Lecture 1 - Abelian Groups - I
Lecture 2 - Abelian Groups - II
Lecture 3 - Abelian Groups - III
Lecture 4 - Abelian Groups - IV
Lecture 5 - Abelian Groups - V
Lecture 6 - Abelian Groups - VI
Lecture 7 - Commutative Rings - I
Lecture 8 - Commutative Rings - II
Lecture 9 - Commutative Rings - III
Lecture 10 - Chinese Reminder Theorem
Lecture 11 - Fermat's Little Theorem and Wilson's Theorem
Lecture 12 - Prime ideals and maximal ideals
Lecture 13 - Ideals in a PID
Lecture 14 - Ideals in a UFD
Lecture 15 - Gauss Lemma
Lecture 16 - Field Extensions
Lecture 17 - Finite Fields
Lecture 18 - Multiplicative groups of finite fields
Lecture 19 - Legendre Symbol
Lecture 20 - Quadratic Reciprocity
Lecture 21 - Zero sets of polynomials
Lecture 22 - Ring of quadratic integers - I
Lecture 23 - Ring of quadratic integers - II
Lecture 24 - Gaussian integers
Lecture 25 - Ring of quadratic integers - III
Lecture 26 - Ring of quadratic integers - IV
Lecture 27 - Ideal class group of quadratic fields
Lecture 28 - Binary quadratic forms
Lecture 29 - Binary quadratic forms and ideal class group of imaginary quadratic fields - I
Lecture 30 - Binary quadratic forms and ideal class group of imaginary quadratic fields - II
Lecture 31 - Binary quadratic forms and ideal class group of imaginary quadratic fields - III
Lecture 32 - Binary quadratic forms and ideal class group of imaginary quadratic fields - IV
Lecture 33 - Units in the rings of quadratic integers
Lecture 34 - Integral solutions of the equation 𝑥 2 - 2𝑦 2 = 1
Lecture 35 - Dirichlet's approximation theorem
Lecture 36 - Brahmagupta - Pell's equation
Lecture 37 - Congruent Numbers - I
Lecture 38 - Congruent Numbers - II
Lecture 39 - The n = 4 case of the Fermat's Last Theorem
Lecture 40 - Congruent Numbers and Elliptic Curves
Lecture 41 - Sum of two squares theorem
Lecture 42 - Sum of four squares theorem
Lecture 43 - Sum of integer cubes
Lecture 44 - Rational cube sum problem
Lecture 45 - Affine and Projective Spaces - I
Lecture 46 - Affine and Projective Spaces - II
Lecture 47 - Elliptic Curves - I
Lecture 48 - Elliptic Curves - II
