Modular Arithmetic: Foundations and Applications

Related lectures (51)

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

Explores modular arithmetic and its role in the RSA cryptosystem for error detection.

Introduces number theory and its essential applications in cryptography.

Explores the Euclidean algorithm, Bézout's identity, extended Euclid algorithm, and commutative groups in mathematics.

Introduces Cartesian product and induction for proofs using integers and sets.

Explores the composition of applications in mathematics and the importance of understanding their properties.

Explores prime numbers and Euclid's Theorem through a proof by contradiction.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Explores the history and concepts of Number Theory, including divisibility and congruence relations.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores the proof of the Prime Number Theorem and its implications in number theory.

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

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

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Discusses optimization techniques, focusing on local and global extrema in functions.

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