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I am presently working on my undergraduate thesis in mathematics. My work consists mainly of analyzing a handful of sources, internalizing proofs and methods and then fleshing out the rough outline given to me by my advisor. To a large extent I am simply trying to grasp what was done in other sources, and then doing the same thing myself, adding my own twist.

How do I cite or refer to the sources I am using? In which places is it appropriate?

For instance, if I include a theorem from some source, internalize the proof strategy and then formulate a proof without peeking at the source, should I mention the source of the theorem?

I am now halfway done and have only 3 citations.

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    The fact that you are writing an undergraduate thesis is utterly irrelevant. If you use a source, you must cite it. If a result if not originally yours, you must cite its original source (or at least a credible and accessible secondary source). Every time.
    – JeffE
    Commented Aug 2, 2016 at 15:19
  • So when I include a standard theorem from a textbook for example, it is always necessary that I say something along the lines of "The following theorem is taking from [1]: ... " beforehand, right? @JeffE
    – iwriteonbananas
    Commented Aug 2, 2016 at 15:39
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    There's a general exception for textbook-level material, since otherwise you fall down an infinite rabbit hole. However, you should include a sentence like "We use several standard results in algebraic topology; for further background, see Hatcher [5] or Munkres [8]." unless you expect your audience (by default: you six months ago) to be intimately familiar with those results already.
    – JeffE
    Commented Aug 2, 2016 at 15:49
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    Is it acceptable if I preface a subsection by a sentence like "Throughout this subsection we largely follow the account laid out by Hatcher in [5]." so I won't have to cite Hatcher [5] again before every lemma/theorem? @JeffE
    – iwriteonbananas
    Commented Aug 2, 2016 at 16:06

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How do I cite or refer to the sources I am using?

Different institutions/publishers prefer different citation styles, there is a whole range to choose from. Popular ones include IEEE, MLA, Chicago, Elsevier, etc. You ought to refer your thesis writing guidelines as mentioned by your institution or ask your advisor for further clarifications on this one.

In which places is it appropriate?

If you understand why citing is important, you would know that you ought to cite every source you refer. Especially considering that your academic thesis is work you claim as your own, you ought to differentiate between what comes from you and what comes from others.

If I include a theorem from some source, internalize the proof strategy and then formulate a proof without peeking at the source, should I mention the source of the theorem?

Yes, you should. The theorem proof may be yours but the theorem itself isn't. As @JeffE suggested, cite the original source of the theorem, if you could find it. Otherwise, search for another secondary, yet credible and accessible, source of information that would point to your theorem.

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