Mathematica Link for Excel

Excel Link for Mathematica , what a great product. All the time I have wasted in the past... I was actually using Mathematica -without- Excel. Unbelievable. Mathematica's Table and Excel's sheets are the perfect marriage. What a combination. - And it works. I am impressed.

Video mini-demo Excel Mathematica link

The ExcelLink for Mathematica is a very nice product and works in a way as can be expected as the mini-demo below shows. There are of course two potential groups of users of the link: 1) users interfacing with a Mathematica Notebook, 2) users interfacing with an Excel sheet.' The follow mini-demo shows the ExcelLink from the perspective of the Mathematica Notebook user.



When done with pre-recording this video on my pc I noticed a window with a percentage bar called 'interleaving video' so if I would do this with a mic attached to the PC I could add voice comments, I suppose. Next time, I'll try one.

Mathematica Link for Excel 3.2

I have a pet problem which I will probably never solve entirely but that's why it is such a pet, that problem, I mean. Through only a few lines of well thought out Mathematica code I can generate a matrix which needs to be further analyzed in, for example, Excel. With Excel 2010's huge dimensions this is finally possible. All I need now is a working interface between Mathematica and Excel. I experimented with it in the past, version 2.x, but that ended in a bunch off Add-In errors. - The installer says 'uninstall' previous versions. Why can't the installer do that for me? RED FLAGs! I better wait until tomorrow. I shouldn't be doing this on a Saturday evening anyway.

FORA.tv Mathematics Video

Just visited FORA.tv for the first time. I was watching a music clip on YouTube when I noticed in the right selection ladder the title: "Do scientists have a sense of humour?" That's basicly how I found FORA.tv. They use the tag "The world is thinking". A search on mathematics resulted in 87 videos. Videos of reasonable length, not the 10min YouTube type. For example:

John Barrow: Not Just About the Numbers
An overview of different types of mathematics and its applications. What is mathematics and why does it 'work'? 53min

John Barrow on Codebreaking in Everyday Life
Everything we buy, from books to baked beans, has a product code printed on it. More sophisticated check-digit codes exist on official documents, bank notes and air tickets. 60min

Wilfred Hodges: The Geometry of Music
Geometers study shapes and how they transform into one other. Musicians create shapes and transform them. 55min

And much more. Enjoy FORA.tv.

P.S.
Here is the YouTube teaser...

ToBlogList

Topics I will/might blog about when time permits.

ToBlogList:
3x+1 problem; past and current influence;
OU 2010; M208/MT365 what is wrong with these courses;
Can't wait to start on MST209;
60 or 90 in 2011;
Must narrow the field of what I will be able to study, i.e.: mandatory topics = B10 upto BSc; Complex analysis; Group Representation Theory; Combinatorics.
What deeply fascinate me: Number Theory, Group Theory - the deep connections between the two;

9 divided by 11 = 3000.

An off-topic post. About building 7. If you know what I mean by building 7 then this post is not for you. Otherwise start by watching the short YT-clip in this post. If you dare to confront it, that is. Beware, it might change your life considerably. Don't say I did not warn you! You do not -have to- watch. - One thing though, it is not your opinion they are after...



Is that all? Yes. And it is already working, I am sure.

Or go straight to the Truth.

My first 4D-experiment

What you see are the 3D and 2D projections of the rotation of a tesseract in the Z,W plane in 4D.

Result M208 - TMA05

I scored 75. 11/20 on question 6. I used a methoud using indirect symmetries. Works just as well. I had 18 bricks as an answer -of course-. It is an abstract combinatorial counting problem.

I very much doubt if the person who is tutoring me on M208 really 'owns' the materials or is merely pretending. I suspect the last so a discussion won't work. I haven't got a leg to stand on if I don't score high in the nineties at the exam. Which will be very difficult due to the time constraints anyway.

P.S.
Analysis. The difference between $\mathbf{R}$ and $\mathbf{Q}$ is where mathematics feels more like a creation than an invention. Did mathematics exist before humans populated the earth? Did we discover math or did we create it? This could lead to interesting thought or discussion. Riemann created a function which is continuous but nowhere differentiable. $$f(x)=\begin{cases}\frac{1}{q} \text{ if rational and }x=\frac{p}{q},(p,q)=1\\0 \text{ if irrational}\end{cases}$$

Sophus Lie - Lie Groups

From the book Groups and Symmetries, From Finite Groups to Lie Groups By Yvette Kosmann-Schwarzbach ( and translated by Stephanie Frank Singer ).

