What was added in the latest edition of Math into LaTeX?

I don't think I am breaching copyright by fair use of a promotional extract even if it on its own most of the public available preface by the author.

Many of the changes in this fifth edition are based on Practical LATEX and on my articles “What Is New in LATEX?” in the Notices of the American Mathematical Society [36]–[41] and [43].

Part I. Short Course of the fourth edition was revised under the title Chapter 1.ShortCourse. I renamed PartI:MissionImpossible. This part now has a second chapter:

And a few more things ... The new Chapter 1 is what you absolutely, unquestionably must know to write your first TEX document. It’s only 30 pages long, should not take more than a few hours to read and understand. No typing is necessary, the files you need are provided for you.

The new Chapter 2 adds a few more topics that is helpful to know such as the aux files, what is their role, how to handle them. It deals in some detail with error messages. Finally, it contains Brian Davey’s list of LATEX mistakes most often made by authors.

To create “vectorgraphics” illustrations (see page 349 for an example), manyusers switched to Till Tantau’s TikZ package. We introduce TikZ in Chapter 13. We hope that the few commands we discuss are sufficient to get you started.

I carefully revised all the material in this book. One would think that this is not necessary in a fifth edition. But as Fred says, there are infinitely many typos in any book, and even our best efforts remove only finitely many. And so many of the links have changed...

Finally, I should mention that I renamed the awkward user-defined commands to custom commands. How come I have not thought of this before?

For the Preface, a full list of contents, Chapter 17 preview on "BOOKS" (unfortunately only first 2 pages) and several other preview bits (including Chap 1 and 2 mentioned above) plus a chunk of 4th edition and lots of working samples see the publishers previews at https://www.springer.com/gp/book/9783319237954

I am not aware of what is new in LaTeX maths since 2007 and what would be highlighted here, but the topic maths of CTAN is a good start to investigate, where of course there are new packages for typesetting mathematics (and even specifically statistics).

But for a statistics book, a major point should be the concept of literate programming in LaTeX to change your workflow.

The concept is even older that fist edition of The LaTeX Companion, and the first implementation with the R language using Sweave is older that the second edition, but from 2012 is being implemented with a new tool, knitr that allow much more options. This, joined to the development of R in last years, with several others packages for LaTeX integration (xtable, stargazer, etc.) make this an awesome tool.

A newer step is, however, use knitr but in R Markdown and finally, built on top of R Markdow, bookdown have been made specifically to wirte statistical books.

Of course, this not off-topic, as R Markdown and bookdown can produce a PDF (among other formats) via a LaTeX conversion.