A basic course in number theory

A basic course in number theory by Indian Institute of Technology Bombay

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Created by IIT Bombay Staff Last updated Wed, 30-Mar-2022 English


A basic course in number theory free videos and free material uploaded by IIT Bombay Staff .

Syllabus / What will i learn?

Week 1:Factorization of numbers, primes

Week 2:GCD, Euclid’s algorithm, properties of primes

Week 3:Arithmetical functions, examples

Week 4:Dirichlet product, M​öbius 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



Curriculum for this course
0 Lessons 00:00:00 Hours
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Description

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

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Material price :

Free

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