A basic course in number theory free videos and free material uploaded by IIT Bombay Staff .
Week 1:Factorization of numbers, primes
Week 2:GCD, Euclid’s algorithm, properties of primes
Week 3:Arithmetical functions, examples
Week 4:Dirichlet product, Möbius inversion
Week 5:Congruences, Chinese remainder theorem, primitive roots
Week 6:Quadratic reciprocity law, applications
Week 7:Binary quadratic forms, Gauss’ theory of reduced forms
Week 8:Sums of two squares, sums of four squares
Week 9:Diophantine approximation, theorems of Dirichlet and Liouville
Week 10:Continued fractions, quadratic irrationals
Week 11:Quadratic extensions of rationals, units in the rings of integers
Week 12:Diophantine equations with special reference to Brahmagupta-Pell equation
This course intends to develop the basics of number theory touching upon many essential points such as the prime number theorem, quadratic reciprocity laws, Gauss’ theorem on the classification of binary quadratic forms, Brahmagupta-Pell equations, to quote a few. This course will enable a student to learn more advanced topics in number theory.
INTENDED AUDIENCE :Students with basic knowledge of Mathematics can take this course.
PREREQUISITES :Knowledge of basic group theory and ring theory will be useful but it is not necessary.
INDUSTRIES SUPPORT :None
- 0 Reviews
- 2 Students
- 148 Courses
Write a public review