Lectures related to Elementary Algebra: Numeric Sets

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

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.

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Integers: Sets, Maps, and Principles

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

Proofs: Logic, Mathematics & Algorithms

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

Hadamard Factorisation

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

Fundamental Groups

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

Arithmetic Fundamentals: Equivalence and Irreducibility

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

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Prime Numbers: Euclid's Theorem

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

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.

Composition of Applications in Mathematics

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

Chinese Remainders & RSA

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

Proofs: Contraposition vs. Contradiction

Covers the concepts of contraposition and contradiction in proofs.

Introduction to Analysis

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

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.

Number Theory: Greatest Common Divisor and Prime Factorization

Introduces greatest common divisor, prime factorization, and the Euclidean Algorithm.

Number Theory: GCD and LCM

Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.