phd - Do I need recommendation letters from supervisors if I have a master's?

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.

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   if I have a master's?

   
   


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   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

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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:

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  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).

  
  


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  Ask boss for the soft skills parts

  
  
  

Answer

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):

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  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.)

  
  


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  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.