Weird/Dumb question: What does a thesis do when the non-thesis option means more courses?

Question

Actually, this is my question: which option should i prefer Thesis vs Non-thesis for MS in CS? but I hope this post will not be closed as either off-topic or duplicate because I hope to be specific. There's some more context than the little context below, but it's kinda long to explain and maybe unnecessary. So, suffer with this short weird/dumb question (which could be made only less weird /dumb instead of non-weird/dumb with context).

Observations:

1. I notice some curricula of master's programs in pure math, there's like a thesis option and a non-thesis option. It seems like the only difference is in the non-thesis option, the thesis is replaced by 3 additional courses and a comprehensive examination.

2. In the other question, it says thesis option is more suited to those doing phd afterwards (or the converse: those planning to phd is more suited for the thesis option...idk. or both).

Weird/Dumb Question: Ok so then my confusion is like... I see thesis option has less courses compared to non-thesis. Ostensibly, more courses means more knowledge. But obviously this is wrong because of the previous answers about thesis option as more suitable for future phd applications (or conversely or both). What does a thesis do when the non-thesis option means more courses? I mean, will I actually gain more knowledge working on the thesis as compared to taking those 3 more courses?

• Scope: It's not mandatory, but my ideal answer is for math. Next best thing is for theoretical research. Third best thing is in general.

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A little context:

• My background in applied math: I did bachelor's and master's but in applied math. I want to now go into pure math. I didn't do a thesis in undergrad. In grad, we did have, in my opinion, a 'thesis', but our professors don't actually call it a thesis. (You can refer to my previous questions if you want.) But, Hell, it was tough. It was also so rewarding seeing it hard bound and in those fancy colors. But I didn't quite really learn many new things there. It was more of like experience applying things we already knew. Well it was 'applied' math, so perhaps I shouldn't be so surprised that our sort-of 'thesis' was about 'applying' things. Oh also, it was just a master's (not a PhD or even an MPhil).

• Recently in pure math: I was rejected for pure math phd program in Dec2018 and then again in Mar2021 (in Country A, where I currently live. I'm from Country B, and I might have to go back here for a second master's). Both reasons were simply insufficient knowledge. There was no mention of any lack of 'research ability' or 'skills' or anything (see below re 'research ability' or 'skills').

  • I actually remember reading online (at least in the applied math case) that doing a thesis for master's or even in general taking up master's or PhD in applied math demonstrates to potential/future employers (the context here is banks or financial institutions) 'research ability' or something.

• My preferences: Anyway, I don't mind doing thesis or non-thesis. It's about the same time to complete, and I wouldn't really care if one was longer than the other. I just wanna do whichever gives me more knowledge to eventually apply for a pure math phd (in a european-style university. I'm good enough for some us-style countries, I believe. But I want to do my pure math phd in a country that is unfortunately european-style. The country is Country A, btw). I plan to ask the universities of those master's programs, but I also wanna ask here on stackexchange. Perhaps here on stackexchange, I can even ask the universities better, or at least less dumb/weird, questions.

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Maybe related questions:

1. Why doesn't a master's thesis get read by a PhD admissions committee?

2. Will an off-topic Masters hurt my chances of a PhD place?

   • 2a. In particular, I notice there's an answer here that says

   • "People don't expect miracles from your master's thesis, rather they want to know whether you have the necessary knowledge/skills to embark on a PhD.

   • In relation to this, I am interested in acquiring not necessarily 'skills' or 'research ability' but 'knowledge'. (In this way, I hardly expect 'knowledge' and 'skills' to be separated by a '/', at least in my context.) I sincerely doubt that the professor, or any other professor in the university, who/that rejected me cares about 'skills' or 'research ability', or is probably already convinced enough from my applied math background. I believe the only thing I'm lacking here is knowledge. (Well, I was told I was lacking knowledge, but I wasn't told anything about lacking 'experience' or 'skills' or 'research ability'.)

Answer 1

I can't answer for pure maths, as that is not my field, so what I say might not apply there I guess, but a PhD is a PhD.

The first thing to note is that formal examinations and theses test very different things. The test at the end of a PhD is a thesis, not a formal exam (in the sit down and take a paper sense). Thus, your performance in a thesis is more representative of what your performance in a PhD might be.

Doing a PhD is about research, it is not about knowledge. In a PhD you might be learning things, but a PhD is not about learning, it is about the generation of new knowledge. A thesis will test/develop your ability to:

• Find new directions to take something to places no one has ever taken them before
• Think about the wider disciplinary context in which your work takes place and use this context to guide which directions will be most fruitful/most useful to the discipline. Be able to explain the relevance of your new knowledge to others in the discipline and recognize how it fits in with their work.
• Advance several different lines of research simultaneously
• Deal with the fact that most of those lines will be dead ends, and you will have to discard most or all of them.

