jenn3d

I came across a free tool for visualizing Coxeter polytopes, jenn3d. I suppose this program visualizes the Coxeter groups of polytopes. Polytopes are geometric objects in the n-th dimension with flat sides.



Link: jenn3d.org

Gephi

I just discovered a new ( free, open source ) tool for graphs and networks. What Photoshop is for pictures, Gephi ( supposedly ) is for graphs. Software is definitely a requirement for Graph Theory. I haven't looked at Gephi in-depth yet, I might. It is exciting though. There is so much going on. When you turn away from a certain area for just a brief period things might have changed quite a lot when you get back. I 'worked with' ( read: used to study graph theory ) Mathematica with the Combinatorica package which is really a gem by itself.

Link: Gephi

Unexpected behavior of C2mm symmetry.

#openuniversity# #m336# #symmetry#

I read that a US Senate Commission is worried about the F-35 project because they are building planes while the testing of the F-35 is in full progress. The thing is that the Joint Strike Fighter ( F-35 ) is in fact a flying super-computer running on state-of-the-art software. Sound engineering principles don't apply to these machines. Software is never 'done'. Software is always in development and in testing and ( just ) released at the same time. There will be upgrades for the F-35 until the end of its life. Politicians think ( or say they think ) that when the plane is done, its done.

This thought crossed my mind because planning, by definition, implies uncertainty about the future. Unexpected things can happen, will happen, at a moment when its least expected.

To the point.

Mathematics is unpredictable too. From time to time you'll see unexpected things. Among various other topics I am studying plane symmetries at the moment. I have several books well illustrated with all sorts of patterns that can occur. For me, programming is an effective way to study, so I wrote a program that plots patterns using the symmetries I am studying. One of these symmetries is C2mm which is basically rotating a diamond lattice 90, 180, 270 and 360 degrees. While I was testing the C2mm symmetry in Graphica ( the name of my symmetry program ) I noticed that the patterns are very sensitive to the center of rotation.

I made a video ( of only part of the screen for size and performance reasons ). The second half of the video shows several unexpected patterns while changing the center of rotation. Watch and you may experience the same awe that I felt. All I expected was that the symmetry could generate a diamond lattice from a triangle.

TeXnicCenter 2.0 Alpha 4

TeXnicCenter have released Alpha 4 of TeXnicCenter, the LaTeX IDE for Windows.

More at: http://www.texniccenter.org/

Graphica at Google Code

Graphica is now a real project. I don't know how many projects get started, I do know a lot of them die unfinished. I can only say that I hope this won't happen to Graphica. I will try to push it forward at a steady pace. It is not that I thought about it yesterday and well, started a project to 'see what happens'.

- I have been thinking about it for years.
- I silently programmed a prototype in Mathematica,
- made an extensive study of Mathematica graphics,
- studied how to develop a language-to-language compiler in Java,
- spec'ed the language,
- selected the Java frameworks, and tools to start with,
- chose a license

so: it's time to start hacking! At last. All I need now is a home for my code to live:

Graphica at Google Code.

The book will never die.

A lot has been written about real paper books versus ebooks. Both have their distinct advantages and disadvantages. I have to admit that I read mostly ebooks. They are cheaper and easier to get, store and carry. Mathematics ebooks often have the PDF format. So you need a reader that can handle PDFs. If you use your PC or laptop than a PDF reader is all you need. Most people know Adobe Reader but there are much better programs than Adobe around. With free readers, just like Adobe. My PDF reader of choice is Foxit Reader 5. What I particularly like about Foxit is that it is lightweight, i.e. loads and acts fast. Foxit uses tabbed reading, like internet browsers. If you were in the middle of five books, close Foxit, the program nicely remembers which books you were reading and on what page you left. Most of all, I like the feature that I can highlight what I read. It is almost as if I was reading in a paper book.

Link:
- Foxit Reader 5.

About M381 (1)

Regular readers of this blog know that I have a sort-of rage-button like the Hulk: it is called MathCad. Thank God, I have the anti-dote almost always open and ready: Mathematica. I am not going to repeat why MathCad is a danger to your mental health, but I have to press the MathCad button at least once.

In almost all mathematics courses you can do at the Open University there is software involved. They either deliver a standard package, or ship custom software especially developed for the course ( i.e. MT365 ). The house-package of the Mathematics Department of the Open University is MathCad, version 2001. I have argued that MathCad alone is a reason -not- to choose for the Open University. What a disgrace...

( Calming down. )

They do however recognize that software, computers, tools are relevant in mathematics. Especially in Number Theory computers are used in active research. Another area where they use software in active research is: mathematical logic. Stronger: research in Number Theory is impossible without computers.

