FloatingPoint Blog

Writing about Mathematics is not that popular. Sure, most people don't care about math, as I do. Anyhow, here is a first url-bundle of Math Blogs / sites about Math.

Please note, this is not a list of resources on Math, or Encyclopedias, and such. There are several of those, too. Later on, perhaps, I'll put up a Freemind page (export) of them, also.

• URL Bundle of Math Blogs

Glen

PS. Note: Over time, I'll add more to the page, above. So, be aware, just check in a year or so.

Example of a barchart from Maple.

Notebook on MaplePrimes of Barchart Demo.

Testing display issues - you can look, if curious.

Glen

Best way to show Math - outside of xhtml MathML on my own web site.

The MaplePrimes web site lets me publish my Notebooks, for everyone.

This review is written in 2009. A lot is happening on the Scientific Processing front. Your average PC is faster, than ever. [Actually, most people are saying, computers are fast enough, even though Moore’s law is still climbing.) Multiple cores are now the new processor standard, with eight cores to occur, soon. Microsoft is switching us all to 64-bit systems, if we want it or not. (Don’t ask the average person about Vista. You will hear what I mean.) Math software, Wikipedia, the universe inside the Internet, computers with several monitors, advanced graphics for everyone, speech recognition getting closer – every day, videos as the new data stream, and visualization tools – capable to see everything, from our World (mapped and Satellite views) to anything we can name or tag. ]

Full Apple vs Oranges Article

Glen

Timothy Cole in his Article - Title: Thoughts about Publishing Mathematics on the Web - tells exactly one of the largest problems, with most implementations of MathML. What is it?

• Search for: cole thoughts publishing mathematics
• Google Cache Link: (otherwise, you can download his PDF)
• After following the above link; Find "digital" - this will take you to the section, mentioned.

A human reader viewing will ... immediately recognize that the entity “e” appearing in both has a semantically different meaning in the two contexts.

Content from the Digital Mathematics Library of T. Cole's PDF. This is why, I am talking so much about MathML, and not just showing mini-images of x squared equations.

However, look at this page. A conference of Mathematicians, about preserving Math, searching Math, cataloging Math, and paper to XML issues, besides concerns of Publishers.

Yet, look at the date!!! It is over five years old, and there still is not a "known convention" / just how it is done, way to put an equation onto a Web Page.

So, if you have an issue with how - I'm writing MathML content? I don't care, just doing it this way, until the W3C clears up the issue, and gets everyone to follow their ruling. This is the best working solution, I have found, and Google should scrap these math pages - fine.

Glen

If you want to publish equations to MathML?

1. Microsoft Word 2007 with the Insert Equation feature, does a fantastic job, of supporting, storing, writing, keeping, and printing Equations with MathType.
2. Next, yes, my hard core MathML pages on here, require the MathPlayer from Design Science.
3. Save MathML from Maple or Mathematica - forget it! Publish Math in MS Word without MathType - forget it. Too many Apps dump as invisible data in GIF graphics.
4. The whole purpose of why the W3C created the MathML standard was?

The whole story in my MathType article.

Glen

MathML - the Quest !!!

b crowell really nails it here. Ben's Home Page

• The majority of users, who have IE with no plugin, should see some kind of graceful degradation.
• Firefox users should see the math displayed correctly.
• The tiny minority of users who have MathPlayer+IE should see the math displayed correctly.

Unfortunately, you just can't accomplish this by any reasonable technique. The technique I've ended up using for the web browser version of my own physics textbooks is to use mod_rewrite to serve mathml to Firefox 3+ users, and serve a version with bitmapped renderings of the equations to everyone else.

Quote Slashdot

More to follow in next Post.

Glen

Next Topic: Have you heard of? Pyats?

A Pythagorean triple consists of three positive integers a, b, and c, such that a * a + b *b = c * c.

Personally, I prefer my own format, my classic.

from Wikipedia

Of course, we all know about the (3, 4, 5) Triple. Continued on this MathML page.

Glen

If you click - on this Notebook to view. You'll see the large black triangle on Maple's Community Web Site.

Maple Notebook

= You can click it, and the section under it, will collapse, then expand.

Glen

What is the problem? How do you solve it? Read Polya’s book? Sure, but who has time?

Let’s say, you are given $10 and need to buy some paper, and cannot afford to pay sales tax.

How much, can you spend? Assuming your rate of Tax is 8%

See My Word Doc: Here.

Maple Notebook

Glen

How does one read a Maple Worksheet (MWS)?

