A Basic Course In Number Theory

Explore and learn the basics of number theory with this course

IIT Bombay and NPTEL

About the Course

This 12-week comprehensive course covers the basics of number theory, touching on essential topics such as the prime number theorem, quadratic reciprocity laws, Gauss's theorem on the classification of binary quadratic forms, and Brahmagupta-Pell equations. Designed to provide a solid foundation, the course will enable students to understand fundamental concepts and theorems in number theory. By the end of the course, students will have the knowledge and skills necessary to pursue more advanced topics in the field, equipping them for further academic study or research in mathematics.

Table Of Content

1.What You Will Learn?

2.Who Should Go For It?

3.Points to Note

4.Summary

What You Will Learn?

The course provides a comprehensive curriculum to dive into various aspects of number theory. Here's a glimpse of the key topics covered:

Factorization of numbers, primes

GCD, Euclid’s algorithm, properties of primes

Arithmetical functions, examples,

Dirichlet product, Möbius inversion

Congruences, Chinese remainder theorem, primitive roots,

Quadratic reciprocity law, applications

Binary quadratic forms, Gauss’ theory of reduced forms

Sums of two squares, sums of four squares

Diophantine approximation, theorems of Dirichlet and Liouville

Continued fractions, quadratic irrationals

Quadratic extensions of rationals, units in the rings of integers

Diophantine equations with special reference to Brahmagupta-Pell equation

Who Should Go For It?

It is designed for individuals with a foundation in specific areas to ensure they can grasp the concepts effectively and will be an ideal choice for those undergraduate students who wish to understand and apply their knowledge of:

Mathematics enthusiasts

Undergraduate mathematics students

Graduate students in mathematics or related fields

Mathematics educators

Professionals in STEM fields

Points To Note

This free course offers a fantastic opportunity to gain valuable knowledge in number theory.

It prepares mathematics enthusiasts for advanced and exciting career opportunities.

The course provides high-quality video lectures to thoroughly enhance the learning experience.

Depending on their final score, students can earn one of four certificates: Gold, Silver, Elite, or Completed.

Summary

Field of Study:	A Basic Course In Number Theory
Type:	Free Course
Duration:	12 Weeks
Mode of Learning:	Online
Average Salary Offered:	The average salary offered in this field ranges from ₹ 6 LPA to ₹ 25 LPA depending upon your skills, experience, and level of knowledge.
Employment Roles:	Data Scientist Quantitative Analyst Cryptographer Software Engineer (Specializing in Security) Research Scientist

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