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Note: What appears below, with permission, is a slightly edited version of unofficial advice from MGSA, the UC Berkeley Mathematics Graduate Student Associate, with Berkeley specific information removed. Information specific to filing a doctoral thesis at UC Davis can be found via the Grad Studies website.
There are several websites dedicated to Using LaTeX to Write a PhD Thesis. But since you're in the UC Davis math department, your best bet is to use a template that was specifically created for UC Davis math students. Here is a very nice template created by Tyrell McAllister, updated in 2015 by Jeff Irion with minor changes in order to conform to the format that the Office of Graduate Studies requires, and again in 2019 by John Challenor to remove the headers and the previous degree line from the title page.
Once you pass your Qual, download the dissertation template! Fill in some basic info (name, major, committee members' names, etc.), and add to your dissertation while you work on your research. After all, it's easier to write and cite as you go than to do it months/years later when that stuff isn't fresh in your mind.
(Thanks to Megumi Harada) Steps to your goal:
This is an unofficial guide. Please see Preparing & Filing Your Thesis or Dissertation for the official set of instructions.
As of Spring 2019, the documents you will need to bring are as follows (see the official checklist here).
The three documents with signatures obviously must be physical copies. The other item can be emailed to the Academic Advisor when you set up your appointment.