Early Algebraic Variety, Coordinate Ring

Early Algebraic Variety, Coordinate Ring

10:18:00   Algebraic,

I wrote this up, because i don't want to forget it, I made a pdf files about variety, but hasn't finished it yet... It is hard to keep things alive in your mind, if you don't get used to it a lot, after I manage to bear algebraic geometry...

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The Zariski Topology and The ring of Regular Function

The Zariski Topology and The ring of Regular Function

19:44:00   Algebraic Geometry,

We know generalized the notation of Algebraic Curve defined in [ALGE I]. Here $k$ is an algebraic closed field. We say a subset of $\mathbb{A}^n$ is closed set if  the elements of $X$ are the common roots of some (system) of polynomial equations in algebraic closed field $k$. That...

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Bacot-Bacot tentang definisi limit

Bacot-Bacot tentang definisi limit

00:28:00  

Salah satu tantangan bagi seorang pengajar Kalkulus adalah bagaimana memberikan penjelsan pada konsep limit yang menggambarkan hubungan yang jelas antara intuisi dan definisi. Kebanyakan orang yang berlatar math, jika ditanya "limit itu apa?" maka bagi yang tau definisi akan langsung menjawab menggunakan epsilon-delta, lalu apabila ditanya lebih lanjut, "mengapa...

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[Part II] The first attempt in the difference of pi(x) and Li(x)

[Part II] The first attempt in the difference of pi(x) and Li(x)

23:43:00   Analytic Number Theory,

Following the post from Part I , where we have $$T_1(s)=\zeta(s) - 1 - \frac{1}{s-1}$$ $$T_2(s)=\ln(s-1)+\ln \zeta(s),$$ $$T_3(s)=\sum_{p \text{ is prime}}\frac{1}{p^s}-\ln\zeta(s).$$ and $T_i(s)$ has derivative of order $n$ for $s\rightarrow 1^+$.  Now consider  $$-\frac{d^n T_3(s)}{d s^n} - \frac{d^n T_2(s)}{ds^n} - \frac{d^{n-1} T_1(s)}{ds^n}$$ by our previous result, the above derivative...

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[Part I] How does the prime connect to Zeta Function?

[Part I] How does the prime connect to Zeta Function?

20:38:00   Analytic Number Theory,

I looked back to my previous post about Riemann Hypothesis, Defining The Zeta Function.. Well, even It was said there that the theorem plays an important role in Number Theory,  but all of the things I put there are likely a complex analysis rather than a Number Theory (of...

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Mendefinisikan fungsi Zeta Riemann, dan Riemann Hypothesis.

Mendefinisikan fungsi Zeta Riemann, dan Riemann Hypothesis.

04:27:00   Analytic Number Theory,

Walaupun cabang ini berada pada area Teori Bilangan, namun post yang saya buat ini, lebih pekat ke analisa kompleks, pada kenyataannya, pada post ini kita tidak membicarakan hubungan zeta function dengan bilangan prima. Definisi awal (bukan definisi yang sebenarnya) dari Fungsi Zeta Riemann diperoleh dari Deret Dirichlet $$\zeta(s)=\sum_{n=1}^{\infty} \frac{1}{n^s}\qquad\Re(s)>1$$ ...

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