Registrations are invited for Online Basic Course in Number Theory by NPTEL and IIT Bombay. The last date of registration is August 7, 2023.

About NPTEL

The National Programme on Technology Enhanced Learning (NPTEL), a project funded by the Ministry of Human Resource Development, provides e-learning through online Web and Video courses in Engineering, Sciences, Technology, Management and Humanities.

About IIT Bombay

The Indian Institute of Technology Bombay is a public research university and technical institute in Powai, Mumbai.

Course Details

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.

Course Layout

  • 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.

Eligibility

Students with basic knowledge of Mathematics can take this course.

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Prerequisites

Knowledge of basic group theory and ring theory will be useful but it is not necessary.

Course Certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by them in person at any of the designated exam centres. The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Certificate will have your name, photograph and the score in the final exam with the breakup. It will have the logos of NPTEL and IIT Bombay.

Date and Time of Exam

29 October, 2023 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

How to Register?

Interested students can register online via this link.

Click here to view the official notification for Online Basic Course in Number Theory by NPTEL and IIT Bombay.