These facts are not even mentioned in M381. There are many open source tools available for Number Theory, even more for Mathematical Logic. Not a word about it in M381. One, if not -the- reason is the fact that course development in the Open University is done in a project organization. A project is created with the objective to create course X which will then be used for the next 10 or so years. It is exactly the opposite of what one would expect of a university education. It is not reasonable to expect the Open University to be at the forefront of mathematical research. Simply because other universities in the UK have that role. But it is reasonable to expect more than a static expose of 19th century Gauss number theory and early 20th century logic from Church, Turing and Goedel. In fact, the field is presented as abstract and of theoretical importance only. But Number Theory and Mathematical Logic are extremely relevant and applicable in many industries! But I did not learn that from the course and that is sad.

It took me a lot of work but I found some relevant learning tools in the fields of number theory and mathematical logic. More about those later in this blog.

(*) - I may have misunderstood the concept of 'University' in the UK. I think many universities in the UK are what we call in the Netherlands 'schools'. They deliver professionals with a degree in all fields through excellent education but they don't do research and so on. They don't add to the body of knowledge. They process and transfer knowledge. That description fits the Open University as well. - A marketing issue is that students like to have a 'university' education. And marketing people love empty heads boxes, they have a fancy word for it too: the 'packaging'. Does that make sense?

Mosaic view

Have you tried the new Blogger Mosaic view of this blog yet? Or the new Blogger Snapshot view?!

Some of my favourite tools

A while back in my 'How to learn from failure post' I wrote about monitoring results. That post assumed to much fore knowledge with my readers about Admin Scales and so on. Admin Scales are essential to me, I have considered writing a post about them but the subject is 1) off-topic and 2) often alienates people, which is not my intention.

Planning, execution of plans and recording efforts and results come before the implementation of a system based on statistics ( and ethics ). As an individual you want the benefits of planning and control but not the costs. Investing too much time in planning makes it inefficient in no-time. Most people work with some form of a todo list. Often in digital form managed by an iPhone app or similar. Todo lists and so forth only work under certain conditions as brilliantly discovered by David Allen, the inventor of GTD. Since 'GTD', most personal planning systems are adaptions of his method. Allen's company sells an Outlook add-on as an example of a good technical implementation of GTD. They also support Personal Brain for example.

Admin Scales have a BE, DO and HAVE dimension. For the DO dimension I use MindManager ( have been using it for brainstorming for more than 10 years ) in combination with MyLife Organized ( MLO ). MLO imports MindManager mindmaps, has a desktop version and App versions for iPhone, Blackberry, PocketPC and Android(soon). MLO is NOT a normal todo list program. Once you get adjusted to it, it acts like someone who thinks with you and knows which item of your huge ( hierarchical ) todo list you should do first. It has an outliner view and a do-now view. It is a phenomenal piece of software but it takes time to appreciate all the features.

[News] - Springer.com releases LaTeX Search

The Springer LaTeX search lets you search through over 2,660,787 LaTeX code snippets to find the equation you need.

Try it here: http://www.latexsearch.com/

Note-taking

I found a way to enter LaTeX in Personal Brain thoughts. Exporting a plex to a website is simple. I hope to demo it soon. I publish my work via Opera Unite which means that I don't have to upload files to a server because the web server runs as an Opera process / thread on my computer. I don't leave it on 24/7 though. The exciting part is that you can use Personal Brain to:
- manage your mathematical notes in LaTeX ( plexes of 300,000 thoughts exist );
- query thoughts;
- reorganize database structure instantly;
- publish thoughts to a website;
- export thoughts to other programs;
- import thoughts ( Mathematica, for example can export notebooks to LaTex ).

Personal Brain is a sort of Mind Manager without the constraint that everything has to fit in a tree structure. They have a Microsoft sort of version scheme: home, business, enterprise. The home version is free, it's not an expiring trial.

Personal Brain website

Galois Theory (2)

The polynomial F(x) = x^8 - 40x^6 + 352x^4 +960x^2 - 576 has 8 ( real ) roots : +/- Sqrt(2) +/- Sqrt(3) +/- Sqrt(5). ( See image above. ) The symmetry group of the roots is abelian and has order 8, all elements have order 2, so the group is isomorphic to C2 X C2 X C2.

I have found another introductory book on Galois Theory for undergraduates ( to support my study of Weintraub's Galois Theory I think, for the moment anyway. )


It comes with AlgFields ( download here ), a system of Maple and Mathematica routines for calculating with low-dimensional number fields and finite fields.

Competition leads to innovation!

