Analytic Number Theory, as the name suggests, uses tools in real analysis (sequences, series, integrals, etc.) and complex analysis to study facts about primes and functions related to primes. These facts are established thru various computations. There isn’t a whole lot of “theory” floating around – more like nifty tricks and techniques one would utilise to infer useful facts about primes and their properties. If you are interested in number theory, you should definitely check out analytic number theory.
While the prerequisite states that group theory and complex analysis are prerequisites for this course, it uses facts from them only sparingly. Basic number theory is not required to have a head start in this module. Also, the course follows Hildebrant’s Analytic Number Theory course in UIUC closely. Another book that was helpful to me in furnishing some understanding in the earlier chapters is Apostol’s “Introduction to Analytic Number Theory”.
Proofs revolving these topics are dense! So be warned! However, the result are much more important than the proofs.
Assessment-wise 40% CA (Midterm and Homework), 60% finals. Weekly homework where you do 4 out of 6 questions and two midterms – one before recess week and the other one in week 10.
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