Learn · A Basic Course in Number Theory
Lecture 54 of 63Week 11
Lecture 54 : Continued fraction expansion for real numbers - II
Prof. Shripad Garge · IIT Bombay
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All the lectures
- 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