Mathematica 6 is slow

Fom some expert forum ( non-Wolfram of course )

I also read things said in wolfram forums. The issue is totally different. There is no way to change or play with options. In our case the integral is straight forward with no singularities at all! Something like this:

F[t_]:=NIntegrate[e^t ((a+b)-3a^2 )^8, {a,0,b},{b,0,3}]
Plot[F[t],{t,0,4}]

That's it. No singularities.. no cut-off's nothing. Pure and simple double integral. When you try with v6.0 it does it 5 or sometimes 7 times slower than v5.2.

Let's assume there is something we miss in these calculations.. ok?

Let's go back to Wolfram's built in function called Benchmark; to test how fast it handles 15 various problems. On both versions this command exists. You give a try on both.. you still come out with the result that overall Mathematica 6.0 is slower than Mathematica 5.2.

This is the reality of it. Maybe v6.0 while calculating it also thinks how to decorate the result and show it nicely with colors and so on.. But who needs to wait 5 times more for "loox" as you said, right?

I hope Wolfram will take care of this issue. Meanwhile I will stick to v5.2.
Or even 4.1 which is btw faster than 5.2 :)

Try before you buy, or better wait until 6.1 or so.

Example of a finite vector space

The vector space of dimension 2 over the finite field GF(3) is isomorphic to the abelian group Z3 X Z3.

gap> b:=One(GF(3))*[[1,0],[0,1]];
[ [ Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3)^0 ] ]
gap> V:=VectorSpace(GF(3),b);

gap> Dimension(V);
2
gap> Size(V);
9
gap> Elements(V);
[ 
[ 0*Z(3), 0*Z(3) ], 
[ 0*Z(3), Z(3)^0 ], 
[ 0*Z(3), Z(3) ], 
[ Z(3)^0, 0*Z(3) ],
[ Z(3)^0, Z(3)^0 ], 
[ Z(3)^0, Z(3) ], 
[ Z(3), 0*Z(3) ], 
[ Z(3), Z(3)^0 ], 
[ Z(3), Z(3) ] 
]

Wallpaper groups

Wallpaper groups are two-dimensional symmetry groups, intermediate in complexity between the simpler frieze groups and the three-dimensional crystallographic groups (also called space groups).

Discover the wallpaper patterns with the Kali Java applet.

How it's like to remember 22,500 digits of Pi

The Boy with the Incredible Brain ( Channel 5 rip on Google Video )

Remember Max Cohen in the movie Pi when the little child with the calculator asks him to do some difficult calculation? Daniel Tammet, beats Max and Daniel is real. But probably just as mad as Max. His disease is called autism.

I don't believe in his brilliance. If he was so brilliant why does he spend time learning the digits of Pi instead of coming up with some new identities for Pi which will deepen the understanding of Pi in the entire mathematical community? The researchers researching him aren't mathematicians but people who think math and arithmetic are one and the same.

Tammet is clever in the way he exploits his ability. There is nothing wrong with that. I don't expect any breakthroughs in science of him though. The real geniuses are working hard, day and night, far away from the publicity.

In the movie he meets the real Rain Man. He is certainly amazing. When you ask Rainman a questions like: "If Churchill would still live today, how old would he be and on what day of the week would be his birthday?" he answers immediately, and correct, of course.

People like Rainman and Tammet are called savants.

Abstract Algebra

Algebra is a branch of mathematics.

Algebra may also mean:
* elementary algebra
* abstract algebra
* linear algebra
* universal algebra
* computer algebra

In addition, many mathematical objects are known as algebras.

In logic:
* Boolean algebra
* Heyting algebra

In set theory:
* algebra over a set
* sigma algebra

In linear algebra, and the study of vector spaces:
* algebra over a field
* associative algebra
* commutative, anticommutative, and super- algebras
* Lie algebra

In ring theory:
* algebra over a commutative ring (or R-algebra)

In category theory:
* F-algebra
* F-coalgebra

In the relational model:
* Relational algebra

Hilbert's Hotel

The hotel manager David Hilbert had a very large hotel, in fact, it had infinitely many rooms numbered 1, 2, 3, ... The hotel was very popular and every room was occupied. One day a new guest arrived.
-Is there any free room?
-No, Mr. Hilbert said.
-Oh, what a pity, the guest said and started to walk away.
-But wait, you can still get a room.

The new guest was very confused by this and asked how that could be possible.
-I'll just ask the guest in room number 1 to move to room number 2, the guest in number 2 move to room 3, the guest in room 3 move to number 4, and so on, and then you can have room number 1.

The guest was very happy with this and called his friends to tell them about this fantastic hotel. Then one day they all arrived at the same time.
-Hello, we are countably many people, and we want a room each. Mr. Hilbert felt reluctant to ask each guest to move to a new room an infinite number of times. That would be very unpleasant, and they will never finish either. Luckily he got a brilliant idea.
-I'll let guest in number 1 move into number 2, guest in number 2 move into number 4, guest in number 3 move into number 6, number 4 to number 8 and so on. Then you can move into any room with an odd number; they will all be free, and there will be rooms for all of you.

Now all the new guests got a room on their own.

By Daume on PlanetMath

Mathematics Podcast

Check out Math Mutation Podcast for short podcasts for people of all ages, where we explore fun, interesting, or just plain wierd corners of mathematics that you probably didn't hear in school. ( ... You never know what might bring you the next idea you'll be working on. ...)

LEGO Difference Engine

Long before the age of electronic computers, even before Alan Turing invented the theoretical Turing Machine, Charles Babbage invented a mechanical computer which he called the Difference Engine. Andrew Carol rebuilt one using LEGO.


Click to enlarge

Problem ( Group Theory )

Show that, then prove.

Let G be a group in which each proper subgroup is contained in a maximal subgroup of finite index in G. If every two maximal subgroups of G are conjugate in G, then G is a cyclic group.

Group Theory

An introduction to the theory of groups / Joseph Rotman --4th ed.
1995 Springer Verlag ISBN 0-387-94285-8




More is less. While browsing through this book I realized how little I know about the subject. How long will it take before I can conider myself 'current' in the field? And that's only Group Theory. There are a few other topics I would like to know more about... - Every Coin Has Two Sides. The other side of the coin of fascination is fear.

The magic of PI

Download the Pi poster in PDF format below and start zooming in, you'll find the first 350,390 digits of Pi on one single page. The power of what you can do with PDF.

Lie Group E8

From Science Daily:

Mathematicians have mapped the inner workings of one of the most complicated structures ever studied: the object known as the exceptional Lie group E8. This achievement is significant both as an advance in basic knowledge and because of the many connections between E8 and other areas, including string theory and geometry.