Apply to math Ph.D. programs If I were to apply to a Ph.D. program for mathematics and in the application mentioned that my intended field of study would be something in algebra, would the admissions committee be interested in a paper on graph theory that I wrote and gave a talk about at an AMS conference for undergraduate research?  I think I did some good work (for an undergraduate), but I don't know if application reviewers would value work in graph theory for somebody looking to go into an algebra related field. If it matters at all, the paper was on various forms of dominating sets.
Value of having done applied math research when applying to PhD programs in pure math I will be a second year math under-grad in September, and currently doing an internship at applied math research institute. Most probably, I will come up with a research paper at the end of the internship.  However, my interest after my bachelors is to do PhD in pure math from a top math school.My question is this:     Would the admission committee consider my current research since it is in applied math?    In addition, if anyone can suggest me some ideas on how can I bridge the gap between my paper in applied math and my interest in analysis, I would be extremely grateful.  P.S.:  is a related but different question also of mine.
Good books on complex numbers I searched on this site but I found posts asking for books on complex analysis which I guess is not what I want.   I want a book on problems concerning with roots of unity, argand plane, exponential form, inequalities etc. Some examples : , , .  I don't think these types of problems are covered in a analysis book but I don't know. I think I want a book on algebra of complex numbers.   Are these topics covered in analysis book ? If not, please suggests some books on this topic. I guess my question is bit vague, sorry for that. :).      As suggested in the comments I would like to have books similar to .