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
