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Finding Gemstones | On the quest for mathematical beauty and truthOn the quest for mathematical beauty and truth
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Finding Gemstones | On the quest for mathematical beauty and truth | mathematicalgemstones.wordpress.com Reviews
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On the quest for mathematical beauty and truth
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Finding Gemstones | On the quest for mathematical beauty and truth | Page 2
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On the quest for mathematical beauty and truth. Newer posts →. The Fundamental Theorem of Symmetric Function Theory. July 6, 2012. This little gemstone is hidden within the folds of algebraic combinatorics, but certainly deserves its name. Just as the Fundamental Theorem of Arithmetic gives us a way of writing common objects (numbers) in a canonical form (prime factorization), the Fundamental Theorem of Symmetric Function Theory allows us to express any symmetric function in a useful canonical form.
September | 2012 | Finding Gemstones
https://mathematicalgemstones.wordpress.com/2012/09
On the quest for mathematical beauty and truth. Monthly Archives: September 2012. This blog has moved. September 2, 2012. Please visit http:/ www.mathematicalgemstones.com. Where this blog will be updated from now on. This blog has moved. The 3x 1 problem! Summary: Symmetric functions transition table. A bridge between two worlds: the Frobenius map. Blog at WordPress.com.
mariamonks | Finding Gemstones
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On the quest for mathematical beauty and truth. I am currently a graduate student in mathematics at UC Berkeley. This blog has moved. September 2, 2012. Please visit http:/ www.mathematicalgemstones.com. Where this blog will be updated from now on. The 3x 1 problem! August 12, 2012. Summary: Symmetric functions transition table. August 4, 2012. A bridge between two worlds: the Frobenius map. July 29, 2012. There is a reason I’ve been building up the theory of symmetric functions in the last few pos...
Addendum: An alternate proof of the FTSFT | Finding Gemstones
https://mathematicalgemstones.wordpress.com/2012/07/13/addendum-an-alternate-proof-of-the-ftsft
On the quest for mathematical beauty and truth. The Fundamental Theorem of Symmetric Function Theory. Theme and variations: the Newton-Girard identities →. Addendum: An alternate proof of the FTSFT. July 13, 2012. Last week I posted about the Fundamental Theorem of Symmetric Function Theory. Zarathustra Brady pointed me to the following alternate proof in Serge Lang’s book. While not as direct or useful in terms of changing basis from the. Assume for contradiction that the. To have minimal degree. In the...
The Fundamental Theorem of Symmetric Function Theory | Finding Gemstones
https://mathematicalgemstones.wordpress.com/2012/07/06/the-fundamental-theorem-of-symmetric-function-theory
On the quest for mathematical beauty and truth. Circles of Apollonius… and magnetism! Addendum: An alternate proof of the FTSFT →. The Fundamental Theorem of Symmetric Function Theory. July 6, 2012. First, some background on symmetric functions. Like generating functions, symmetric functions arise naturally in combinatorics, and the coefficients are often the point of interest. In the poetic words of Herbert Wilf in his book generatingfunctionology. I claim, and aim to demonstrate here, that. Is a symmet...
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Characters of the symmetric group | Mathematical Gemstones
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On the quest for mathematical beauty and truth. Skip to primary content. Skip to secondary content. Characters of the symmetric group. May 21, 2012. Last week, I sat down to compute the character table of $S 5$ for the first time in several years. It turned out that it was possible to laboriously use this theory to compute the characters one at a time, by finding an explicit matrix representation for each irreducible representation. However, I still had a nagging feeling that there should be a faster...
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Mathematical Garden | Various ideas and concepts in mathematics
Various ideas and concepts in mathematics. Soap Film and Minimal Surface. Connes’ Distance Function. Soap Film and Minimal Surface. September 6, 2014. The geometry of soap films and soap bubbles. If we dip two wire rings into a solution of soapy water, then what is the surface formed by the soap film? This question is known as the. Or the Plateau problem. This post proposes to discuss a simple solution based on variational calculus and elementary computations. Continue reading →. August 27, 2014. However...
MATHEMATICAL GEMS - Home
Mathematical Gems from Philip Lloyd. Philip Lloyd has been a very successful mathematics teacher in New Zealand since 1967. Philip's personal guiding principle or philosophy:. To teach Mathematics using REASONS. Mathematics must not be taught as “a set of rules to follow”. It needs be taught with. There is a big difference between:. Rdquo; a thing and “ Understanding. For example, m ost students “. Rdquo; that 2. To the power 0. 1 but few “. Rdquo; WHY it is 1. To INSPIRE students the secret is. X = 1 an...
Mathematical Gemstones | On the quest for mathematical beauty and truth
On the quest for mathematical beauty and truth. Skip to primary content. Skip to secondary content. Hockey sticks on planet ABBABA. April 1, 2018. On the planet ABBABA, the inhabitants have a binary language where the only two letters in their alphabet are A and B. The language is incredibly efficient and complex in that. Finite sequence of A’s and B’s is a valid word. How many of the words in this language have exactly five A’s and at most five B’s? The CW complex structure of the Grassmannian. Let̵...
mathematicalgemstones.wordpress.com
Finding Gemstones | On the quest for mathematical beauty and truth
On the quest for mathematical beauty and truth. This blog has moved. September 2, 2012. Please visit www.mathematicalgemstones.com. Where this blog will be updated from now on. The 3x 1 problem! August 12, 2012. I have exciting news today: The first ever joint paper by Monks, Monks, Monks, and Monks has been accepted for publication in Discrete Mathematics. It’s an addictive and fun problem to play around with (see http:/ xkcd.com/710/. But it is frustratingly difficult to solve completely. Websites, whe...
Mathematical Genius Award
Admission card of MGA 2017-18. You are visitor No. -. Toppers - Ist Rank. Toppers - IInd Rank. Toppers - IIIrd Rank. Is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Click here for detail.
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A civilisation is a dynamical system that supports endogenous cultural development through economic activity aggregated across elements of its data. I am a mathematician. In this paper I will describe, what, from a mathematical point of view, I see as a major and fundamental weakness in the historical approaches to study civilisation the absence of a scientifically credible, consensus definition of the term civilisation. I will offer a mathematical solution to this historical problem. Remains without a c...
