Lectures related to Modular Arithmetic: Understanding RSA Cryptosystem

Modular Arithmetic: Introducing Z/mZ

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Modular Arithmetic: Inverses and Equations

Explores modular arithmetic, emphasizing inverses and equations in Z/mZ, with practical examples and exercises.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Modular Arithmetic: Operations and Properties

Explains modular arithmetic operations and properties, including commutative rings and multiplicative inverses.

Modular Arithmetic: Properties and Examples

Covers modular arithmetic properties, computation examples, and commutative rings.

Number Theory: Division, Remainder, Congruence

Covers number theory, division, remainder, congruence, prime numbers, integer representation, and the Euclidean algorithm.

Algorithms for Big Numbers: Z_n and Orders

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Prime Gaps and Multiplicative Sieve Inequalities

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Number Theory: Modular Arithmetic

Explores modular arithmetic, congruence, and number manipulation in a mathematical context, showcasing the power of modular reduction and the tricks of casting out nines.

Linear Equations and Matrices: Solution Methods, Elementary Operations

Explores solution methods and elementary operations for linear equations and matrices, demonstrating techniques to simplify systems and obtain solutions.

Rudiments of Number Theory

Introduces modulo arithmetic, Euclid's algorithm, and congruence in number theory.

Number Theory: Prime Numbers and Modular Arithmetic

Explores prime numbers, modular arithmetic, Wilson's theorem, and complexity analysis.

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Number Theory: Modular Exponentiation Examples

Covers examples of modular exponentiation, complexities, Lame's Theorem, Collatz Conjecture, and prime numbers.

Modular Arithmetic: Operations and Polynomials

Covers modular arithmetic operations and polynomial calculations modulo N with various examples.

Matrix of Cofactors and Inverse Matrix Formula

Covers the concept of the matrix of cofactors and a formula to calculate the inverse of a matrix.

Arithmetic Functions: Multiplicative Functions and Dirichlet Convolution

Covers multiplicative functions, Dirichlet convolution, and the Mobius function in arithmetic functions.

Binary Operations: Addition and Multiplication

Covers binary operations, including addition and multiplication of integers represented in binary form.

Quotients of Groups by Relations of Equivalence

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.