Bharat Rakshak

Eric Demopheles

Thanks, sir. That is interesting. I did come across Octonians but did not pursue at that time. Frobenius Theorem is simple and beautiful in its negative result. The Octonions can be obtained from Quaternions via the Cayley-Dickson construction . Another way of generalization is via Clifford Algebra...

Eric Demopheles

Rahulji - Sorry, and thanks for pointing it out. I have edited my response. I liked your other problem, and like to point out a beautiful part (which is not clear in Eric Demopheles's solution - how does one know that (sqrt(2)^(sqrt(2)) is irrational? ) Yes, this is better and simpler. But the Gelf...

Eric Demopheles

Amber G , Just a request . Pls make font size very small. The question is trivial for people like you who take complex numbers with breakfast , lunch as well as dinner. But for those who have been in coding and left complex numbers after B Tech \ M Tech, the question is a good mind bender. Just a r...

Eric Demopheles

My original question got answered. In that post I was trying to propose why not say a base field with 8-tuple as follows: e_0 = 1 e_i.e_i = -1, for 1 <= i <= 7 \Pi_{i=0}^{i=7}e_i = -1 and the field is defined as \Sigma_{i=0}^{i=7}a_i.e_i, a_i is real Following your link, that Frobenius Theorem esse...

Eric Demopheles

matrimc wrote: <deleted as the link provided by EricD "Frobenius Theorem" essentially nails my doubt>

Glad to read that it was useful. Did your original question get answered, or was it something else that you asked in this newer post?

Eric Demopheles

Prof. Mehta's notes says there are only three possibilities - real, complex and quaternion. I am going to sleep on the question of why only these three possibilities. The answer has to be simple as this is mentioned in passing in the third slide itself. Cannot think of why it is obvious. I haven't ...

Eric Demopheles

what kind of name is Demopheles. it is a greek name? is that the name of some famous mathematician and if not who's name does it represent. Demopheles = lover of people. It is used sparsely in some philosophical discourses etc., for example here: https://ebooks.adelaide.edu.au/s/schopenhauer/arthur...

Eric Demopheles

From: http://terrytao.wordpress.com/2014/08/12/avila-bhargava-hairer-mirzakhani/ Tao, BTW, is right now one of the expert in Random Matrix theory and has done lot of work... So the techneques devloped by M. Mehta is now finding applications in many fields (Not only nuclear physics but also string t...

Eric Demopheles

EricD: I have not read Hardy's apology but what I read about it is that it is more of an explanation piece rather than the book length exposition which is What is Mathematics?. I will have to read it one of these days. Also I have downloaded the short article "the unreasonable effectiveness of...

Eric Demopheles

Terrence Tao's posts are also interesting: http://terrytao.wordpress.com/2014/08/12/avila-bhargava-hairer-mirzakhani/ http://terrytao.wordpress.com/2014/08/13/khot-osher-griffiths/ Re: Gowers, there are criticisms about him, for example: http://owl-sowa.blogspot.in/2013/05/about-timothy-gowers.html ...

Eric Demopheles

Quanta Magazine usually has good articles on mathematics, suitable for general audience, yet without too much dumbing down. Erica Klarreich is an especially good journalist in this regard. Unfortunately, for cutting edge stuff, the situation is always like this: http://simonsingh.net/wp-content/uplo...

Eric Demopheles

Preet Bharara would fit right in there too. What was the name of the Prosecutor in The Count of Monte Cristo? Villefort or de Villefort or Gerard(as opposed to his father Noirtier) de Villefort. The French procureur du Roi did appear to have certain additional powers compared to an Indian prosecuto...

Eric Demopheles

This is probably an "easy" problem, but one that I would appreciate an answer from the resident gurus. Consider the n*(n-1)/2 entries in a lower triangular matrix (entries below the main diagonal). Assume the cells are indexed sequentially in a one dimensional 2-tuple array as follows (ex...

Eric Demopheles

Eric - I think you are misunderstanding what Neshant asked.. (Or at least what I think he asked :). There are two different problems. yy For my version (modified from Neshant's.., and clearly stated). the correct answer was given by ArmentT (or RM)'s hint. Actually I had the solution and exactly th...

Eric Demopheles

(For example in 12 coins .. If I understand the problem correctly .. You have heads .., 1,5,6(flipped twice),7,11,12(flipped twice)... in all 6 coins (12/2=6). Correct? 12 coins, flipping: Flipped zero times: 1 Flipped Once: 2, 3, 5, 7, 11. Flipped Twice: 4, 9. Flipped Thrice: 6, 10. Flipped Five T...

Eric Demopheles

Mirzakhani's and Avila's names were mentioned as possibilities prior to the last Fields Medal announcements too; but they did not win then. Bhargava's Ph. D. was in the news for contributions to Gauss's composition laws, was somewhat silent for a few years, and then his subsequent newsbreaking major...

Eric Demopheles

It is very interesting to know that Laplace had such a book which got translated into Hindi. No doubt, a master like him would have written a book with great content. Do you remember who was the translator? I have had to look at many French mathematical papers. Most people in mathematics would have,...

Eric Demopheles

Amber G. wrote:FWIW - One of the best book related to above I have seen is Laplace's original treatise.

What is Laplace's book about?

Eric Demopheles

That problem of measure article is amazing. I always had an "intuitive" idea of measures and why the common understanding of measure fails with uncountable and infinite general spaces (0 x Infinity == undefined issue), I am glad to know that my intuition was close to the current understan...

Eric Demopheles

Terry, BTW has one of the best blog for general public, if any one is interested in Math. I have recommended that blog previously and recommend it very highly. Come to speak of it, Terrence Tao is a great analyst and has made many great posts on real analysis and measure theory. He has published hi...

