NT2 (MSC-Math 2nd)

UNIT-I

Farey sequences, Continued fractions, Approximation of reals by rationals, Pell’s equations, Minkowski’s a theorem in Geometry of Numbers and its application [Scope as in 6 & 7 of ‘Introduction to the Theory of Numbers’, 5th Edition, by Niven, Zuckerman & Montgomery.]

UNIT-II

Partitions [Scope as in Chapter 10 of ‘Theory of Numbers’, 5th Edition, by Niven, Zuckerman & Montgomery], Order of magnitude and average order of arithmetic functions, Euler summation formula, Abel’s Identity, Elementary results on distribution of primes. [Scope as in Chapters 3 & 4 of ‘Introduction to Analytic Number Theory’ by T. M. Apostol.]