Burnside's Lemma and coloring graph (first insight)

Burnside's Lemma and coloring graph (first insight)

03:45:00   Algebraic Combinatorics,

Months ago, while helping my junior working his skripsi, I learned about a theorem in algebraic combinatorics called Polya's Enumeration Theorem. Actually I already known this handy theorem before, but haven't give it much thought before. Before explaining about Polya's Enumeration Theorem, it is cultural to explain first...

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Generating the Oxolodon Space

Generating the Oxolodon Space

06:44:00   anonymous,

What is Oxolodon? It's just a strange term that I made it up myself (you can check by typing "oxolodon" into google, then the term oxolodon only belongs to this blog or any link directed here :p) Well, I'm a little bit "stuck" after graduating from the bachelor degree...

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accepted mathematical problem

accepted mathematical problem

06:25:00  

I found some problems that i doubly call them a mathematics competition problems, one example is: Problem 1: "The autopsion result that propofol was found in the death body of the king of pop, Michael Jackson. Dr Murray told the police that he gave the propofol in effort to...

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soal simulasi

soal simulasi

10:20:00   soal-soal,

Problem Misalkan $a$ dan $b$ adalah bilangan positif yang memenuhi $a+b=1$, Buktikan $$\left(\frac{a}{a+x} \right)^{a+x} \left(\frac{b}{b-x}\right)^{b-x} < e^{-2x^2}$$ untuk setiap $x\in (0,b)$ Donald E. Knuth Solution: Tetapkan $a$ and $b$ dengan $a+b=1$. Misalkan $$f(x)=e^{2x^2} \left(\frac{a}{a+x} \right)^{a+x} \left(\frac{b}{b-x}\right)^{b-x}$$ yang didefinisikan untuk $x\in[0,b)$. Akan ditunjukkan bahwa $f(x) <...

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Pelatihan Tim ISOM

Pelatihan Tim ISOM

08:13:00  

Hari ini aku membahas soal-soal ISOM (International Scientific Olympiad in Mathematic) bersama-sama Tim ISOM Indonesia 2009. Ini dia soal-soal nya: 1. Misalkan $f(x)$ adalah fungsi yang kontinu piecewise dan terdifferentiable di $[0,a]$. Jika $f(0)=0$ buktikan bahwa $$\int_0^a |f^{\prime}(t)f(t)| dt \leq \frac{a}{2} \int_0^a f^{\prime}(t)^2\,dt$$ 2. Jika $G$ suatu grup hingga,...

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