I have a terrible hand-writing and I'm very good at typing, so I had an idea about taking my math lecture notes using a computer.
I've tried using a simple syntax (using purely ASCII) but it's getting harder and harder, so I need something a bit more sophisticated.
Friend suggested Latex, but said that I probably won't be able to write it fast enough to use it in "real-time". It also has a quite learning curve.
I'm on Mac os X. What would you suggest?
I personally only take math lecture notes in $\LaTeX$; there are several benefits to doing this and I don't think it's as hard to learn as you think it is. I certainly don't have a problem with keeping up with lecturers. See this blog post and some of the answers at this MO question.
Qiaochu's suggestion of LaTeX is also what I would recommend. In this vein, I find it useful to define large numbers of keyboard shortcuts (this can be easily done in vim, for instance, which can be downloaded for Mac OS X). For instance, I map "5thm" to a theorem environment, and I usually have Greek letters expand when about half of them is typed (e.g. \alp -> \alpha). I have done this (cf. my website for examples of notes with source code) and don't generally have a problem keeping up with the lecturer. Commutative diagrams are slightly trickier, but they can be done. If you want to live-TikZ your notes, I'm afraid I can't help; but you should learn LaTeX first!
Using a word processing system is likely to be much slower for typesetting symbols. If the learning curve for LaTeX bothers you (and it's not that bad with a little practice), you might try LyX.
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).
With pen&paper, iPad's camera and my fingers -- but hopefully in the future with VimLatexSuite and Vim but I am too slow in using it although I can touch-type much faster than average people.
For a very long time, I have tried to use Vim here but also looked for Emacs. However, the Vim LatexSuite developers have not responded to problems such as mentioned here (a script which comes with all kind of macros a bit like with TeXShop in Mac but ready macros and platform-independent) so I take notes with normal pen&paper and then with iPad photograph them. You can see how I take notes here with iPad. Someties during lectures, lecturer or a co-worker just mentions a good book -- ok I will take a photo of it and add it to my notes. Sometimes during lectures I want to screeshot something let say from Wikipedia, ok I will do it. I do this kind of note-taking with Notes Pluss -app in iPad but trying to use more GoodNotes because faster to use, I miss so much during lectures while using Notes Plus because slow to use. With iPhone 4/5, you can however take this kind of images faster because the images can be synced fast to iCloud so making the use of Notes Plus a bit less painless -- its developer has however said that he tries to simplify the UI in the future.
I use vim most of the time but I think inefficinetly, particularly when not getting any help to problems like above. I try to get better in it by solving puzzles in services such as VimGolf.com here.
I am still not satisfied in how I take notes, I feel there must be better ways -- still investigating.
Highly recommended threads
I think that this question depends on how computer-savvy one is, and how complicated the formulas/notes are. For complicated diagrams and pictures, a paint program such as Window's Paint Shop should be ok.
For formulas and other details, I think a math program like Mathematica or Maple should be fine, as long as one knows the basics. This can really structure the notes, and adds the benefit of easily making a copy of the notes and then be able to play around with the functions and quickly see the results. It's hard to do this outside of a math program, and math programs are so easy to work with.
LaTeX can really structure and organize notes, but it quickly gets complicated, even for fairly simple formulas, so one needs to have a fair amount of experience/proficiency with it. On the other hand, the math programs, while costing some money, are usually designed to have an easy learning curve.
So I'd generally recommend a combination of mostly math software, along with a paint program for really complicated diagrams. One can easily copy the diagram into the math software later, when one has more time. Many math programs have the option of saving the notes in LaTeX form, so you get the added benefit of LaTeX, too, when using some of the software, such as Mathematica.
See this (site about software for writing math). Also this pertains to math typesetting on Mac OS X.
