Riemann Hypothesis for Dummies?

Riemann Hypothesis for Dummies?

05:23:00   Analytic Number Theory,

First, i'm sorry if the title is a little bit offensive. I just wonder if there's such a thing as "Riemann Hypothesis For Dummies", while the original statement of the conjecture itself would require at least advance undergraduate complex analysis, and (no math undergraduate is dummy right?).  I'm...

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[ALGAE IV] Rational Curve and Rational Function.

[ALGAE IV] Rational Curve and Rational Function.

22:41:00   Algebraic Geometry,

It has been months, and i actually has got quite far reading algebraic geometry, but i don't spare a time to share it here. Let's continue the previous posts (and to remind me more about what i have learned). As we already learn that any irreducible rational curve $f(x,y)=0$...

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OSN 2010 hari kedua

OSN 2010 hari kedua

03:41:00   Olimpiade Matematika,

Soal hari kedua sedikit lebih susah dari hari pertama, ini adalah solusi untuk soal-soal hari kedua (keuali soal no 8, dengan alasan yang sama). Untuk solusi untuk soal no 5,  ide awal nya (invariant principle) bukan ide saya sepenuh nya (at the beginning I even didn't understand the...

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OSN 2010 hari pertama

OSN 2010 hari pertama

21:19:00   Olimpiade Matematika, soal-soal,

Sedikit rileks, dengan soal-soal SMA, yang tidak mudah dan lumayan menarik. OSN tahun ini diadakan di Medan. Berikut adalah soal-soal beserta solusi nya (kecuali soal no 2, karena saya kurang begitu paham geometri). Solusi saya tulis sedetil mungkin, agar (menurut pendapat saya) mendapat nilai penuh di OSN untuk...

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17th IMC Day 1. [part 1] Problem 1, Problem 2, Problem 3.

17th IMC Day 1. [part 1] Problem 1, Problem 2, Problem 3.

04:21:00  

In this part 1, i'll give some solution of the previous IMC 2010 problems. The problems are relatively easy compared to the last year.  Problem 1.  Let $a\leq b$ where $a$ is a positive real number $$\int_a^b(x^2+1)e^{-x^2}dx\geq e^{-a^2}-e^{-b^2}.$$ Solution: Okay, this is too easy for IMC, first we prove...

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[ALGE III] The Field Of Rational Function of The Irreducible Variety

[ALGE III] The Field Of Rational Function of The Irreducible Variety

00:33:00   Algebraic Geometry,

Let $X$ be an irreducible curve given by $f(x,y)=0$ in the algebraic closed field $\mathbb{F}$, then we define the set $$\mathbb{F}(X)=\left\{\left.\frac{p(x,y)}{q(x,y)} \right\lvert p,q \in \mathbb{F}[x,y] \mbox{ and } f(x,y)\not | q(x,y) \right\}$$  Then $\mathbb{F}(X)$ contains the rational functions of two variables $x$ and $y$. We say two elements of...

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[ALGE II] Rational Parametrization of Algebraic Curve

[ALGE II] Rational Parametrization of Algebraic Curve

07:52:00   Algebraic Geometry,

From the previous post, we know that any algebraic curve in the algebraic closed field can be decomposed into irreducible curves, which is a unique representation. So, it would be natural to look deeper on the irreducible curve. Recall that an algebraic curve $X$ defined by the equation $f(x,y)=0$,...

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[ ALGE I ] Introduction to the Plane Algebraic Curve

[ ALGE I ] Introduction to the Plane Algebraic Curve

22:24:00   Algebraic Geometry,

Well i'm going to retell what i've  studied from the algebraic geometry books so far.. one of my favorite book is the Basic Algebraic Geometry: Varieties in Projective Space  By Shafarevich. Let $\mathbb{F}$ be an algebraic closed field. An algebraic curve $X$ is the set of points $(x.y)$ defined...

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Just an exam problem

Just an exam problem

11:12:00   soal-soal,

Soal Misalkan $$A={\underbrace{(999 \cdots 9)}_{\mbox{2008 buah}}}^{2009} \qquad \mbox{dan} \qquad B={\underbrace{(999 \cdots 9)}_{\mbox{2005 buah}}}^{2009}$$ Tunjukan bahwa digit dari B dapat diperoleh dari A dengan cara menghapus beberapa buah digit nya. Solusi: Untuk $0\leq m \leq 2009$ misalkan $$A_m=\sum_{k=0}^{m} \binom{2009}{k} 10^{2008k} (-1)^{k+1} \qquad B_m= \sum_{k=0}^{m} \binom{2009}{k} 10^{2005k} (-1)^{k+1}$$ Jadi $A_{2009}=A$ dan...

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