This site does not load particular fast in Internet Explorer 9beta or Opera 10, which are my preferred browsers. Thank God, we have a choice in browsers. Different browsers for different people. Functionality wise I still love Opera, although I don't like its default look and feel I have found a sexy skin for it. - It takes IE and Opera a few seconds to completely load this blog, i.e. all widgets and processing the MathJax. I tried the latest Google Chrome today and it looked as though the site was loaded in about a second. Further inspection showed it was an optical illusion because left down I noticed the MathJax was still processing. Still, the Google Chrome has everything of a fast browser. Lean and mean like a Porsche car, sort of. I am sure my friends in Norway, the Opera whiz-kids, will leap and frog Chrome once more.

Competition leads to innovation. It is the reason why browsers keep getting better and Microsoft Word and Excel are getting more lame by every new "release".

SciLab

By accident I encountered the SciLab package. It has been around for a quite a while, so it must be good considering the competition. It's free and open source as well.

MInd Manager or MindView (2)

MindView looks promising but unfortunately it is useless for my needs: it has only one calendar. Where corporations are compared to pyramids, the individual is a pyramid upside down. Tiny corporations with a sales departmant, finance department, and so on. ( Using that methaphore studying takes place in the R&D department. ) It is however a corporation with one staff member: unless we look at the hours of the week as staff...
I use mind manager to branch out ideas, thoughts, entirely free format. Some branches are mirrored in JVCGannt, MM's project management add-in. In these branches I add concrete tasks to be executed. In the planner they are assigned a resource: work, study or personal. For these resources I have created a calendar. The STUDY calendar has the hours which I have reserved for study as work hours. The hours assigned for work and personal are non-workable hours in that calendar (and so on). With MindView's one calendar limitation I can't use it to setup my plans. Other planning tools are out of the question because they don't have MindMap integration. So I'll stick with Mind Manager for a bit longer. - MindManager does have MS Project integration though. But it is of course completely over the top to maintain, what is in essence a to do list, in MS Project.

MInd Manager or MindView (1)

Present Time. I failed to meet the MST365-TMA02 deadline. I already informed the tutor. ALthough I have a valid explanation this should not have happened. ( I have to assign myself the condition of 'Danger' and apply its Formula. )
From the book Learning Strategies for College Success I learned that the components of academic self-management are:
- motivation ( OK );
- time management ( - );
- study methods ( ? );
- physical environment ( OK );
- social ( -/? );
- monitoring ( this blog ).
I'll work on trying to improve time-management for a bit. I have used Mind Manager for brainstorm and planning purposes for ages. But Mind Manager has some issues as a planning tool actually ( i.e.: Gannt views through a 3rd party program JVC Gannt ). I am loyal to the programs that helped me but it is time to have a look at MindView.

TeXnicCenter 2.0 Alpha 3 is available

A third Alpha version of the new TeXnicCenter 2.0 has been released. I have issued MT365-TMA01 in handwritten format btw, but that's an exception.

UPDATE:
Tested with done TMA's and template for mathematics book Springer style. No bugs or issues found. Decided to use this version for the next M208 TMA.

MathJax

Yesterday I found MathJax. Thanks to Twitter, btw. Twitter can be very helpful in the process of collecting valuable information from the web.

MathJax in brief:
High-quality display of LaTeX and MathML math notation in HTML pages
Supported in most browsers with no plug-ins, extra fonts or special setup for the reader
Easy for authors, flexible for publishers, extensible for developers
Supports math accessibility, cut and paste interoperability and other advanced functionality
Powerful API for integration with other web applications

We are now able to write math on the web.
\[\sum_{k=0}^{n} {n \choose k} = 2^n \]

No plugins needed. Use simple Latex. If you don't know Latex let Mathematica write it for you.

( testing ... LaTeX )

The probability of getting \(k\) heads when flipping \(n\) coins is:

\[\sum_{k=0}^{n} {n \choose k} = 2^n \]
\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]

An Identity of Ramanujan

\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} =

1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}

{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]

( ... more later !!! )

Software TIPS

I made two software 'discoveries' today. Must have stuff, really.
- 1. Asymptote. A graphics programming language really, directly includable in Latex. Sort of a steep learning curve but so has Latex and that was an investment that paid off for everyone who learned it. That is I never heard of someone who regrets to have learned Latex.
- 2. Dropbox. The definitive solution for sharing data between your computers ( desktop(s), laptop and phone ). Free up to 2GB. It creates an extra folder on all your systems. I am setting it up right now.

External Links:
http://asymptote.sourceforge.net/,
http://www.dropbox.com/

Dropbox is ideal for syncing your iTunes Library file over your PC, Laptop and iPhone.