature, music and art is spent teaching these protocols."

First lecture seems very promising.

"But one or two asked a question that I really had trouble answering. The question was not an obvious ones like: what is polynomial time, or what is NP. The question was: Why is proving PNP an important result?"

Every position of Rubik's Cube™ can be solved in twenty moves or less.

"10/1/09 update — well, it’s been nearly a year, and I should say not everything in this rant is totally true, and I certainly believe much less of it now. Current take: Statistics, not machine learning, is the real deal, but unfortunately suffers from bad marketing. On the other hand, to the extent that bad marketing includes misguided undergraduate curriculums, there’s plenty of room to improve for everyone."

"Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. At TEDxNYED, Dan Meyer shows classroom-tested math exercises that prompt students to stop and think."

"Several days ago Lance wrote about "Is Complexity Math or Science?", and in that context wrote "We don't do experiments...", which has caused me to overreact. // I'm not sure who he meant by "We" -- I guess complexity theorists -- but I found the statement very strange at the time. I do experiments all the time."

A legendary problem and the battle over who solved it. by Sylvia Nasar and David Gruber

MiŠ, autor: Branimir Dakić, br. 35, 2006.

"U posljednje se vrijeme u raznim našim javnim glasilima moglo pročitati više kritičkih osvrta na nastavu i učenje matematike u našim školama. Nažalost, ti su tekstovi površni, uglavnom tmurno obojeni, nerijetko destruktivni i tragovi koje ostavljaju za sobom neće doprinijeti boljitku naše škole, posebice neće biti poticajni za učenje matematike. Ovom je pak tekstu zamisao dati jedan pogled „iznutra“, onako kako problem vidi jedan iskusni nastavnik matematike. " ... "Jedan od problema učenja matematike jest predugo trajanje opismenjavanja. No, kao što bez jezične pismenosti nema suvisle pismene komunikacije ni lijepog literarnog štiva, tako nema ni znanja, pa onda ni primjene matematike bez solidne matematičke pismenosti. Usmjeriti nastavu matematike isključivo u primjere njezine konkretne, nerijetko sasvim banalne primjene, neprihvatljiva je krajnost jednako tako kao što je neprihvatljivo nastavu matematike svesti na puko manipuliranje apstraktnim činjenicama. "

"Sažetak. Međunarodna matematička olimpijada koja danas predstavlja svjetsko prvenstvo učenika srednjoškolaca u rješavanju zahtjevnih matematičkih problema bliži se svojoj pedesetoj godišnjici. U ovom članku dan je kratki povijesni pregled, opis natjecanja i osvrt na neka druga matematička natjecanja."

"I try to maintain a list of books and lecture notes freely available on the web."

"Svrha ove stranice je objaviti što veći broj zadataka s natjecanja iz matematike (uključujući i njihova rješenja)"

"I've just discovered that the excellent PBS documentary A Brilliant Madness that looks at the life of Nobel-prize winning mathematician, John Nash, is available online either as streamed video or as a torrent."

"This may be the first documentary I've ever seen that I thought was too short. It's about obsessive paper hackers who fold extreme origami. They make paper do things you would never believe. Sheets are folded into impossible shapes, in impossible ways. Some origami unfolds in almost lifelike gestures. The folders use computers, math, craft, art, and sheer will power to turn uncut paper into anything, even all things. I could watch them do this for hours. It's magic. It's deep. It will change your mind about paper. They know things ordinary mortals do not. This documentary will bewitch you, making you ask for more."

"The paradox states that all natural numbers are interesting. The "proof" is by contradiction: if there were uninteresting numbers, there would be a smallest uninteresting number - but the smallest uninteresting number is itself interesting, producing a contradiction." :-))

"U utorak, 3. studenog 2009. s početkom u 17 sati u predavaonici P104 PMF-Matematičkog odjela održat će se sastanak Seminara za metodiku nastave matematike (poslijediplomski seminar)." Bilo je odlično, www.idi.hr navodno će biti sličnih istraživanja.

"But this result is proved by a counting argument that gives no clue about how to find such an a or how to establish that a given number a has that property. Such questions are the domain of computational number theory. There are a number of beautiful tricks in the area that make it particularly well suited to being discussed in the Tricki." ...

"A girl told her father that history was much easier when he was in school. "Why?" he asked. She responded "Because there was so much less of it."" And nice quote by Richard Posner at the end.

Obavijest na connect portalu. Za diskusiju.

"Novi broj objavljen je na potpuno redizajniranoj web stranici, koja osim novog izgleda, donosi i novu tehnologuju unosa matematičke notacije, što će olakšati kreiranje članaka za math.e. Nova web stranica također sadrži informacije o matematičkim događanjima u Hrvatskoj, kao i izbor matematičkih blogova (za sada samo na engleskom, ali se nadamo da će se uskoro naći i hrvatski matematičar-bloger)." Super, baš sam se pitao što je s math.e :-)

"In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems." Great read (via T. Tao)

"The truth is that most computer scientists will rarely need to use any piece of “useful” math. What they will constantly need to use is “mathematical maturity”: being comfortable with formal definitions and statements, being able to tell when a proof is correct, knowing when and how to apply a theorem, and so on."

"Gotovo svaki drugi učenik koji je na probnoj državnoj maturi ljetos pisao test iz matematike na višoj razini pao je na ispitu, iako je za dvojku bilo dovoljno točno riješiti samo 20 posto zadataka."

