Problems

Quadratic Formula

Pythagorean Theorem

Sum of first n Squares

Law of Cosines

Legendre's formula

Euler's Identity

Euler's Lesser-Known Identity

Normal Distribution

Fourier Transform

Wave Equation

Navier-Stokes Equation

Black-Scholes Equation

Relativity

Chaos Theory

Definition of the Derivative

Euler's Formula for Polyhedra

Gravitation

AM-GM

Stirling's Approximation

Stokes' Theorem

Divergence Theorem

Cauchy-Schwarz Inequality

Area of a Circle

Definition of tau

Sophie Germain Identity

Pascal's Identity

Hockey-stick Identity

Vandermonde's Identity

Combinations

Heine's Identity

Binomial identity

Hermite's Identity

Matrix Determinant Lemma

Euler Product of the Riemann-Zeta function

Irrationality of the Square Root of 2

Heron's Formula

Continued Fraction for pi/2

Sophomore's Dream

Identity involving pi and e

Representation of the Golden Ratio

The Sum of all Positive Integers

Inverse of a complex number

Definition of Convolution

Definition of the Kronecker Delta function

Bayes' Theorem

Probability Density Function of the Student's t-distribution

De Morgan's laws

Determinant of a 2 times 2 matrix

Sawtooth Function

Definition of Graham's Number

Burnside's Lemma

Continuum Hypothesis

Pythagorean Identity

Double Angle for sin

Double Angle for cos

Fermat's Last Theorem

Fermat's Little Theorem

Euler's Theorem

QM-AM-GM-HM Inequality over 3 variables

Extended Law of Sines

Integration by Parts

Definition of Perfect Numbers

Gaussian Integral

Definition of an Integral

Quantum Fourier transform

Recursive definition of the Hadamard transform

Imaginary numbers

Sum of Cubes

RSA Decryption Algorithm

Contraposition

Equation of a spring

Sum of reciprocals of partial sums of ℕ

Binet's Formula

Sum of first n Cubes

The Basel Problem

Root Mean Square

The Harmonic Series

Tupper's Self-Referential Formula

Hölder's Inequality

Rearrangement Inequality

Law of Tangents

Euler's Arctangent Identity

The Dirichlet Convolution

Sum of a Row of Pascal's Triangle

Definitions of Catalan's Constant

Series Representation of Apéry's Constant

Definition of the Euler-Mascheroni Constant

Green's First Identity

Cauchy-Riemann Equations

Cauchy's Integral Formula

Cauchy's Differentiation Formula

Functional Equation for the Riemann-Zeta Function

Well-ordering Principle

Asymptotic Formula for the Dirichlet Divisor Function

Prime Number Theorem

Cumulative Distribution Function of the Gaussian Distribution

Chernoff Bound

Union Bound

Law of Total Probability

Linear Least Squares Estimator

Definition of the Dilogarithm

Leibniz's Determinant Formula

Euler-Lagrange Equations

Sum of Divisors

Einstein Field Equations

Second Fundamental Theorem of Calculus

Abel's Summation Formula

Lagrange's Theorem

Catalan Numbers

Ising Model Hamiltonian

Borwein Integral

Parseval Gutzmer Formula

Fubini's Theorem

Coarea Formula

Equation of a Torus

Ampère-Maxwell law

Gauss's Flux Theorem (differential form)

Gauss's law for Magnetism

Maxwell–Faraday equation

Eigenvalue Formula

Collatz Function

Gamma Function

Laplace Transform

Taylor Series

General Solution to First-Order Linear Differential Equations

Fibonacci Binomial Coefficients Identity

Bellman Optimality Equation

Definition of a Well-founded Relation

Estimation Lemma

Chaitin's Constant

Cauchy's Differentiation Formula

Defintion of the Quasi-Stationary Distribution

Addition of Sound Levels in Decibels

Fast-Growing Hierarchy

Feigenbaum-Cvitanović Functional Equation

Feynman's Trick

Lorentz Factor

Time Dilation

Gauss's Flux Theorem (integral form)

Doppler Effect

Bernoulli's Equation

Relation between K_p and K_c

Van der Waals Equation

Maxwell-Boltzmann Distribution

Cayley-Hamilton Theorem

Chudnovsky's Formula for pi

Residue Theorem

The Fundamental Group of the Circle

Definition of the Operator Norm on a Finite Dimensional Banach Space.

Green's Theorem

Portfolio Variance

Newton's Method

Shannon Entropy

Pinsker's inequality

Condtional Entropy

Beta Function

Moist Adiabatic Lapse Rate

Cardano's Formula

General Cubic Formula

Tangent Sum of Angles Formula

Inner Product of Continuous Complex Valued Functions

Definition of a Psuedorandom Generator

Generalized Stokes' theorem

Cartan's magic formula

Ridge Regression

Evidence Lower Bound (ELBO)

Langevin Dynamics (Overdamped)

Schrodinger's Equation

Heisenberg's Uncertainty Principle

Principle of Inclusion-Exclusion

General Principle of Inclusion-Exclusion

Spectral Decomposition

Wigner Transform of the Density Matrix

Power Mean

Alternating Harmonic Series

Mertens' therorem

Rademacher Complexity

Definition of the Euler Totient Function

Wigner Semicircle Distribution

Quaternion Multiplication Formula

Dirac Equation

Center of Mass

Sackur-Tetrode equation

Force-Potential Relation

Riemann Zeta Function