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STEM Concepts

Follow an equation, work through an example, or check an assumption. Browse 69 concepts across mathematics, physics and computing.

All📐Mathematics(19)⚛️Physics(12)🔄Algorithms(7)🏗️Data Structures(8)🤖Machine Learning(10)🧠CS Theory(5)🖥️Systems(2)🌐Networking(3)⚙️Engineering(2)🧪Chemistry(1)
P(A∣B)=P(B∣A)P(A)P(B)P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}P(A∣B)=P(B)P(B∣A)P(A)​
Mathematics

Bayes' theorem

Update a probability when new evidence arrives.

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n(Xˉn−μ)σ→dN(0,1)\frac{\sqrt{n}(\bar X_n-\mu)}{\sigma}\xrightarrow{d}N(0,1)σn​(Xˉn​−μ)​d​N(0,1)
Mathematics

Central limit theorem

Why averages can look normal even when individual observations do not.

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I=\int_a^b f(x)\,dx
Mathematics

Definite Integral

Calculate the area under a curve between two points

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f'(x)=\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}
Mathematics

Definition of Derivative

The instantaneous rate of change of a function

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theory

Mathematics

Effective sample size

More rows do not always mean more independent evidence.

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Av=λv,v≠0A\mathbf{v}=\lambda\mathbf{v},\qquad \mathbf{v}\ne0Av=λv,v=0
Mathematics

Eigenvectors

Directions a linear transformation stretches without turning away from their line.

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e^{i\pi} + 1 = 0
Mathematics

Euler's Identity

The most beautiful equation connecting e, i, π, 1, and 0

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ES⁡α(L)=11−α∫α1VaR⁡u(L) du\operatorname{ES}_{\alpha}(L)=\frac{1}{1-\alpha}\int_{\alpha}^{1}\operatorname{VaR}_{u}(L)\,duESα​(L)=1−α1​∫α1​VaRu​(L)du
Mathematics

Expected shortfall

The average loss in the worst part of a loss distribution.

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theory

Mathematics

Fat-tailed distributions

Distributions that give extreme outcomes more weight than a normal model.

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g=1n∑t=1nlog⁡(1+rt)g = \frac{1}{n}\sum_{t=1}^{n}\log(1+r_t)g=n1​t=1∑n​log(1+rt​)
Mathematics

Geometric growth

Why gains and losses compound rather than cancel.

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df(t,Xt)=(ft+μfx+12σ2fxx)dt+σfx dWtdf(t,X_t)=\left(f_t+\mu f_x+\tfrac12\sigma^2 f_{xx}\right)dt+\sigma f_x\,dW_tdf(t,Xt​)=(ft​+μfx​+21​σ2fxx​)dt+σfx​dWt​
Mathematics

Itô's lemma

The chain rule gains an extra term for Brownian motion.

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f∗=arg⁡max⁡f∈FE[log⁡(1+fR)]f^* = \arg\max_{f\in\mathcal{F}}\mathbb{E}[\log(1+fR)]f∗=argf∈Fmax​E[log(1+fR)]
Mathematics

Kelly criterion

Choose exposure by expected compound growth, subject to survival.

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MDD⁡=max⁡t(1−Wtmax⁡s≤tWs)\operatorname{MDD}=\max_t\left(1-\frac{W_t}{\max_{s\leq t}W_s}\right)MDD=tmax​(1−maxs≤t​Ws​Wt​​)
Mathematics

Maximum drawdown

The largest fall from a previous wealth peak.

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E_{n+1}=E_n-\frac{f(E_n)}{f'(E_n)}
Mathematics

Newton's Method

Iteratively find roots of functions with rapid convergence

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a^2 + b^2 = c^2
Mathematics

Pythagorean Theorem

The fundamental relationship in right triangles

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x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Mathematics

Quadratic Formula

Solve any quadratic equation ax² + bx + c = 0

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y=mx+b
Mathematics

Slope-Intercept Form

The equation of a straight line

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theory

Mathematics

Statistical power

How likely a test is to detect a specified real effect.

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V=\frac{4}{3}\pi r^3
Mathematics

Volume of a Sphere

Calculate the volume of any sphere from its radius

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