I’m doing some math right now and I’m an idiot, nothing’s working. Just saying. Good night! NFM
- Thread starter LionJim
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Abstract. Given any graph G, the (adjacency) spread of G is the maximum absolute difference between any two eigenvalues of the adjacency matrix of G. In this paper, we resolve a pair of 20-year-old conjectures of Gregory, Hershkowitz, and Kirkland regarding the spread of graphs. The first states that for all positive integers n, the n-vertex graph G that maximizes spread is the join of a clique and an independent set, with 2n/3and n/3vertices, respectively. Using techniques from the theory of graph limits and numerical analysis, we prove this claim for all n sufficiently large. As an intermediate step, we prove an analogous result for a family of operators in the Hilbert space over L2[0,1]. The second conjecture claims that for any fixed e ≤ n2/4, if G maximizes spread over all n-vertex graphs with e edges, then G is bipartite. We prove an asymptotic version of this conjecture. Furthermore, we exhibit an infinite family of counterexamples, which shows that our asymptotic solution is tight up to lower order error terms.
I keep hearing about Occam's razor, but i don't know what it is.
Most likely, it's a razor owned by someone named Occam.
Most likely, it's a razor owned by someone named Occam.
Math? You should get in touch with my soon to be 9 year old granddaughter. She convinced her parents to teach her how to use TEX on her computer and is now working on a book "Introduction to Field Theory".
William of Occam was a 14th century Franciscan monk. His razor was designed for manscaping the tonsure on the top of his head.
I *hate* TeX--because it is infinitely customizable, and authors expect us to be able to handle all (and use) of their customizations.
You might like this story... I was a brother at Acacia Fraternity at Penn State. Acacia is all about Pythagoras (historically Acacia traces back to sons of Freemasons). In fact our pledge pin is a 3/4/5 triangle inside a circle. As part of pledge ship, you had to memorize the proof to the 47th problem of Euclid... and I mean memorize the full proof, step by step. Something like this...
A seriously beautiful proof is that of Euclid’s 47th. Not that hard to memorize once you understand the trick, and it’s a lot of fun to move yourself around the triangles. Respect.
I’m a sucker for pretty proofs and you’ll find quite a few in Euclid. There are some mistakes and in some places the axioms need to be strengthened, but Elements is is a miraculous work, written with total integrity. It’s jaw-dropping that it was written about 300 BC.
I’m a sucker for pretty proofs and you’ll find quite a few in Euclid. There are some mistakes and in some places the axioms need to be strengthened, but Elements is is a miraculous work, written with total integrity. It’s jaw-dropping that it was written about 300 BC.
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Like it or hate it, to get anything published in many mathematics journals the manuscript has to be submitted in TeX.
The trouble is that our authors (I work for a scientific publisher) expect to get the exact same look and feel that they get from other publishers. But those other publishers have proprietary versons (the original is Open Source) that are set up for their own publishing processes--and we can't use them because they are proprietary.
Ah, that explains a lot. I love the look of the papers in the Journal of the AMS, which uses AMS-LaTex.
Our friend Chris H just got his doctorate, in case you didn't know. Anyhoo, he told me that every homework assignment had to be typeset in Tex.
Ok help me out here what is TeX?? Sounds like it is some sort of Word for Math typing
Do you buy it? Is it a free download?? Tia
Maybe it's something that allow maths guys to give 'em what they promise so they don't sneak by
TeX is a typesetting system that allows one to print mathematics the way it is supposed to look.
There are now several ways you can do it since some word processors now convert the mathematics portions to TeX. Originally you had to have a UNIX or LINUX operating system to use it.
A link to it ...
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