1. It takes a while, to find this. However, the answer is negative. You cannot read Maple Notebooks plain. As this page, plainly states.
2. However, as shown in this post. You can view a Maple Notebook, online, from MaplePrimes. Online viewing with printing is not supported from Wolfram.
3. If you want the PDF, of my notebook? Some are on Scribd, too. Although, for the moment, I don't have too many there.
4. For example, my demonstration of a Quadratic Notebook.
5. What does the competition have? Wolfram Demonstrations Project
6. ?
7. However, there are several problems with Mathematica. Licensing and super expensive to start and isn't top notch in everything, either. (Maybe close? But - so what.)
8. Check out - MacSlash. If you perform, a minor upgrade on your OS. Maplesoft won't bump you. Mathematica will say, "sorry, you're no longer registered." Like you did something illegal.
9. The whole point of the Mathematica Reader with Wolfram is? When your "only paid" for a yearly subscription / ie, purchased the program - expires. Your "once, I loved it" program turns into just a pathetic Reader.
10. So, now you see, why I am a Maple fan. Even if, it isn't as Functional-program code savvy as Mathematica. Maple is powerful, too. Which, seems to be a key point, everyone overlooks.

Glen

Here it is, the first page of my Math Musings.

Math Musings

Click: the Talk Func varx plus one Child.

Glen

= Hasn't been used too much, since 2008. However, I have plans to diversify a bit. So, check out my math posts.

Nullx Blog

Enjoy Glen

= World War II history fascinates me. Especially, discussions of the scientists behind it. VonNeumann, Einstein, Bohr, Heisenberg, Teller, and Oppenheimer.

Quote:

George Pólya and the Heuristic Tradition
Fascination with Genius in Central Europe

by Tibor Frank
....

Despire what we know about the social conditions which nurtured and even forced out the talent of these many extraordinary scientists, how this occured still remains somewhat mysterious. Stanislaw Ulam recorded an interesting quote from John von Neumann when describing their 1938 journey to Hungary in his Advdentures of a Mathematician.

I returned to Poland by train from Lillafüred, traveling through the Carpathian foothills. ... This whole region on both sides of the Carpathian Mountains, which was part of Hungary, Czechoslovakia, and Poland, was the home of many Jews. Johnny [von Neumann] used to say that all the famous Jewish scientists, artists, and writers who emigrated from Hungary around the time of the first World War came, either directly or indirectly, from these little Carpathian communities, moving up to Budapest as their material conditions improved. The [Nobel Laureate] physicist I[sidor] I[saac] Rabi[25] was born in that region and brought to America as an infant. Johnny used to say that it was a coincidence of some cultural factors which he could not make precise: an external pressure on the whole society of this part of Central Europe, a feeling of extreme insecurity in the individuals, and the necessity to produce the unusual or else face extinction[26].

An interesting fact about Jewish-Hungarian geniuses at the turn of the century was that several of them could multiply huge numbers in their head. This was true of von Kármán, von Neumann and Edward Teller. Von Neumann, in particular commanded extraordinary mathematical abilities. Nevertheless, there is no means available to prove that this prodigious biological potential was more present in Hungary at the turn of the century than elsewhere in Europe[27].

Unquote:

Glen

Here is the method. Seems too simple. Just breathe it in. You can solve anything with these basic steps. Assuming it is solvable?

Glen

Quote:

Polya's Heuristics Chart:

The List
Taken from Polya's How to Solve It
UNDERSTANDING THE PROBLEM
To understand the problem, first ask yourself:
What is the unknown?
What are the data (the given)?
What is the condition?
Then
Draw a figure.
Introduce suitable notation.

DEVISING A PLAN
Then find the connection between the data and the unknown.
Have you seen it before or have you seen the same problem in a slightly different form?
Do you know a related problem?
Look at the unknown! And try to think of a familiar problem having the same or a similar unknown.
Could you restate the problem?
If you cannot solve the proposed problem try to solve first some related problem.

CARRYING OUT THE PLAN
Carrying out your plan of the solution, check each step.
Can you see clearly that the step is correct?
Can you prove that it is correct?
After you have an answer, examine the solution obtained.

LOOKING BACK
Can you check the result?
Can you derive the solution differently?
Can you see it at a glance?
Can you use the result, or the method, for some other problem?

Unquote:

If you don't know of George Polya? I highly recommend you check him out.

= His most popular book was "How to Solve IT"

See here for the Wikipedia Entry on George Polya.

= He published a common man's book for teaching everyone, how to think.

How to Solve It! in 1957. Sure, this doesn't seem like much of an accomplishment. However, consider the times, and how many decades since then. American Education has gone through several changes, since the 60s even. Plus, students today are getting more reliant on technology than ever. I digress.

Anyhow, pick it up. Read it. It won't take you more than three days or just skim it.

= In my opinion, the number one purpose of the book, is to consider. How do you think about problems. ie, Heuristics, the field Polya pioneered.

Glen