A basic course in number theory

By Prof. Shripad Garge | IIT Bombay

Learners enrolled: 6921

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

Summary

Course Status :	Completed
Course Type :	Elective
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Postgraduate
Start Date :	14 Sep 2020
End Date :	04 Dec 2020
Enrollment Ends :	25 Sep 2020
Exam Date :	20 Dec 2020 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

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

Books and references

1. (Alan Baker) A comprehensive course in number theory

2. (Niven, Zuckerman) An introduction to the theory of numbers

Instructor bio

Prof. Shripad Garge

IIT Bombay

I am an assistant professor at the mathematics department, IIT Bombay. My research interests are in group theory and number theory.

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 us in person at any of the designated exam centres.
•The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
• Date and Time of Exams: 20 December 2020, Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
•Registration url: Announcements will be made when the registration form is open for registrations.
• The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
•Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE:
• Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
• Exam score = 75% of the proctored certification exam score out of 100
•Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75.
•If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
• 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. It will be e-verifiable at nptel.ac.in/noc
•Only the e-certificate will be made available. Hard copies will not be dispatched.

SWAYAM Helpline / Support