What factors do I consider before deciding to ask my summer research guide for a recommendation for grad school? I've currently finished two years of undergraduate study in physics. I'm at the end of a close to two month summer research program in math, at one of the best universities in my country. While I'd applied for a mathematical physics type project, the problem I was assigned has to do more with math and my job is to make a program in order to understand (the outcome of) this problem. My background in mathematics is not good, since the way it works where I study is that there is an extremely small math component in a physics degree and some extremely important concepts in math were excluded from this math component. While I have been studying independently, my course is generally lacking in rigour and depth in coursework so there always ends up being a lot of independent study that I need to do. 

I wish to apply for a Master's program in Physics once I complete my undergrad (I'm doing a three year degree) and I'm considering applying to places in the UK and/or Europe. My background in math and my never having had formal education in CS certainly put me at a disadvantage during this internship. However, I am unable to decide if I should be asking this professor for a letter of recommendation in case my applications require one from a summer research guide or someone in such a position. 


This is the only such research internship that I will be doing before applications begin (which happen in 2 months) so I do not have the option of asking anyone else for this specific position. 
I'm also not sure how having only one summer research experience, and that too not in physics, plays out while I apply for a Master's in physics. 
I'm also quite disillusioned at this point regarding just going forward with physics itself because it seems like I already have heaps and heaps of catching up to do and I'm feeling extremely overwhelmed and unsure of whether this is something that I'm good enough to do. I've always wanted to do physics and I enjoy learning and I understand that this is simply one summer, but I am quite anxious at this point. 


I'm unsure of what to do, specifically regarding the recommendation. Any help would be greatly appreciated. Thanks.
I am unable to decide if I should be asking this professor for a letter of recommendation


Of course you should be asking!

Specifically, you should be asking whether this professor is willing to write you a strong letter of recommendation. The word “strong” (or a similar synonym) is crucial here. You want to make it clear that a weak letter may do more harm than good, and you’d much rather receive honest negative feedback now, face to face, while you still have some time to improve, than to risk spoiling your application.

Stop trying to read the professor’s mind.  Stop trying to imagine all the impostor-syndrome-inspired weaknesses that the professor could write about. Every applicant has weaknesses.  Just ask.


  unsure of whether this is something that I'm good enough to do


Do not listen to the Impostor Syndrome. There is no such thing as being good enough; what matters is what you do.

And what you are doing is pursuing an internship that addresses the gaps you perceive in your own background. You see a gap in formal CS preparation (even though that preparation is rare among programmers, and even rarer among physics students), but you are addressing it by learning to program anyway. You see gaps in your mathematical background, but you are pursuing a mathematics internship that requires you to do a lot of independent study.  You are deliberately working outside your comfort zone to strengthen your background—of course you feel overwhelmed!

In short, you’re acting exactly like a researcher.

I agree with Buffy. From out here, it looks like you’ll be fine. Keep up the good work!