alunstokes / math712paper

A Thorough Write-up of Course Notes for: O-minimality & the Pila-Wilkie Theorem at the Fields Institute, Winter 2022

McMaster MATH 712 Course Notes

O-minimality & the Pila-Wilkie Theorem -- Fields Institute Graduate Courses 2022

What if I just want the final PDF?

That would be book.pdf then.

What is this?

A series of notes documenting and augmenting the module on o-minimality and the proof of the Pila-Wilkie Theorem (plus some applications) given by Dr Gareth Jones (University of Manchester) at the Fields Institute between January and February of 2022 as the first in a series of three modules -- which together comprised a graduate course in o-minimality and its various applications I took through McMaster University as an MSc student. Mistakes are almost certainly present, and the document is currently unfinished, not including the last lecture on applications of the Pila-Wilkie theorem.

Compiling

You can produce a .pdf file by running the following in the base directory:

pdflatex -synctex=1 -interaction=nonstopmode book.tex
makeindex book.idx
bibtex book
pdflatex -synctex=1 -interaction=nonstopmode book.tex
pdflatex -synctex=1 -interaction=nonstopmode book.tex

You will get errors running this code (See issues for multiply-defined citations) and the references will be off at the end of each chapter, but this will be addressed in the short future. This is no longer true! We use book-end citations, and the wicked witch of chapter-end citations has been doused with a water-pail full of not caring.

This should be error-free (by the end; LaTeX builds will always have intermediate errors when using BibTeX, etc.), and a final book.pdf file will be produced however, and broadly resembles what it should. that is now correct as is should be! Rejoice!

Just a Couple Questiaronis for Ya

Please don't call them that, but yes?

1. Why is the directory structure so bad?

   -Poor planning. Move on -- it may or may not be fixed.

2. Why the strange naming convention for chapters?

   -svmono.cls provides a single chapter-ed exemplar directory from which I drew inspiration (see: copied). Blame whoever put that together.

3. Will 2. be fixed?

   • Maybe

4. I love you; you can do this

   • Me too and we shall see.

math712paper's Issues

Multiply-defined labels

Caused by re-using the same bibliography file (part_1.bib) in chapter_12_refs.tex as chapter_11_refs.tex. Not a huge issue in all honesty but annoying.

Fix the directory structure

Come on now this is just no good

Bad chapter labelling

Pretty self-explanatory. Using 11 to mean chapter 1 section 1 is not clear. Use semantic labels.