I take notes by typing, and use a Mac.

I use a plain text notepad application, and type in mostly-ASCII but don't hesitate to use the full range of Unicode. In particular, I have a customized keyboard layout with many dead keys which lets me type arrows, logic/set symbols, superscripted and subscripted symbols, and Greek letters. (I created the layout using Ukelele.)

(Also note that the default Mac keyboard layout has π, Ω, µ, √, ≈, ∫, ∆, ∂, ∞, ≠, ±, ÷, ≤, ≥, ·, ∑, and ∏ already!)

I also don't hesitate to use LaTeX notation if it's convenient, and invent my own notations; for example, if the lecturer writes $\frac{a+b}{c+d}$, then I write `a + b // c + d`

, where the `//`

stands for a “low-precedence division sign” to make up for the loss of one dimension in the notation.

In the extremely rare occasion where I want to produce a nice LaTeX document and have this note text to start from, I convert it by hand (plus a LaTeX preamble which makes the Greek letters and mathematical symbols work directly without conversion to `\alpha`

etc.) — I've only done that maybe twice. As a general rule, anything that was an assignment to hand in, I wrote in LaTeX directly (including intermediate algebraic steps not included in the final document).

By request, an example. These are my unedited original notes from the fourth lecture of a “Calculus III” class. At the time I was generally familiar with the concepts of this material, but I wanted to make sure to write down the notation (e.g. choice of variable symbols) and terminology (e.g. “symmetric equations”) used in this class.

```
Lines
Identify by the position vector of a point on the line r_0 = <x0, y0, z0>,
and a vector D = <a,b,c> giving the direction of the line.
Vector parametric equation:
r(t) = r_0 + tD
Parametric equations:
x = x0 + a t
y = y0 + b t
z = z0 + c t
Solve each one for t and set equal to get the symmetric equations:
x - x0 // a
= y - y0 // b
= z - z0 // c
= t
Example 1: Find the equations for the line through these two points
```

The indentation for grouping is done with tabs, so it's only one keystroke. I probably cut-and-pasted the repeated equation lines rather than retyping them. Note that I have omitted the subscript marker `_`

in the coordinate subscripts because it is obvious in context.

Here's a later section on partial derivatives. This is where the Greek-incorporating keyboard layout comes in handy — I can write down what the lecturer is showing without having to write out the names of the letters or invent alternate notation (such as `[w]`

to stand for `ω`

, which I did before I made the keyboard layout).

```
Example 3:
Rewrite ∂u/∂x - ∂u/∂t = 0 [wave eqn with speed set to 1] in terms of the variables
ξ = x - t, (xi)
η = x + t (eta)
∂u/∂x = ∂ξ/∂x ∂u/∂ξ + ∂η/∂x ∂u/∂η = ∂u/∂ξ + ∂u/∂η
∂u/∂t = ∂ξ/∂t ∂u/∂ξ + ∂η/∂t ∂u/∂η = -∂u/∂ξ + ∂u/∂η
∂u/∂x - ∂u/∂t = 0 <=> 2∂u/∂ξ = 0.
Therefore ∂u/∂ξ = 0, u is constant wrt xi, so u is a function only of η.
Therefore our solution is u = F(η) = F(x+t).
```