1901$$\begin{array}{c}P\left(\frac{X_{1}+X_{2}+\cdots+X_{n}-n_{\mu}}{\sigma \sqrt{n}} \leq x\right) \\rightarrow \\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{x} e^{-t^{2} / 2} d t\end{array}$$
Lyapunov’s theorem in probability theory is a theorem that establishes very general sufficient conditions for the convergence of the distributions of sums of independent random variables to the normal distribution.
Lyapunov functions (also called the Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions.

# Formulas 🧮 数学公式 1825-1896

1825$$\oint_{\gamma} f(z) d z=0$$
Cauchy’s integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorphic function. Cauchy’s formula shows that, in complex analysis, “differentiation is equivalent to integration”: complex differentiation, like integration, behaves well under uniform limits – a result that does not hold in real analysis.

# Formulas 🧮 数学公式 1500-1799

1500$$\begin{aligned}&x^{3} + mx = n\&\Rightarrow\&x=\sqrt[3]{\sqrt{\frac{n^{2}}{4}+\frac{m^{3}}{27}}+\frac{n}{2}}-\sqrt[3]{\sqrt{\frac{n^{2}}{4}+\frac{m^{3}}{27}}-\frac{n}{2}}\end{aligned}$$
At some point in the early 1500’s, an Italian mathematician named Scipione del Ferro determined a general solution for what is known as the depressed cubic equation. This is cubic equation without any $x^{2}$ terms. The general form is : $x^{3} + mx = n$ . As it turns out, any cubic equation of the form $x^{3} + bx^{2} + cx + d = 0$ can be written as a depressed cubic, but that came later.

# Frozen ☃️ 冰雪奇缘

Born with the power of ice and snow, Elsa is the firstborn daughter of King Agnarr and Queen Iduna, the older sister of Queen Anna, and the former queen of Arendelle. Throughout most of her young life, Elsa feared that her powers were monstrous. Therefore, she isolated herself from the world as a means of protecting her family and kingdom. Elsa’s anxieties would eventually trigger a curse that plunged Arendelle into an eternal winter. Through Anna’s love, however, Elsa was able to control her powers and live peacefully amongst her people with a newfound self-confidence.

# IELTS 📚 雅思考试

The International English Language Testing System, or IELTS, is an international standardized test of English language proficiency for non-native English language speakers. It is jointly managed by the British Council, IDP: IELTS Australia and Cambridge Assessment English, and was established in 1989. IELTS is one of the major English-language tests in the world.
Year started: 1980, 40 years ago
Purpose: To assess the English language proficiency of non-native English speakers.
Fee: Around 250 USD
Knowledge / skills tested: Listening, reading, writing and speaking of the English language.
Score / grade validity: 24 Months

# The Big Bang Theory ⚛ 生活大爆炸

The Big Bang Theory is an American television sitcom created by Chuck Lorre and Bill Prady, both of whom served as executive producers on the series, along with Steven Molaro, all of whom also served as head writers.

# Julia Roberts 👩🎤 朱莉娅·罗伯茨

Julia Fiona Roberts was born in Smyrna, Georgia, to Betty Lou (Bredemus) and Walter Grady Roberts, one-time actors and playwrights, and is of English, Irish, Scottish, Welsh, German, and Swedish descent. As a child, due to her love of animals, Julia originally wanted to be a veterinarian, but later studied journalism. When her brother, Eric Roberts, achieved some success in Hollywood, Julia decided to try acting.

# Brad Pitt 🧔🏻♂️ 布拉德·皮特

William Brad Pitt was born William Bradley Pitt on December 18th, 1963, in Shawnee, Oklahoma, and was raised in Springfield, Missouri. He is the son of Jane Etta (Hillhouse), a school counselor, and William Alvin Pitt, a truck company manager. He has a younger brother, Douglas (Doug) Pitt, and a younger sister, Julie Neal Pitt. At Kickapoo High School, Pitt was involved in sports, debating, student government and school musicals.

# Rice 🌾 大米

Rice is the seed of the grass species Oryza sativa or less commonly Oryza glaberrima. As a cereal grain, it is the most widely consumed staple food for a large part of the world’s human population, especially in Asia and Africa. It is the agricultural commodity with the third-highest worldwide production, after sugarcane and maize.

# Korean 🇰🇷 공부하다 1

Sejong Korean 1한국어와 한글한국어
한국어는 한국의 공용어이다.
한국어를 사용하는 인구는 한반도에 거주하는 인구와 해외 한국계
한국어는 사용 인구로 볼 때 세계 13위 안에 드는 언어이다.
언어별 인터넷 사용자 수 순위에서 한국어 사용자는 세계 10위 안에 든다.