Once  you understand the concept of a 'group' you can hardly imagine that there were days that you didn't understand groups or worse: that you were completely ignorant about them. That's basically how important groups are, they are as fundamental to mathematics as numbers or graphs. - Although Lie Groups aren't part of M208 or courses I planned for next year I am studying them. I am making progress but it's slow. I am no longer in complete darkness but there is a lot of mist.

Programming 4D rotations, SO(4).

Just had a ( minor ) cognition. I was trying to figure out a formula for rotating around a 4-dimensional line. As will become clear soon I did not make much progress. But let's start from the beginning.

If you follow my blog you might have seen videos of a Mathematica program I wrote. You can select a cube or tetrahedron, then from a list of all the rotationaxes of that polyhedron and rotate the object with a rotation slider control. The rotation is visible as well as a projection of it in 2D. - I wanted to extend this to 4-D. So take a 4D polyhedron, i.e. a tesseract. Show the rotation-axes (...) rotate it and show projections in 3D and 2D. - In order to do so I would need 4D rotationformulas, I supposed that they would depend on an axis and an angle just like in 3-D.

The 4D space is simply created by adding an ( imaginary ) axis. Points in 4D have four coordinates. Concepts like distance and angle are similar to the defintions for 2D and 3D. In 2D we rotate around a centre of rotation, a point. But extend 2D to 3D and you see that a 2D rotation is actually a 3D rotation around the z-axis. Thinking along these lines there is no such thing as rotating around a line in 4D. In 4D and above we rotate around planes and the six standard rotational planes in 4D are the XY, XZ, YZ, UX, UY and UZ planes. - This makes perfect sense because if you rotate a cube in 3D along one of the standard rotation axes X, Y and Z the equivalent 4D rotations are those in the YZ, XZ and XY planes. The remaining three rotations seem to distort the cube or make it disappear all together, while in 4D-reality the cube would remain fixed of course.

It turns out that the formula for rotation are simple. Setting up a hypercube is not too difficult either. Haven't added it to the program though.

What might prove difficult though is finding ( computable ) data of the symmetry groups of the 4D-polyhedra.

This website 4D Euclidean Space was very helpful in learning and compiling this data.

Usage of TabView in Mathematica

Creating a tabbed view user-interface is as simple as: TabView[{a->1,b->2}]. A more realistic example is shown in the video below.

Bookmarks

I have been storing bookmarks for over four years now on Delicious but I have failed to organize them in a way I like. My interests have changed dramatically, I think that I could erase half of the bookmarks that I stored. Anyway, now that Google supports Pages I can tick away 'Developing Personal Website' from my ToDo list and use Blogger instead. For starters, I added a Links page to this site.

New Youtube Video

I made a tiny Mathematica program which demonstrates all the 23+1 rotations of the Cube. If you haven't done Group Theory yet: the Cube has four diagonals, which can be permuted in 4! = 24 = 23+1 ways. The 23+1 rotations create just these permutations. - I joined Facebook ( at last ), found an M208 study group but with disappointing little discussion. Here is the video:

Vinay Deolalikar

Vinay Deolalikar ( mathematician working for HP Computers ) claims to have solved one of the $1,000,000 open problems of the Clay Institute: P=NP? I think the P stands for Polynomial Time, which is used in the field of modelling of the computation process itself which goes back to Alan Turing. - My motto is: "Every Problem has a Solution".

Einstein's dice

Einstein once said "God does not play dice". What sort of dice was Einstein thinking of?

Group Theory - Exercise - Continued

I have been working on the problem that I published last week....

S3
Element - Order - Permutation Sign - Transpositions
() - 1 - +1 - ()
(1,2,3) - 3 - +1 - (1,2)(1,3)
(1,3,2) - 3 - +1 - (1,3)(1,2)
(1,2) - 2 - -1 - (1,2)
(1.3) - 2 - -1 - (1,3)
(2,3) - 2 - -1 - (1,2)

Now take the following subgroup of A5:
() - 1 - +1 - ()
(3,4,5) - 3 - +1 - (3,4)(4,5)
(3,5,4) - 3 - +1 - (3,5)(3,4)
(1,2)(4,5) - 2 -  +1 - (1,2)(4,5)
(1,2)(3,4) - 2 -  +1 - (1,2)(3,4)
(1,2)(3,5) - 2 -  +1 - (1,2)(3,5)
This is a group with S3 structure but conisting entirely of even permutations.

If any group of n elements is a subgroup of A(n+2) it must have an isomorphic copy consisting of all positive permutations.