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Math Awareness Month
An anonymous reader writes: April is Mathematics Awareness Month. Mathematics of the Cosmos is the 2005 theme: Mathematics is at the core of our attempts to understand the cosmos at every level: Riemannian geometry and topology furnish models of the universe, numerical simulations help us to understand large-scale dynamics, celestial mechanics provides a key to comprehending the solar system, and a wide variety of mathematical tools are needed for actual exploration of the space around us."
Most models of the universe are mixed signature, (normally Lorentzian), so they can approximate special relativity in the limiting cases.
Applets and other software that demonstrates mathmatical principles.
h .html
l ash/
http://www.edinformatics.com/il/il_math.htm
http://smard.cqu.edu.au/Database/Teaching/JavaMat
[Physics]
http://faraday.physics.utoronto.ca/PVB/Harrison/F
Open a new window or tab, enter "about:config" to get to the configuration settings.
Right-click, select "New", then "Integer", and for the name of the value type in "privacy.popups.disable_from_plugins".
Set this to 2.
Voilà! The problem seems to be caused by Flash content that launches popups, and this disables that function.
Whois says it's not commander taco (unless he went to hella trouble):
Server Used: [ whois.pir.org ]
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I plan to celebrate April (and May, and possibly June) by reading Roger Penrose's The Road to Reality an entertaining tome of but 1100 pages that purports to teach the reader all the math he needs to understand modern physics. Penrose is the ultimate optimist, but I must confess, I'm having difficulty after only chapter 8 (Riemann surfaces and complex mappings) of 34. Maybe, if I don't pay too much attention to the math, I'll breeze right through it. But then, that would defeat the whole purpose of Math Awareness Month.
For the layperson, number theory and permutations are very accessible and interesting. These areas of math don't require alot of prior knowledge of obscure topics, formulea, or theories that won't really interest most people. Plus, there is a possibility (albeit a very slim one) that you could solve some interesting problem whereas most types of math require alot of topic specific knowledge just to understand the problem, let alone solve it.
"Those that start by burning books, will end by burning men."
Some of my favorites:
"Topics in Algebra" by Herstein
"Topology" by Hocking and Young [Dover]
"Counterexamples in Topology" by Steen & Seebach [Dover]
"A Mathematical Introduction to Logic" by Enderton
"Galois Theory" by Stewart
Bell's "Men of Mathematics" is not to be missed.
KFG
If you're really interested, and have a little more background, you should read Hatcher's "Algebraic Topology." It's available free at his home page.
In the USA, 'mathematics' is abbreviated to 'math'. In the UK, it is abbreviated to 'maths'. Since the UK comprises England amongst other countries, and England created the English language, the abbreviation 'maths' would appear to be a perfectly valid -- if not even 'more correct' -- usage.
Oh, and chaps: it's aluminium.
Tubal-Cain smokes the white owl.
Given a good grasp of topology, and presuming you enjoy that, a couple of directions to aim for are Differential Geometry (which gets you a nice understanding of General Relativity, the shape of the universe, and that sort of thing), or if you want to head in a more pure direction, Algebraic Topology. Both those topics are "hard" in the sense that they may require material from other fields, advanced calculus for Differential Geometry, modern algebra for Algebraic Topology. Both are interesting topics in their own right though, and it should be easy enough to pick up a textbook on one of those for some background reading before starting in on your topic of choice.
Jedidiah.
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SMETE
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Daffodil*
*Just a fancy way of saying a front-end to online libraries.
WikiVersity School of Mathematics
The best hands-on mathematics experience, hands down, is at
http://www.cut-the-knot.org/
The topics are accessible, and often accompanied with applets.
I've used this material to give math talks to high school kids - they love it.
Here is a real favourite:
Make a polygon by picking a bunch of points on graph paper (just the grid intersection points) and connecting these points by straight lines. The spiky looking thing is technically called a lattice polygon. A really cool way to calculate the area is to (A) count the grid points strictly inside the polygon (B) count the grid points lying exactly on the edges and vertices, then do (A)+(B)/2-1 Voila!
The applet and explanation is here:
http://www.cut-the-knot.org/ctk/Pick.shtml
(However, the so-inclined may prefer to fool around with this by themselves, first!)
There are many^(many) phenomena out there like pick's theorem. Call them math paradoxes, or theorems, or whatever, but there's lots of mathematics that is easy to perceive and is mysterious as anything. Mathematics awareness can begin by first learning about and experiencing these brain bending phenomena, and then SEEKING an explanation.