Mathematical Notation and Cheatsheet
Understanding mathematical notation is useful to read papers and also be able to write your own equations and understanding of a problem. In this tutorial we will work on walking through understanding the Greek Alphabet, then notation for mathematical operations, and then using LaTex to write equations.
Greek Alphabet
| Symbol | Name | Latex |
|---|---|---|
Α α |
Alpha | \alpha |
| Β β | Beta | \beta |
| Γ γ | Gamma | \gamma |
| Δ δ | Delta | \delta |
| Ε ε | Epsilon | \epsilon |
| Ζ ζ | Zeta | \zeta |
| Ι ι | Iota | \iota |
| Κ κ | Kappa | \kappa |
| Λ λ | Lambda | \lambda |
| Μ μ | Mu | \mu |
| Ν ν | Nu | \nu |
| Ξ ξ | Xi | \Xi |
| Ο ο | Omicron | \omicron |
| Π π | Pi | \pi |
| Ρ ρ | rho | \rho |
| Τ τ | Tau | \tau |
| Υ υ | Upsilon | \upsilon |
| Φ φ | Phi | \phi |
| Ψ ψ | Psi | \psi |
| Ω ω | Omega | \omega |
Mathematical Operations
Equality/Similarity
| Symbol | Name | LaTex | Example |
|---|---|---|---|
| = | Equality | = | x=y if x and y = 1 |
| ≠ | Inequality | \ne | x≠y if x = 0 and y = 1 |
| ≈ | Approximation | pi≈3.14 | |
| ≡ | Identity | ||
| < | Less Than | x <y | |
| ≤ | Less Than or Equal to | x≤y | |
| ≺ | Precedes | x≺y | |
| ≻ | Succeeds | x≻y |
Set Theory
Basic Logic
Linear Algebra
Vector
Vector use \vec{} to call out a vector in LaTex.
if $\vec{u}=(u_1,u_2,u_3) $ and $\vec{v}=(v_1,v_2,v_3)$
Addition: $\vec{u} +\vec{v} = (u_1+v_1,u_2+v_2,u_3+v_3)$
Substraction: $\vec{u} - \vec{v} = (u_1- v_1,u_2-v_2,u_3-v_3)$
Scaling: $\alpha\vec{u} = (\alpha u_1,\alpha u_2,\alpha u_3)$
Dot Product: $\vec{u}\cdot\vec{v} = u_1v_1 + u_2v_2 + u_3v_3$
Cross Product: $\vec{u} \times\vec{v} = u_2v_3-u_3v_2,u_3v_1-v_3u_1,u_2v_1-u_1u_2$
Length: $||\vec{u}||=\sqrt{u^2_1+u^2_2+u^2_3}$
Matrix Operations
References
http://assets.press.princeton.edu/chapters/gowers/gowers_I_2.pdf