# Theses and dissertations that originated on math.SE

In a comment to my question about published papers that originated on math.SE Asaf asks about master's theses. I think it would be interesting to have a list of those as well. So, that's what this thread is for: A list of master's theses and doctoral dissertations that originated on math.SE.

As with the question about papers, perhaps each answer could link to a question or answer on the main site, along with a brief summary of the content of the thesis or dissertation.

• Should we also list dissertations that were never finished because the author hung out on Math.SE too much? – user53153 Feb 27 '13 at 18:41
• @5pm: If I could finish my masters with a pretty nice thesis (not just saying that on myself, it got great reviews from the referees); I think everyone can. I mean, who here is actually on math.SE more than me? At most you can be here as much as me. :-) – Asaf Karagila Feb 27 '13 at 18:48
• @zyx While the exact proportion depends on the educational system, many of master-level theses are not published in the form of papers. Not all PhD theses are published in this form either. – user53153 Feb 28 '13 at 18:05
• @5pm, my previous comment was meant partly as a joke, but I do think it would be a good idea to change the title of the older question to "Papers, theses, dissertations and publications that ...." and consolidate all into one thread. – zyx Mar 2 '13 at 3:39
• I dunno, but this is gonna be one hell of a paper if anybody ever figures it out. – Alexander Gruber Mar 12 '13 at 20:20
• @Alexander Did you ever publish your solution then? – user1729 Oct 27 '14 at 9:52

The main part behind my masters thesis was actually the development of my answer: Axiom of choice and automorphisms of vector spaces.

I have rewritten and extended the argument to remove the need for atoms, and to be done directly in ZF by forcing. The thesis itself assumes knowledge of basic forcing arguments (but explains symmetric extensions, choice principles, and another technical construction I ran into needing).

The last chapter of the thesis is a problem introduced to me by Andres Caicedo which I somewhat explained [after finishing my thesis, though] in this answer: For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$.

In the process I also gave various examples which were developed from small questions I had asked on MathOverflow.

The thesis was titled "Vector Spaces and Antichains of Cardinals in Models of Set Theory". My advisor was Uri Abraham. The thesis can be found on my homepage.

• Why no link to your thesis? – Michael Greinecker Feb 27 '13 at 19:50
• Too lazy to do it now? Oh well, I'll post one. :-) – Asaf Karagila Feb 27 '13 at 19:51

I wrote my thesis "Implementation of an algorithm for verifying the non-negativity of a multilinear function in a hypercube". It is an applied topic (PRA) and an irritating thing is that terminology such as multilinear function itself is defined differently between different domains so I asked a lot of questions.

I have summarised some questions below, I still feel there is a lot of possible research topics related to optimising non-negativity check with different kind of data characterised with different kind of MLFs. I think versatile approaches are graph-theoretical, number-theoretical and polytopical approaches. Basic idea is to get the non-negativity check of MLF to certain unsolved problems or earlierly well known problems -- I have over 50-100 pages of mathematical investigation on this that I may work on in the future. I also parallised the computation to Aalto Triton supercomputer, not covered in the thesis. My thesis mostly covers the implementation, necessary data-structure (idea originated from hypercubes) and not much focus on algorithm development or mathematical investigation above, requirement by instructor.

Summaring some questions

1. What does multilinear function mean?: I made sure that I understood the domain, I was flabbergasted because some mathematical definitions and PRA definitions were different so took some time to relearn.

2. Speeding up a multilinear function: showing an example optimisation strategy with the bound-check (invented by my instructor Antti).

3. By which pkg to visualize a hypercube graph: I wanted to perfect my LaTex and make it easier for future research to investigate hypercubes.