1 A keyboard can enter other characters and scripts than just the Latin characters that are plastered on it. You don't need to switch away from your primary keyboard language to access them: You can set up your system with a key that you hold down to insert character codes into a document. This is great if you just want to enter a few symbols from a different script every once in a while like when writing math notes.

2 The procedure for Mac OS (I don't use linux desktop or windows, sorry!) to enable and enter unicode symbols: System Preferences -> Keyboard->Input sources -> "+" -> scroll down to select "unicode Hex input". Now if you switch to this keyboard you can input any unicode code by holding down the "alt" key on your keyboard and typing in the code (e.g. to type "ℝ" I would hold option and type "211d"). I've remapped my enter on my numpad to alt to enter symbol codes in more quickly with Karabiner elements.

3 Maybe I'll get around to learn LaTeX (the formatting language typically used to put math symbols and into papers and books) but using unicode codes is extremely fast and fits my needs for what I want to do. Unicode symbols can be entered straight into files as opposed to having to be coded and then compiled into a pdf (or other formatted mediums) like LaTeX has to be.

4 I have a list below of the symbols I use for my mathematics studies. I'll keep updating this page if (when) I need new symbols for my studies. How I use it is by doing a english word search that jumps to the list item.

## List (in no particular order):

### Computational

- 2716 ✖ multiplication
- 00f7 ÷ division
- 221a √ sqrt
- 221b ∛ sqrt³
- 221c ∜ sqrt⁴
- 222b ∫ integral
- 222c ∬ integral double
- 222d ∭ integral tripple
- 27cc ⟌ long division
- 2032 ′ first derivative
- 2033 ″ second derivative
- 2034 ‴ third derivative
- 2202 ∂ partial derivative
- 2211 ∑ sum
- 00ba º degree
- 2260 ≠ not equal
- 2261 ≡ if and only if, idential
- 2262 ≢ not identical
- 2264 ≤ less than or equal to
- 2265 ≥ greater than or equal to
- 2270 ≰ not less than or equal to
- 2271 ≱ greater than or equal to
- 2248 ≈ roughly is equal to

### Greek letters

- 2206 ∆ delta
- 03b8 θ theta- used for angles
- 03a6 Φ phi
- 03b6 ζ small letter zeta
- 03b8 Θ Capital theta
- 03c4 τ tau

### Sets

- 211d ℝ real
- 2115 ℕ natural
- 2124 ℤ integers
- 211a ℚ rational
- 221e ∞ infinity
- 2200 ∀ for all
- 2205 ∅ null-set
- 222a ∪ union
- 2229 ∩ intersection
- 2203 ∃ there exists
- 2208 ∈ element of
- 220b ∋ contains as a member

### Constants

- 212f ℯ euler
- 2148 ⅈ imaginary
- 2107 ℇ euler's constant
- 03c0 π pi

### Geometric

- 223f ∿ sin θ
- 27c2 ⟂ perpendicular
- 2220 ∠ angle
- 299c ⦜ right angle
- 2221 ∡ angle opening counter-clockwise
- 29aa ⦪ angle opening clockwise
- 22bf ⊿ right triangle
- 27c0 ⟀ three dimensions

### Super and Sub letters and symbols (unicode is incomplete with its index of latin characters)

- 1d43 ᵃ super a
- 1d47 ᵇ super b
- 1d9c ᶜ super c
- 1d48 ᵈ super d
- 1d49 ᵉ super e
- 1da0 ᶠ super f
- 1d4d ᵍ super g
- 02b0 ʰ super h
- 2071 ⁱ super i
- 02b2 ʲ super j
- 1d4f ᵏ super k
- 02e1 ˡ super l
- 1d50 ᵐ super m
- 207f ⁿ super n
- 1d56 ᵖ super p
- 02b3 ʳ super r
- 02e2 ˢ super s
- 1d57 ᵗ super t
- 1d58 ᵘ super u
- 02b7 ʷ super w
- 02e3 ʳ super r
- 02b8 ʸ super y
- 1dbb ᶻ super z
- 207a ⁺ super plus
- 207b ⁻ super minus
- 2070 ⁰ super 0
- 00b9 ¹ super 1
- 00b2 ² super 2
- 00b3 ³ super 3
- 2074 ⁴ super 4
- 2075 ⁵ super 5
- 2076 ⁶ super 6
- 2077 ⁷ super 7
- 2078 ⁸ super 8
- 2079 ⁹ super 9
- 2090 ₐ sub a
- 2091 ₑ sub b
- 1d62 ᵢ sub i
- 2092 ₒ sub o
- 1d63 ᵣ sub r
- 1d54 ᵤ sub u
- 1d65 ᵥ sub v
- 2093 ₓ sub x
- 1d67 ᵧ sub y
- 2080 ₀ sub 0
- 2081 ₁ sub 1
- 2082 ₂ sub 2
- 2083 ₃ sub 3
- 2084 ₄ sub 4
- 2085 ₅ sub 5
- 2086 ₆ sub 6
- 2087 ₇ sub 7
- 2088 ₈ sub 8
- 2089 ₉ sub 9