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23 posts tagged with algebra.

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## Animated math

Essence of linear algebra - "[Grant Sanderson of 3Blue1Brown (now at Khan Academy) animates] the geometric intuitions underlying linear algebra, making the many matrix and vector operations feel less arbitrary." [more inside]

## The word algorithm derives from his name.

The word algebra stems from the Arabic word al-jabr, which has its roots in the title of a 9th century manuscript written by the mathematician Al-Khwarizmi. The

*Kitab al-mukhtasar fi hisab al-jabr wal-muqabala*(The Compendious Book on Calculation by Completion and Balancing) was a pioneering piece of work - offering practical answers for land distribution, rules on inheritance and distributing salaries. This treatise also underpins the science of flight and the engineering behind the fastest car in the world. via## It's too early on a Monday morning for this hot math nonsense, come on

## Eigendemocracy: crowd-sourced deliberative democracy

Scott Aaronson on building a 'PageRank' for (eigen)morality and (eigen)trust - "Now, would those with axes to grind try to subvert such a system the instant it went online? Certainly. For example, I assume that millions of people would rate Conservapedia as a more trustworthy source than Wikipedia—and would rate other people who had done so as, themselves, trustworthy sources, while rating as untrustworthy anyone who called Conservapedia untrustworthy. So there would arise a parallel world of trust and consensus and 'expertise', mutually-reinforcing yet nearly disjoint from the world of the real. But here's the thing:

*anyone would be able to see, with the click of a mouse, the extent to which this parallel world had diverged from the real one*." [more inside]## Geogebra

Geogebra is an interactive geometry tool which started as a free clone of Geometer's Sketchpad, but is now also an algebra, statistics and calculus tool. It is available for download for Windows, Mac, Linux, iOS and Android, or as a web app. [more inside]

## Visual Patterns.

Visual Patterns. Here are the first few steps. What's the equation?

## Computerized Math, Formal Proofs and Alternative Logic

Using computer systems for doing mathematical proofs - "With the proliferation of computer-assisted proofs that are all but impossible to check by hand, Hales thinks computers must become the judge." [more inside]

## noncommutative balls in boxes

Morton and Vicary on the Categorified Heisenberg Algebra - "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." [more inside]

## Counting

Counting is one of the first and simplest concepts most people are taught. But when you get beyond simple 123s, counting can become an advanced subject all its own. Essentially the science of counting, combinatorics is a key component of everything from abstract algebra to probability (PDF). [more inside]

## Never tell me the odds.

Measure-theoretic probability: Why it should be learnt and how to get started. The clickable chart of distribution relationships. Just two of the interesting and informative probability resources I've learned about, along with countless other tidbits of information, from statistician John D. Cook's blog and his probability fact-of-the-day Twitter feed ProbFact. John also has daily tip and fact Twitter feeds for Windows keyboard shortcuts, regular expressions, TeX and LaTeX, algebra and number theory, topology and geometry, real and complex analysis, and beginning tomorrow, computer science and statistics.

## Explorations of a Recreational Mathematician

Let's say you're me and you're in math class, and you're supposed to be learning about factoring. Trouble is, your teacher is too busy trying to convince you that factoring is a useful skill for the average person to know with real-world applications ranging from passing your state exams all the way to getting a higher SAT score and unfortunately does not have the time to show you why factoring is actually interesting. It's perfectly reasonable for you to get bored in this situation. So like any reasonable person, you start doodling.[more inside]

## "The coroner’s report from Argentina makes slighting mention of a brain tumor..."

"Back in 1993 I was tutoring my sister in algebra. Her quizzes and tests were always made of word problems with a running storyline involving many recurring places and characters. I tied the fate of the main characters to how well she did on the previous quiz, so a good performance brought them good fortune. Unfortunately, one test she completely bombed, and, well, this is a transcription of the quiz she got next." [more inside]

## The beauty of roots

The beauty of roots. From Dan Christensen and Sam Derbyshire via John Baez. If you like algebra: these are plots of the density in the complex plane of roots of polynomials with small integral coefficients. If you don't: these are extravagantly beautiful images produced from the simplest of mathematical procedures. Explore the image interactively here.

## unbump.

## I want my MathTV

MathTV is a real problem solver for many. It is also found on YouTube, and is free. Here is some background.

## Why Learn Algebra? I'm Never Likely to Go There.

EducationFilter: California becomes the first state to mandate all 8th graders take Algebra; in part because U.S. students constantly trail their peers from other nations in mathematics. At least one person thinks it's a bad idea ("If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?"). Here's the algebra curriculum 8th graders will have to learn. [more inside]

## A "Harmonious" Path

Accidental Astrophysicists: "They started with algebra and ended up learning about gravitational lensing (PDF)." [Via linkfilter]

## We are weird. And somewhat echoey.

KnowHow2Go wants you to take on the tough classes - such as Biology, Foreign Languages, and Algebra II - to prepare yourself for college.

## Logo-rithms

Logólogos makes mathematical equations out of the 'creative' process of logo design.

also a good example of "you don't need to speak the same language" blogging

also a good example of "you don't need to speak the same language" blogging

## Twisty megapost

Walter Randelshofer's Pretty Patterns collection (for Rubik's cubes up to 5x5x5) is one of the nicest twisty puzzle sites going. It's based on his CubeTwister software, which you can download (including a lovely OS X standalone). If you really want a treasure trove of twisty polyhedra, check out gelatinBrain's enormous collection of java applets (which unfortunately don't do so well on macs). Are those things even physically possible? Really? Mini bonus: Randelshofer also hosts an archive of fondly-remembered Amiga animations.

## Cut The Knot

Interactive mathematics miscellany and puzzles, including 75 proofs of the Pythagorean Theorem, an interactive column using Java applets, and eye-opening demonstrations. (Actually, much more.)

## It's math set to music!

The Klein Four is a group of math students at the Northwestern University who delight in bringing you various lovely, well-sung A Capella songs infused with their very own and very nerdy flavour. They're not the newest of the web, having released their first CD in 2005, but witty lyrics and five-part harmonizing are definitely worth checking out. I did do a search for this and didn't find anything. Please don't kill me.

## MathFilter(edout)

The Value of Algebra: "

*Gabriela, sooner or later someone's going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers.*"Page:
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