"Stoga se bojim da učenici koji budu položili takvu maturu neće biti adekvatno pripremljeni za nastavak školovanja, posebice ne na tehničkim fakultetima. Razlučivost mature bit će lošija od razlučivosti koja se temelji na prijemnim ispitima, što znači da će fakulteti dobiti lošiji odabir studenata." - prof. N. Elezović

by Timothy Gowers & Michael Nielsen. "The 'Polymath Project' proved that many minds can work together to solve difficult mathematical problems. Timothy Gowers and Michael Nielsen reflect on the lessons learned for open-source science." ... "The working record of the Polymath Project is a remarkable resource for students of mathematics and for historians and philosophers of science. For the first time one can see on full display a complete account of how a serious mathematical result was discovered. It shows vividly how ideas grow, change, improve and are discarded, and how advances in understanding may come not in a single giant leap, but through the aggregation and refinement of many smaller insights."

Predavanja s priprema.

"Interview with Dr. John Nash at the 1st Meeting of Laureates in Economic Sciences in Lindau, Germany, September 1-4, 2004. Interviewer is freelance journalist Marika Griehsel. Dr. Nash talks about the impact the Prize had on his life, his talent for mathematics as a child (5:38), the work that gave him the Prize (9:03), gives some advice to young students (13:07), talks about important economic issues of today (15:26), and shares his thoughts about the movie on his life, 'A Beautiful Mind' (21:18)."

"The document "mpdemo.pdf" contains over 300 MetaPost example illustrations. These MetaPost examples demonstrate a wide range of MetaPost capabilities. Most of these illustrations are used in my differential geometry book. " Very nice examples.

by William Aspray, March 1, 2005.

"There are many kinds of surprises in mathematics and theory: here are some examples", nice post by Lipton

Nice math films... "I Want To Be a Mathematician: A Conversation With Paul Halmos", "Julia Robinson and Hilbert's Tenth Problem", "N is a Number: A Portrait of Paul Erdös"...

Personalized math swiss army knife.

Dostupni su časopisi Matka, Matematičko-fizički list, PlayMath, Poučak.

What would Hilbert do?

Mathematical Methods in Theoretical CS: "We'll review some theoretical computer science "pearls", particularly those using mathematical tools that I think might find more applications. Our focus will be mainly on explicit constructions of combinatorial objects and lower bounds for restricted computational models."

"Alonzo Church is interviewed by William Aspray on 17 May 1984 at the University of California at Los Angeles."

"The UK Qualifications and Curriculum Authority is considering introducing a new A’level course (in Britain, A’level is the exam that is taken at the end of high school) called “Use of Mathematics”. As one might expect, this idea has not met with universal approval, and there is now a campaign to stop the idea in its tracks."

"Together with Marc Mézard, I am writing a book. It should be an introduction to a rich and rapidly evolving research field at the interface between statistical physics, theretical computer science/discrete mathematics, and coding/information theory. It should be accessible to graduate students an researchers without specific training in any of these three fields."

Clay mathematics institute lectures

Detexify2 - LaTeX symbol classifier

Recent news about Conway's Game of Life

by Paul Lockhart. "...the most blistering indictment of K-12 “math” education I’ve ever encountered." - S. Aaronson and I agree :)

Contributors: Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford / John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry / Philip Welch, Professor of Mathematical Logic at the University of Bristol

Lectures by Tim Gowers.

Class, for those that have not had a course in game theory, Ben Polak teaches Econ 159 which is available from Yale. The course is excellent. I will list all here, but break-out theme which I think you need to review.

Post about "Cantor’s first proof that the reals are uncountable". Great history insights.

If you have visited the Tricki recently, then you will already know that it has gone live. I’ve delayed posting about it until we were sure that everything was fully transferred: if you visit the prelive site you are now automatically redirected to the proper site, which you can also get to by clicking here. The URL is http://www.tricki.org.

Thomas Andrew "Tom" Lehrer (born April 9, 1928) is an American singer-songwriter, satirist, pianist, and mathematician. He has lectured on mathematics and musical theater. Lehrer is best known for the pithy, humorous songs he recorded in the 1950s and 60s.

Group theory is the study of the algebra of transformations and symmetry. While that sounds a bit esoteric (and it certainly can be), what it means is that it looks at the ways you can turn, rotate, or stretch one pattern or do-hickey back onto itself - which is something that puzzles like the Rubik's Cube and pictures like the ones Escher drew have in common.

It’s been a long time coming, but the Tricki is now on the point of going fully live. If you need convincing that this is a stronger statement than earlier and almost identical statements I have made on this blog, then click here to be taken to the site.

Welcome to a brand new Wiki-style site that is intended to develop into a large store of useful mathematical problem-solving techniques. Some of these techniques will be very general, while others will concern particular subareas of mathematics.

Good documentary about Erdös.

Boris Pavković (1931 – 2006) Portrait of a distinguished teaching expert and popularizer of mathematics

Obavezni kolegij na trećoj godini Preddiplomskog sveučilišnog studija Matematike - smjer nastavnički. Prof. Dujella. Skripta za kolegij.

Ah...

Nice blog post about Erdös, Probabilistic Method and new Quantum Method

"a personal view of the theory of computation" Great blog posts on theory of computation with interesting history details.

Archive of problems with solutions