NPTEL : NOC:A Basic Course in Number Theory (Mathematics)

Co-ordinators : Prof. Shripad Garge


Lecture 1 - Integers

Lecture 2 - Divisibility and primes

Lecture 3 - Infinitude of primes

Lecture 4 - Division algorithm and the GCD

Lecture 5 - Computing the GCD and Euclid’s lemma

Lecture 6 - Fundamental theorem of arithmetic

Lecture 7 - Stories around primes

Lecture 8 - Winding up on `Primes' and introducing Congruences'

Lecture 9 - Basic results in congruences

Lecture 10 - Residue classes modulo n

Lecture 11 - Arithmetic modulo n, theory and examples

Lecture 12 - Arithmetic modulo n, more examples

Lecture 13 - Solving linear polynomials modulo n - I

Lecture 14 - Solving linear polynomials modulo n - II

Lecture 15 - Solving linear polynomials modulo n - III

Lecture 16 - Solving linear polynomials modulo n - IV

Lecture 17 - Chinese remainder theorem, the initial cases

Lecture 18 - Chinese remainder theorem, the general case and examples

Lecture 19 - Chinese remainder theorem, more examples

Lecture 20 - Using the CRT, square roots of 1 in ℤn

Lecture 21 - Wilson's theorem

Lecture 22 - Roots of polynomials over ℤp

Lecture 23 - Euler 𝜑-function - I

Lecture 24 - Euler 𝜑-function - II

Lecture 25 - Primitive roots - I

Lecture 26 - Primitive roots - II

Lecture 27 - Primitive roots - III

Lecture 28 - Primitive roots - IV

Lecture 29 - Structure of Un - I

Lecture 30 - Structure of Un - II

Lecture 31 - Quadratic residues

Lecture 32 - The Legendre symbol

Lecture 33 - Quadratic reciprocity law - I

Lecture 34 - Quadratic reciprocity law - II

Lecture 35 - Quadratic reciprocity law - III

Lecture 36 - Quadratic reciprocity law - IV

Lecture 37 - The Jacobi symbol

Lecture 38 - Binary quadratic forms

Lecture 39 - Equivalence of binary quadratic forms

Lecture 40 - Discriminant of a binary quadratic form

Lecture 41 - Reduction theory of integral binary quadratic forms

Lecture 42 - Reduced forms up to equivalence - I

Lecture 43 - Reduced forms up to equivalence - II

Lecture 44 - Reduced forms up to equivalence - III

Lecture 45 - Sums of squares - I

Lecture 46 - Sums of squares - II

Lecture 47 - Sums of squares - III

Lecture 48 - Beyond sums of squares - I

Lecture 49 - Beyond sums of squares - II

Lecture 50 - Continued fractions - basic results

Lecture 51 - Dirichlet's approximation theorem

Lecture 52 - Good rational approximations

Lecture 53 - Continued fraction expansion for real numbers - I

Lecture 54 - Continued fraction expansion for real numbers - II

Lecture 55 - Convergents give better approximations

Lecture 56 - Convergents are the best approximations - I

Lecture 57 - Convergents are the best approximations - II

Lecture 58 - Quadratic irrationals as continued fractions

Lecture 59 - Some basics of algebraic number theory

Lecture 60 - Units in quadratic fields: the imaginary case

Lecture 61 - Units in quadratic fields: the real case

Lecture 62 - Brahmagupta-Pell equations

Lecture 63 - Tying some loose ends