Now you need a knowledge base to be able to do these things. Or rather, you need to demonstrate that you have the necessary skills to go away and learn what you don't know when you need it. But success in a PhD is not primarily measure in the amount of knowledge you have.

For most students, they have spent a long time in education, learning things they have been told to learn, and, if they are lucky, applying that knowledge to new situations. For this majority, skills/experience at generating new knowledge/scholarship is the weak point. Being good at exams =/= being good at research..

That said, it might be that you have already demonstrated these skills in the master's degree you already have, and for you it is the missing knowledge that is holding you back.

Answer 2

Ian Sudbery's answer is excellent, but here's something more. A general aspect is that students tend to think that things are learnt by being told. This runs counter to most educational research. Discovering things for yourself as required while working with a bigger scope (thesis topic) and applying them in turn with more freedom to make own decisions is usually far more effective for learning than having facts told and having to replicate them in an exam. Admittedly many (but surely not all, probably not even the majority) courses do better than that and use more interesting tasks for assessment, maybe even involving some freedom for own decisions, however by and large "teaching and exam" style learning is normally less effective in the long term than project work.

Things that students should learn when doing a thesis:

• Acquiring knowledge from the academic literature, deciding what is important/relevant and what is not, and applying it to a problem that is not of a kind that was taught in the same or a fairly similar way before (note that you don't only learn the knowledge itself in this way, but also how to do this with new material for the next problem),
• Scientific writing,
• Time planning and structuring the work,
• Strategies for solving hard problems that are not tailored to the methods taught in a course; particularly dealing with mistakes and approaches that don't work,
• Competence to make your own decisions and take responsibility for them.

Now I have to admit that this is a rather idealist view, and that due to thesis supervision, unsuitable topics, or also student's attitude the student may not have "learnt" all of these in the end; however it is of course also true for courses that the students often don't learn all the stuff that is taught. If a student is interested in doing a PhD with me I'd always ask for a thesis and I will actually read it (if maybe not word for word); for me that's in fact the most important qualification. I'd always prefer students with thesis to those without if they are otherwise fairly equal (and 3 courses more than the one without thesis may have will not change that). Obviously this is from a system where the supervisor decides whether to take on a student rather than a commission of people who ultimately don't have to work with the student. (Actually a commission may decide general suitability but the student needs to find a supervisor who agrees to take them on anyway.)

PS: Your first question was already asked (and answered by somebody else and me) here.

Answer 3

Speaking for the milieu familiar to me, mathematics in the U.S. (probably some people would label the work I do as "pure", as opposed to "applied", despite its applications... but, nevermind, let's go with the cliched labels... I'm well acquainted with them, as inaccurate and misleading as they may be.)

And, having been on grad admissions in a (what some people would call) "joint pure and applied math department", I am well acquainted with our criteria, anyway.

A thesis-oriented M.S. does invariably involve more self-actuated, self-selected work, and practicing doing that is a great thing. It is often less informative about the accumulated historical record of math stuff (which, in some contrast to other subjects, does not become "wrong" (usually), even if maybe less relevant in some cases).

A course-oriented M.S. is more "automated", and can be stultifying, but is (at best) far more informative in a scholarly sense (if the courses are chosen wisely, as opposed to being chosen to make the easiest possible path).

Only rarely would a PhD admissions committee look at an M.S. thesis. Most of what would be informative should be clear from the title and the abstract (and the advisor's comments about it).

Yes, I have observed that some aggressively-self-styled "applied" grad students (whether M.S. or aiming for Ph.D.'s) misconstrued "applied" as some sort of license to not know much... This is a ghastly self-deceit. Yes, there is also much useful computer science and other "natural sciences" to know (and engineering), to meaningfully apply mathematics... but ignorance of mathematics is not so helpful in that! :)

(Being in a hurry is understandable, but often leads to error... :)

A possibly amazing thing about mathematics and its applications in the practical world is that abstraction is very, very useful. A great economy and simplifier in many situations. (Not always...) And, as with many things, a 2-fold speed-up (not to mention 5-fold or better) is indistinguishable from miracles or genius. If that can be acquired by study of standard (if "fancy") mathematics, ... well, whoa, I'd take it! :)

So, no, an M.S. thesis will rarely impress PhD admission committees. It can be a plus, if it shows initiative and creativity and such. But/and the coursework, especially if your earlier coursework background was thin, is also something people do not want to see missing... It's nice to be clever and hard working, but failing to take advantage of all the hard work of all the clever people in the past is ... very foolish.