Lectures related to Modular Arithmetic: Inverses and Equations

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

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.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Covers commutative groups and their significance in cryptography.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

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

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

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

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores the Chinese Remainders Theorem, RSA public-key cryptosystem, bijective properties, and key generation for encryption and decryption.

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

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