====== Solutions to Prelim Exams (Updated 20 July 2023) ======

Solutions may not all be correct. If you find something wrong, you're encouraged to send a correct solution, or at least what's wrong and why.

The department posts previous exams on [[https://www.math.ucdavis.edu/grad/exam-prep|this page]]


===== Analysis =====
Greg DePaul put together [[https://github.com/gdepaul/Prelim-Resources/blob/main/Analysis%20Notes.pdf | these excellent notes]] on the the material covered on the exam

Kyle Chickering has combined many of the previous exams (2009-2019) into {{ :analysis_prelims_2009_to_2019.pdf |a single file}}

Jeff Anderson led a project in 2011 to compile solutions to most of the previous exams. {{::preliminarysolutions.pdf| This file}} contains those solutions as well as some tips and references.

Here are some preliminary exam solutions by Jeff Irion and Ryan Halabi:

{{::prelim_solutions.pdf|Prelim Solutions}}

Kyle Chickering posted solutions to various exams given between 2012 and 2020:

 {{ ::krc_analysis_prelim_solutions.pdf | Analysis Prelim Solutions}}

Greg DePaul also helped develop printable flashcards in order to prepare for the exam: 

[[https://github.com/gdepaul/Prelim-Resources/blob/main/analysis_flashcards.pdf | Greg DePaul's Analysis Flashcards]]


===== Applied Math =====

Here is a condensed set of notes which should help cover the first two-thirds of the exam, submitted by Greg DePaul: 

[[https://github.com/gdepaul/Prelim-Resources/blob/main/Applied%20Prelim%20Study%20Guide.pdf | Applied Notes]]

Spring 2020 through ~Spring 2015, by Kayden Mimmack, Qianhui Wan, and Jorge Arroyo:

  * [[https://mimmackk.github.io/ggam-prelim/solutions.pdf|PDF]]
  * [[https://github.com/mimmackk/ggam-prelim|TeX Source]]

The following is a collection of solutions written and compiled by David Haley.  Most of the solutions are complete, although the work is very rough and lacks some detail.

  * {{::ggamf015.pdf|Fall 2015}}
  * {{::ggams015.pdf|Spring 2015}}
  * {{::ggamf014.pdf|Fall 2014}}
  * {{::ggams014.pdf|Spring 2014}}
  * {{::ggamf013.pdf|Fall 2013}}
  * {{::ggams013.pdf|Spring 2013}}
  * {{::ggamf012.pdf|Fall 2012}}

Also Greg DePaul developed a useful tool for visualizing 1D, 2D, and 3D dynamical systems using MATLAB and the SYMS library. You need to have a departmental license installation of MATLAB to run (or your own copy of SYMS): 

[[https://github.com/gdepaul/Dynamical-Systems-Playdoh | Dynamical Systems Matlab Code]]

===== Algebra =====

We have a list of notes which should help those give an idea as to the content which can be seen on the exam, typed by Greg DePaul: 

  * [[https://github.com/gdepaul/Prelim-Resources/blob/main/250A%20Notes.pdf | 250A Notes]]
  * [[https://github.com/gdepaul/Prelim-Resources/blob/main/250B%20Notes.pdf | 250B Notes]]
  * [[https://github.com/gdepaul/Prelim-Resources/blob/main/250C%20Notes.pdf | 250C Notes]]

//Note:// the prelim exam sometimes includes Representation Theory; Homological Algebra is not included in the Algebra Prelim Syllabus

Matt Litmam, Wencin Poh, and a mysterious El Tigre have also worked together to provide solutions for past Algebra Prelims: 

[[https://github.com/gdepaul/Prelim-Resources/blob/main/APS.pdf | Algebra Prelim Solutions]]

===== Topology =====

Material is in the process of being developed. Here are some notes from courses students have taken: 
  * [[https://github.com/gdepaul/Prelim-Resources/blob/main/Topology.pdf|Math 215A]] 

===== Problem Books in Math =====
Some students find it useful to work through batteries of problems with solutions in order to prepare for examinations. Here are some problem books curated by subject. Hope people find these as useful as I did. 

[[https://drive.google.com/drive/folders/1HYUoDr6uFiWuCf7kRPCR1TuCb0hXPyxj?usp=sharing| Problem Books]]

//Note:// you need to be logged into your ucdavis email to access these resources.