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Applying for 2018-9 admissions (Missed 2017-8 admissions). Got master's applied math. Want PhD in pure math.

How applicable is the following (source)

a recommendation from someone who only taught a course can mean "this person is a slacker who never bothered to do real work, so they can't find any supervisors to recommend them".

If out of school, delay your application by 1-3 years, and look for work as a lab tech at a university, institute or private company. Make sure not to displease your boss.

  1. if I have a master's?

  2. How might self-study affect applicability? (source)

they can check out your blog, notes etc but probably will not unless they are interested anyway, or it gets hyped up by your letter writers


Contexts:

Application:

  • I'm allowed only 2 or 3 recommendation letters for some local applications, here in Country A.
  • Besides research ability/potential, some Country A local applications are looking for soft skills such as leadership, communication, interpersonal, etc

Me:

  • Bad grades in bachelor's
  • Bad grades in master's for non-pure maths
  • Good grades in master's for pure maths
  • Research: Had a lot of group research projects including a semester-long main research project with 3 supervisors. None of them can give me very strong letters of recommendations

Plan:

  • Ask 1 or 2 profs in pure maths classes for the research ability/potential. Despite little to no research opportunity apart from problem sets, I have done some of my own self-study and researched/asked about some skipped/not elaborated/unclear/wrong parts in classes (not on this stackexchange account).

  • Ask boss for the soft skills parts

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    Why can you not get strong letters from your main supervisors? – Tobias Kildetoft Dec 14 '16 at 8:05
  • @TobiasKildetoft Untreated ADHD, disinterested in finance. (kinda late since i was focused past 6-7 months on learning to improve my work performance instead of self-study or further grad apps) – Jack Bauer Jul 30 '17 at 17:20
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If I see you have been involved in lots of supervised research projects on your CV/statement, but that none of your letter writers are any of your supervisors, I will find that a bit weird, but it wouldn't kill your application. Remember (I feel this has come up in a lot of questions lately), in mathematics research experience is not that important for getting into PhD programs (at least in the US). What is, is having learned and showing a capacity to learn advanced mathematics (as well as work ethic + motivation).

Edit (in response to comments):

  • You seem to want to get a letter from your boss, and that's fine, and it may be helpful, but the point is that typically letters from the workplace don't provide too much insight into academic abilities, unless that letter writer is closely connected to academia (e.g., they have a PhD in your field of study). This is why non-academic letters are usually not sufficient to get one accepted into a good graduate program, and you should get letters from academics as well. (I would try to get at least 1 letter from a pure math prof from your bachelor's and 1 from a prof from your master's.)

  • Certainly having done well in advanced pure math classes, and having successfully gone through a master's in a related area makes you a reasonable case for grad school in pure math. (How much the master's helps depends a lot on the details of program.) Whether what you've done at work will be helpful in evaluating your academic abilities depends on what you were doing (see also the previous bullet point), but at least your boss can address things like work ethic and general intelligence.

Since I don't know the details of your situation, or what your application looks like, I can only say from what I've heard so far, I car guess there are several programs that would take you, but I'm not sure which ones. I would recommend applying to a variety of programs at different levels of competitiveness and see where you get in. It's also a good idea to try asking a couple of your profs advice on applying.

  • Thanks! (kinda late since i was focused past 6-7 months on learning to improve my work performance instead of self-study or further grad apps) What do you think of a letter from pure maths prof for 'showing a capacity to learn advanced mathematics' and letter from my boss for 'showing a capacity to learn advanced mathematics' ? I worked closely with a supervisor for past year since graduation, and whatever supervisor has to say is better than anything any of my profs could write for me. – Jack Bauer Jul 30 '17 at 17:18
  • In master's we worked in groups a lot but didn't have close supervision at least not as close as I think is the case for PhD students and their supervisors. So grades in pure maths + teamwork from master's + close supervision from past year at work is going to be my pitch for 2018-9 applications. What do you think? – Jack Bauer Jul 30 '17 at 17:18
  • Kimball, is 'In my experience, undergraduate students do not often prove new things in pure math. I wouldn't even say master's theses often contain new results. There are a few main reasons for this.' the reason for 'in mathematics research experience is not that important for getting into PhD programs (at least in the US)' ? – Jack Bauer Jul 30 '17 at 17:24
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    @JackBauer I updated my answer to address your first 2 questions. For the 3rd, yes, that's the main reason. – Kimball Jul 31 '17 at 4:27
  • Kimball, edit: I meant boss for 'work ethic + motivation'. And of course thanks!!! – Jack Bauer Aug 2 '17 at 15:04
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A UK-based answer: yes, you need the letters. Yes, a letter from a supervisor is worth more than a letter from a module convener (teaching the student as part of a big group) but then it is generally better if this was an advanced class of five as opposed to a Year-One course of 200.

Let me give two examples at the extremes of the range.

I once did have a brilliant student as part of a taught module and he did contribute to lectures by regularly piping up and asking relevant and perceptive questions. He asked me for a letter of recommendation even though I honestly informed him that letters from supervisors carry more weight. I emphasised how exceptional this person was in my experience, and my letter eventually appeared to have helped him get his spot at a top place.

As a PhD course selector, I was also the recipient of hundreds of such letters. They are mostly useless, because of a persistent myth that you are not allowed to say anything negative. (There is of course a difference between slander and an objectively demonstrable weakness, but practically nobody wants to risk trouble.) So you end up mostly ignoring the (often OTT) praises of the student, scouring the letters for any hints of a red flag.

The worst example was a highly notable academic who praised a student to the heavens even though the academic transcript was exceedingly poor, and the project appeared to have been 3 wks spent by the student alphabetising the academic's personal library. This was a recommendation dripping with falseness if not lechery.

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