1-2017 More on the randomness of randomness.
2 months ago
Open University pure maths study and research blog
A computer scientist claims to have computed the mathematical constant pi to nearly 2.7 trillion digits, some 123 billion more than the previous record.Odd, the item did contain the word 'mathematics' and there hasn't been any other major news pushing the item down on the list. ( Items can stay on the list for weeks ). Maybe I trusted Google a bit too much in providing me with -all- the news throught their excellent google news service.
MathJax in brief:We are now able to write math on the web.
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
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
\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
1. The Golden NumberMore later on this book when I have read (parts) of it. I am curious what he has tell about these topics and what I will learn from it.
2. Shapes and Solids
3. The Fourth Dimension
4. Projective Geometry
5. Topology
6. Bubbles
7. Harmony of the Spheres
8. Chaos and Fractals
9. Relativity
10. Finale
Chaos theory has a bad name, conjuring up images of unpredictable weather, economic crashes and science gone wrong. But there is a fascinating and hidden side to Chaos, one that scientists are only now beginning to understand.
It turns out that chaos theory answers a question that mankind has asked for millennia - how did we get here?
In this documentary, Professor Jim Al-Khalili sets out to uncover one of the great mysteries of science - how does a universe that starts off as dust end up with intelligent life? How does order emerge from disorder?
It's a mindbending, counterintuitive and for many people a deeply troubling idea. But Professor Al-Khalili reveals the science behind much of beauty and structure in the natural world and discovers that far from it being magic or an act of God, it is in fact an intrinsic part of the laws of physics. Amazingly, it turns out that the mathematics of chaos can explain how and why the universe creates exquisite order and pattern.
And the best thing is that one doesn't need to be a scientist to understand it. The natural world is full of awe-inspiring examples of the way nature transforms simplicity into complexity. From trees to clouds to humans - after watching this film you'll never be able to look at the world in the same way again.
P.S.
The graph of K14 has exactly 91 edges.
In any graph the sum of all the vertex degrees is equal to twice the number of edges.
Yesterday I got TMA01 back for DD101.
I’m not that pleased, to be honest. I got 70%, but I was expecting better than that. I was really pleased with what I wrote and I thought I would at least get into the 80s. Then again, this is my first assignment for my first course, so I had no idea what to expect. I have nothing to compare it to.
I’m also confused about the comments I got from my tutor.
They were all very positive, with praise for almost every element of the essay. The only negative comments were for minor technicalities, like having a full stop in the wrong place in a reference and not writing out a place name in full. If I’d read the comments and not looked at the grade, I would have expcted the grade to have been in the 90s!
Oh well, it was a solid pass, I guess. Onto the second assigment, which is due the first week of December!
Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before
(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)