Media Storage Type : DVD-ROM
NPTEL Course Name : Number Theory
NPTEL Subject Matter Expert : Dr. Anupam Saikia
NPTEL Co-ordinating Institute : IIT Guwahati
NPTEL Lecture Count : 60
Lecture Titles:
Lecture 1 - Introduction
Lecture 2 - Decimal Expansion of a Positive Integer
Lecture 3 - Euclid's Algorithm
Lecture 4 - Coprime Integers
Lecture 5 - Prime Numbers
Lecture 6 - Prime Number Theorem
Lecture 7 - Congruence
Lecture 8 - Linear Congruence
Lecture 9 - Simultaneous Linear Congruences
Lecture 10 - System of Congruences with Non-coprime Moduli
Lecture 11 - Linear Congruences Modulo Prime Powers
Lecture 12 - Fermat's Little Theorem
Lecture 13 - Pseudo-primes
Lecture 14 - Greatest Integer Function
Lecture 15 - Euler's function
Lecture 16 - RSA Cryptosystem
Lecture 17 - Arithmetic Functions
Lecture 18 - Mobius Function
Lecture 19 - Dirichlet Product
Lecture 20 - Units Modulo an Integer
Lecture 21 - Existence of Primitive Roots for Primes
Lecture 22 - Primitive Roots for Powers of 2
Lecture 23 - Definition and Examples
Lecture 24 - Gauss Lemma
Lecture 25 - Quadratic Reciprocity
Lecture 26 - Quadratic Residues of Powers of an Odd Prime
Lecture 27 - The Jacobi Symbol
Lecture 28 - Definition and Examples
Lecture 29 - Discriminant of a Quadratic Form
Lecture 30 - Proper Representation and Equivalent Forms
Lecture 31 - Uniqueness of Equivalent Reduced Form
Lecture 32 - Class Number
Lecture 33 - Fermat Primes
Lecture 34 - Primes Expressible as a Sum of Two Squares
Lecture 35 - Sum of Three Squares
Lecture 36 - Finite Continued Fractions
Lecture 37 - Euler's Rule
Lecture 38 - Infinite Continued Fractions
Lecture 39 - Periodic Continued Fractions
Lecture 40 - Conjugate of a Quadratic Irrational
Lecture 41 - Continued Fractions of Reduced Quadratic Irrationals
Lecture 42 - Best Rational Approximation to an Irrational
Lecture 43 - Pell's Equation
Lecture 44 - Riemann Zeta Function
Lecture 45 - Dirichlet Series
Lecture 46 - Lucas Test for Primality
Lecture 47 - Pollard's Method for Factorization
Lecture 48 - Fermat's Factorization
Lecture 49 - Fermat's Conjecture
Lecture 50 - Exercise-1
Lecture 51 - Exercise-2
Lecture 52 - Exercise-3
Lecture 53 - Exercise-4
Lecture 54 - Exercise-5
Lecture 55 - Exercise-6
Lecture 56 - Exercise-7
Lecture 57 - Exercise-8
Lecture 58 - Exercise-9
Lecture 59 - Bibliography
Lecture 60 - Index