Eric Demopheles

ArmenT, Sir, This explanation was a lot helpful in understanding the present-day status of Java. I just browsed and read a few posts on StackOverflow regarding this too. By the way, do Android phone apps use JIT compilations? While we are talking of StackOverflow, how helpful is it for a programmer ...

Eric Demopheles

for large datasets, do you use python on a big box or use pydoop style programming to divide and conquer Depends on the definition of "large" and also if the type of dataset suits parallel processing. If it is just one or two files from a single server for a 10-minute period, probably eas...

Eric Demopheles

in comparison c/c++, how does sage perform? let us say the same algorithm written in sage or in c/c++. SaiK-ji, the problems are such that it wouldn't even occur to me that I could write it in C. What follows is the perspective of an amateur programmer whose main attention is on math. The more comp...

Eric Demopheles

chilarai, ArmenT, Thanks a lot for the explanation on functional programming. It was very helpful. And a lot of food for thought. So the "pure" functions cannot do I/O, access pointers, generate random numbers, etc., right? Although Haskell is interesting from a computer science/programmin...

Eric Demopheles

If you are very much into mathematics and such , you may really enjoy programming in Haskell. (from job market perspective it is a limited market but many banks like standard chartered uses haskell more and more ). I do only very beginner level programming in haskell but love it absolutely. In fact...

Eric Demopheles

^^^ Interestingly, we use C quite a bit at where I work and I'm no systems engineer. We also use python a fair bit, but mostly as a glue language and to write quick management scripts and hadoop jobs. The thing is that, for simple things, there is a lot to write in C that can be done in a couple of...

Eric Demopheles

Python is certainly very popular but not necessarily all that great (from a computer language design perspective). I am curious as to why not sage(math). Sage is enough for math purposes. The desire for a general programming language has other origins. The reason is for job market purposes. You kno...

Eric Demopheles

As I have told here, I took a course in QM by Dirac himself, (he was using his own famous text book on QM ** see note 1). This text book, of course, deals with Dirac's delta function extensively, and of course, its mathematical foundation is very solidly established. There was a "wise guy"...

Eric Demopheles

Re: Vsunder, Regarding Minankshisundaram: I had not read much about Minakshisundaram's works. Thanks for all your descriptions and links. I had not known that he and Patodi had worked on similar things. I was not aware of Minakshisundaram having to leave TIFR because of conflict with K. Chandrasekha...

Eric Demopheles

I have actually a question here. What is the most useful language for scientific computing for a casual user of linux who is comfortable with the command line? I mean a language for general programming tasks too; not something like PARI/GP or SAGE. I am leaning towards Python, but would love to hear...

Eric Demopheles

Re: from the GDF thread(vsunder and others). The Dirac delta function δ(t) of a real variable t is a thing that would be meaningless to define as a function, but can be integrated, either together or multiplied or convolved with other functions, and has the property that: integral from a to b of δ(t...

Eric Demopheles

(His interest in math is still there.. he did his PhD in Theoretical Physics, which some say is nothing but math with purpose..:) ) Indeed. Homological mirror symmetry and other similar recent stuff from physics contributes very deeply and seriously to pure mathematics. Such kind of influence of ph...

Eric Demopheles

Legendre's Conjecture (One of Landau's problem) says that there is at least 1 prime between n^2 and (n+1)^2. Legendre is a great arithmetician. As his brilliance was overshadowed in the presence of the great Gauss, people do not know him much. Let me here make a note to the Quadratic Reciprocity La...

Eric Demopheles

Hindsight is always 20-20. In modern times, the concept of complex numbers may be perfectly logical, but in ancient times, it was not always so. In fact, Bhaskaracharya wrote in his book that a square root of a negative number was absurd and a later commentator of his works presented a proof that a...

Eric Demopheles

Yes to LaTex and also display of simple line graphics. Admins: How difficult is it? If I understand right, this forum is based on phpBB. Maybe this is helpful: https://www.phpbb.com/community/viewtopic.php?f=70&t=2133985 Amber G.ji, Thanks for the links. It seems I missed a lot of pages of very...

Eric Demopheles

matrimc-ji, Amber G.ji, Thanks for your kind words. I did not know that this link was given earlier; sorry about the repetition. Now, something a little more substantive(analytical): There are more primes than there are perfect squares. In fact, in a meaning that can be expressed more precisely, the...

Eric Demopheles

Speaking of primes, there was a nice proof rather recently in 2005 that there are infinitely many of them. This is understandable for everyone: http://primes.utm.edu/notes/proofs/infinite/Saidak.html The original proof is of course cited to Euclid: http://primes.utm.edu/notes/proofs/infinite/euclids...

Eric Demopheles

He got 2014 Frank Nelson Cole Prize in Number Theory for that. Ah, yes. He got the Cole prize. For me the circumstances of the discovery was the most striking, more than the discovery itself. In this connection the following essay, on 'Two cultures of mathematics', is of interest: https://www.dpmms...

Eric Demopheles

Of late my interest in logic is increasing, especially on computability logic. I guess there are not many good books out there for meta-math and other logics. I don't want basic logic books, which I can find. I need little bit advanced. Do you have any recommendations? This should do: Jon Barwise: ...

Eric Demopheles

Do we any evidence for existence, usage or inkling of complex numbers in ancient Indian mathematics/astronomy/trigonometry..etc., anytime before say 1500 CE ? Inkling. Ah. Good word. Yes, there is. Indians had already developed quadratic equations. For example: http://en.wikipedia.org/wiki/Brahmagu...

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