Basic Number Theory - MA523 (Fall 2016)


The syllabus for this course reads as follows: Infinitude of primes, discussion of the Prime Number Theorem, infinitude of primes in specific arithmetic progressions, Dirichlet's theorem (without proof). Arithmetic functions, Mobius inversion formula. Structure of units modulo n, Euler's phi function. Congruences, theorems of Fermat and Euler, Wilson's theorem, linear congruences, quadratic residues, law of quadratic reciprocity. Binary quadratics forms, equivalence, reduction, Fermat's two square theorem, Lagrange's four square theorem. Continued fractions, rational approximations, Liouville's theorem, discussion of Roth's theorem, transcendental numbers, transcendence of e and π. Diophantine equations - Brahmagupta's equation (also known as Pell's equation), Fermat's method of descent, discussion of the Mordell equation.

Classes are held on Mondays and Thursdays in LT-203 from 2pm to 3.30pm. All are welcome.