Lectures related to Elementary Algebra: Numeric Sets

Prime Numbers and Primality Testing

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Proofs: Logic, Mathematics & Algorithms

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

Fundamental Groups

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

Number Theory: Fundamental Concepts

Covers binary addition, prime numbers, and the sieve of Eratosthenes in number theory.

Complex Numbers: Gauss Numbers

Explores Gaussian integers, prime factorization, and number theory concepts related to prime numbers.

Chinese Remainders & RSA

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Integers: Sets, Maps, and Principles Log in to Mediaspace to watch this video

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Untitled Log in to Mediaspace to watch this video

Hadamard Factorisation Log in to Mediaspace to watch this video

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Introduction to Analysis Log in to Mediaspace to watch this video

Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

Arithmetic Fundamentals: Equivalence and Irreducibility Log in to Mediaspace to watch this video

Covers the fundamental theorem of arithmetic, focusing on equivalence and irreducibility of integers.

Fundamental Solutions Log in to Mediaspace to watch this video

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

Graph Sketching: Connected Components Log in to Mediaspace to watch this video

Covers the concept of graph sketching with a focus on connected components.

Advanced Physics I: Orders of Magnitude Log in to Mediaspace to watch this video

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.

Hermite Normal Form: Computation & Properties Log in to Mediaspace to watch this video

Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.

Quantum Order Finding with QPE Log in to Mediaspace to watch this video

Covers the Quantum Order Finding algorithm using Quantum Phase Estimation (QPE), focusing on Shor's factoring algorithm.

Orthogonality and Least Squares Methods Log in to Mediaspace to watch this video

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.