Mathematics in the Movies

Not counting Numb3rs there aren't many movies truly about math. As far as I know anyway. I know of the following movies ( in alphabetical order ):
- A Beautiful Mind
- Flatland
- PI
- Proof.
All these movies are fairly recent. The oldest is PI, from 1998. So that's encouraging. There is a movie about Ramanujan / Hardy in the works. Looking forward to that one.

Programming Mathematica: Finding Perfect Numbers

Find all numbers less than or equal to 10000 which are equal to the sum of their proper positive divisors. These are the so called Perfect Numbers. For example 6 has proper positive divisors 1,2 and 3 ( 1+2+3=6 ).

Finding a solution to this problem can be done with the following Mathematica program.

PerfectQ [n_]:=Apply[Plus,Divisors[n]]== 2n
PerfectSearch[n_]:=Select[Range [n],PerfectQ]
PerfectSearch[10000]

{6,28,496,8128}

See also: An Introduction to Programming with Mathematica

Third Isomorphism Theorem: Visual Example

Let G, H and K be groups such that K is a normal subgroup of H and H is a normal subgroup of G. Then ( G/K ) / ( H/K ) = G / H. This is the Third Isomorphism Theorem or the Chain Theorem.

For example in
D4 (1)
D4 / { e, a2 } = C2 X C2 (2)
{ e, a2, a, a3 } / { a, a2 } = C2 (3)
( D4 / { e, a2 } ) / ( { e, a2, a, a3 } / { a, a2 } ) = C2 X C2 / C2 = C2 (4)
but also:
D4 / { e, a2, a, a3 } = C2 (5)

(1)


(2)


(3)


(4)


(5)

Wolfram Workbench

I almost gave up on finding a copy of Wolfram Workbench. If you are serious about coding in Mathematica it's a must have.

Perfect for scientists, engineers, mathematicians, financial analysts, and educators who want to build applications for technical computing problems, Wolfram Workbench is an integrated development environment (IDE) for Wolfram products such as Mathematica, gridMathematica, and webMathematica.

Mathematica provides a high-level environment that uses a flexible programming language to integrate high-performance computing, a vast collection of algorithms, and tools for visualization, data processing, and document preparation. Programmers who want to develop code written in the Mathematica language can use Workbench to:

* Work with code in a specialized editor
* Debug programs at the source level
* Profile the code's execution
* Develop and run tests
* Work with Wolfram technologies
* Build and deploy Mathematica packages
* Code better in an integrated workgroup environment

Open University UK

I was at a presentation about studying ( mathematics ) at the Open University in the UK. The presentation was held in The Hague, Lange Houtstraat 11. I arrived early which gave me the opportunity to talk to a course consultant prior to the presentation. She answered most of the questions I had. The presentation took about 45 minutes and was very informative. Some interesting facts are:
- 200,000 students world-wide;
- +/- 560 students in NL;
- mathematics is a popular study among Dutch students ;
- most students are in the age group 31-40;
- credits earned don't expire;
- there are no entry-level requirements;
- earning 60 points a year may cost upto 2000 punds a year ( if not more ).

Anyway, I decided that I will register as a student and take my first course in September.

Group Theory Applets

I have found several Java Applets that can aid in learning ( teaching ) some concepts in Group Theory. Find them on ShOp Java Applets.

Examples:

Powers of permutations
Orbits and stabilizers
Fixed sets for orbit counting
Permutations: the symmetric group S4
Cosets, Lagrange and factor groups

(c) Sheffield University Open University Java Applets

Algebraic Graph Theory

I am interested in graphical representations of finite groups. Today I discovered that...

"For every finitely generated group G there exists a graph X such that the automorphism group of X, Aut(X) is isomorphic to G."

An interesting theorem. Well, I thought so anyway. Just had to be. All based on my intuition.

The branch of mathematics which studies this area is called Algebraic Graph Theory.