Lecture 1 : Integers

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Lecture 2 : Divisibility and primes

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Lecture 3 : Infinitude of primes

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Lecture 4 : Division algorithm and the GCD

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Lecture 5 : Computing the GCD and Euclid's lemma

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Lecture 6 : Fundamental theorem of arithmetic

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Lecture 7 : Stories around primes

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

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Lecture 9 : Basic results in congruences

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Lecture 10 : Residue classes modulo n

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Lecture 11 : Arithmetic modulo n, theory and examples

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Lecture 12 : Arithmetic modulo n, more examples

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Lecture 13 : Solving linear polynomials modulo n - I

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Lecture 14 : Solving linear polynomials modulo n - II

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Lecture 15 : Solving linear polynomials modulo n - III

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Lecture 16 : Solving linear polynomials modulo n - IV

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Lecture 17 : Chinese remainder theorem, the initial cases

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

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Lecture 19 : Chinese remainder theorem, more examples

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

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Lecture 21 : Wilson's theorem

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Lecture 22 : Roots of polynomials over ℤp

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Lecture 23 : Euler 𝜑-function - I

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Lecture 24 : Euler 𝜑-function - II

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Lecture 25 : Primitive roots - I

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Lecture 26 : Primitive roots - II

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Lecture 27 : Primitive roots - III

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Lecture 28 : Primitive roots - IV

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Lecture 29 : Structure of Un - I

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Lecture 30 : Structure of Un - II

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Lecture 31 : Quadratic residues

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Lecture 32 : The Legendre symbol

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Lecture 33 : Quadratic reciprocity law - I

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Lecture 34 : Quadratic reciprocity law - II

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Lecture 35 : Quadratic reciprocity law - III

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Lecture 36 : Quadratic reciprocity law - IV

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Lecture 37 : The Jacobi symbol

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Lecture 38 : Binary quadratic forms

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Lecture 39 : Equivalence of binary quadratic forms

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Lecture 40 : Discriminant of a binary quadratic form

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Lecture 41 : Reduction theory of integral binary quadratic forms

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Lecture 42 : Reduced forms up to equivalence - I

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Lecture 43 : Reduced forms up to equivalence - II

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Lecture 44 : Reduced forms up to equivalence - III

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Lecture 45 : Sums of squares - I

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Lecture 46 : Sums of squares - II

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Lecture 47 : Sums of squares - III

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Lecture 48 : Beyond sums of squares - I

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Lecture 49 : Beyond sums of squares - II

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Lecture 50 : Continued fractions - basic results

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Lecture 52 : Good rational approximations

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Lecture 51 : Dirichlet's approximation theorem

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Lecture 53 : Continued fraction expansion for real numbers - I

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Lecture 54 : Continued fraction expansion for real numbers - II

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Lecture 55 : Convergents give better approximations

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Lecture 56 : Convergents are the best approximations - I

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Lecture 57 : Convergents are the best approximations - II

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Lecture 58 : Quadratic irrationals as continued fractions

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Lecture 59 : Some basics of algebraic number theory

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Lecture 60 : Units in quadratic fields: the imaginary case

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Lecture 61 : Units in quadratic fields: the real case

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Lecture 62 : Brahmagupta-Pell equations

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Lecture 63 : Tying some loose ends

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