How to tell my adviser that I want to change our focus?
I'm a PhD student in pure mathematics, so I haven't been in your exact position, but perhaps something close to it.  Nonetheless, allow me to play devil's advocate for a moment.  (Feel free to take all of this with a grain of salt.)


  My approach has always been to understand a topic from the ground up...


I think this is a great attitude.  Being able to go from the foundations to the frontiers of research demonstrates a deep understanding of a subject.  However, I think this approach is also wildly impractical as a young researcher.  Ravi Vakil has written about a different strategy for learning, speaking of "tendrils of knowledge":

'Here's a phenomenon I was surprised to find: you'll go to talks, and hear various words, whose definitions you're not so sure about. At some point you'll be able to make a sentence using those words; you won't know what the words mean, but you'll know the sentence is correct. You'll also be able to ask a question using those words. You still won't know what the words mean, but you'll know the question is interesting, and you'll want to know the answer. Then later on, you'll learn what the words mean more precisely, and your sense of how they fit together will make that learning much easier. The reason for this phenomenon is that mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you'll never get anywhere. Instead, you'll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone; this is much easier to do than learning "forwards".' (Emphasis mine.)

(You can find a similar message in cartoon form here.  Make sure to keep clicking on the images.)

Of course, there is a balance: if you really do not understand the basics of a subject, trying to dive into a research question will be fruitless.


  I know that publications are essential. I want to eventually publish something, but not before I have built my own essential knowledge foundation of our field. Learning the topics thoroughly is more important to me than making a publication, and it seems to me that if one strives to truly understand and advance their field, then publications will come much more easily.


Again, wanting to learn for learning's sake is admirable.  But remember this: You could spend your whole life (and probably more!) studying things that are already known without ever producing anything new.

All right, resigning my post as Lucifer's lawyer, I absolutely think you need to communicate your unhappiness with your advisor.  Just make sure that you aren't overly confrontational.  I think outlining your goals for your last semester and masters program is a great idea, but I'm not sure including a bullet-pointed "what I am looking for in the advisee-adviser relationship" is such a good idea.  Other than that, I am glad to hear that you're open to compromise.

Some advice/questions:

1) Have you ever previously mentioned to your advisor your discontent with your lack of background?  If you haven't said anything yet, for all they know, you're perfectly happy with everything, and this may blindside them a bit.

2) Ask your advisor if you can do a reading course on a topic related to your research.  This way, you will have time to ask questions about the more theoretical aspects of the subject while still moving forward on your research.

3) Does your professor have a research group, or other students working on similar topics?  If so, try turning to them for help when you have questions about fundamentals.  Your peers are sometimes your best resource, and discussing things with your colleagues is sometimes the most effective way to learn something.

4) At my university, students have both a primary and secondary advisor.  I think it's a great system: the secondary can provide another perspective, and can also mediate any potential advisor-advisee conflicts.  Does your university have anything similar?

5) If you're sick and tired of debugging others' code, why not write your own?  My own research is often very computational, and I honestly don't think I really understand an algorithm until I can implement it myself.  That said, there is value in accepting some "black boxes."