What do mathematicians use to make graphs for analysis textbooks?

Question

Apologies if this is not the correct SE for this.

I have been transferring all of my notes to LaTeX and I have been wanting to include some custom diagrams. I often find my self having to find images to add to my notes but they are not quite what I want. I have tried using different graphic software but nothing seems to do it properly. Could anybody suggest to me any software through which I could make diagrams like this?:

Answer 1

I use Mathematica exclusively, and have published perhaps 1000 figures created with it. Here's just a start on yours:

Yes, use MaTeX to add LaTeX expressions in such figures:

Here's a more detailed explanation.

Answer 2

One alternative I have used many times is mathcha.io. It lets you create visually and it outputs Tikz ready to include in your document.

Answer 3

I would suggest Tikz libraries for Latex, which allows you to draw pretty much anything. It is time consuming to learn (and to draw), but results are fantastic. For instance, you guarantee that the letter type in a figure coincides with that in the body of your notes, something which is not in general true when you use other software. The manual is here http://pgf.sourceforge.net/pgf_CVS.pdf

Answer 4

This image I've made in 6 minutes: 2 minutes of drawing in Geogebra and 4 minutes of fine-tuning the exported TikZ code

The image itself is much sharper when compiled as a PDF. Various labels like $R$, $I^+$ etc. can easily be added in the .tex file that Geogebra generates for you when you select Export as PGF/TikZ.

TikZ has a bit of a steep learning curve and you'll have to do some googling if you decide to go down this road, but the payoff is huge as you can extremely fine tune your image and seamlessly incorporate any LaTeX code into it that you can think of.

You can try to compile the image yourself with the code below.

\documentclass[12pt]{standalone}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\usetikzlibrary{decorations.markings}
\begin{document}

%arrowhead placement macro, not generated by Geogebra
\tikzset{->-/.style={decoration={
  markings,
  mark=at position #1 with {\arrow{>}}},postaction={decorate}}}
    
%arrowhead placement macro, not generated by Geogebra
\tikzset{-<-/.style={decoration={
  markings,
  mark=at position #1 with {\arrow{<}}},postaction={decorate}}}


\begin{tikzpicture}[line cap=round,line join=round,>=stealth,x=1.0cm,y=1.0cm]

%axes
\draw[->,ultra thick] (-6,0)--(6,0) node[right]{Re $z$};
\draw[->,ultra thick] (0,-6)--(0,6) node[above]{Im $z$};

%line segments
\draw [line width=1.2pt,->-=.6] (0.6,0.2)-- (5.,0.2);
\draw [line width=1.2pt,<-=.6] (0.6,-0.2)-- (5.,-0.2);

%small circular arc
\draw [shift={(0.,0.)},line width=1.2pt,-<-=.2]  plot[smooth,domain=0.3217505543966423:5.961434752782944,variable=\t]({1.*0.6324555320336759*cos(\t r)+0.*0.6324555320336759*sin(\t r)},{0.*0.6324555320336759*cos(\t r)+1.*0.6324555320336759*sin(\t r)});

%big circular arc
\draw [shift={(0.,0.)},line width=1.2pt,->-=.2]  plot[smooth,domain=0.039978687123290044:6.243206620056296,variable=\t]({1.*5.0039984012787215*cos(\t r)+0.*5.0039984012787215*sin(\t r)},{0.*5.0039984012787215*cos(\t r)+1.*5.0039984012787215*sin(\t r)});

%big radius
\draw [line width=1.2pt,dash pattern=on 3pt off 3pt,->] (0.,0.)-- (-1.8715470558436564,4.640830918894045);

%small radius
\draw [line width=1.2pt,dash pattern=on 3pt off 3pt,->] (0.,0.)-- (-0.38122376447726786,-0.5046468481995906);

%point x
\draw [color=black] (-1.4,0.)-- ++(-2.5pt,-2.5pt) -- ++(5.0pt,5.0pt) ++(-5.0pt,0) -- ++(5.0pt,-5.0pt) node[below]{$z=-1$};
\end{tikzpicture}

\end{document}

Answer 5

Ipe

Ipe is a free drawing editor, easy enough to learn, can produce output with LaTeX/Tikz/PDF/etc., and is pretty powerful. It takes only a minute or two to recreate your diagram. (The arrow heads can even be fine tunes to match those you used, but I'll leave that to you):