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Mathematics
Number Theory (Web)
Syllabus
Co-ordinated by :
IIT Guwahati
Available from :
2012-06-29
Lec :
1
Modules / Lectures
Divisibility and Primes
Introduction
Decimal Expansion of a Positive Integer
Euclid's Algorithm
Coprime Integers
Prime Numbers
Prime Number Theorem
Exercise-1
Congruence
Congruence
Linear Congruence
Simultaneous Linear Congruences
System of Congruences with Non-coprime Moduli
Linear Congruences Modulo Prime Powers
Fermat's Little Theorem
Pseudo-primes
Exercise-2
Number Theoretic Functions
Greatest Integer Function
Euler's function
RSA Cryptosystem
Arithmetic Functions
Mobius Function
Dirichlet Product
Exercise-3
Primitive Roots
Units Modulo an Integer
Existence of Primitive Roots for Primes
Primitive Roots for Powers of 2
Exercise-4
Quadratic Residues
Definition and Examples
Gauss Lemma
Quadratic Reciprocity
Quadratic Residues of Powers of an Odd Prime
The Jacobi Symbol
Exercise-5
Binary Quadratic Forms
Definition and Examples .
Discriminant of a Quadratic Form
Proper Representation and Equivalent Forms
Uniqueness of Equivalent Reduced Form
Class Number
Exercise-6
Integers of Special Form
Fermat Primes
Primes Expressible as a Sum of Two Squares
Sum of Three Squares
Exercise-7
Continued Fractions
Finite Continued Fractions
Euler's Rule
Infinite Continued Fractions
Periodic Continued Fractions
Conjugate of a Quadratic Irrational
Continued Fractions of Reduced Quadratic Irrationals
Best Rational Approximation to an Irrational
Pell's Equation
Exercise-8
Riemann Zeta Function
Riemann Zeta Function
Dirichlet Series
Exercise -9
Additional Topics
Lucas Test for Primality
Pollard's Method for Factorization
Fermat's Factorization
Fermat's Conjecture
Bibliography
Index
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