Lectures related to Complex Numbers: Gauss Numbers

Elementary Algebra: Numeric Sets

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

Arithmetic Fundamentals: Equivalence and Irreducibility

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

Primes and Coprime

Explores prime numbers, coprime integers, and their properties in number theory.

Algebraic Structures: Groups and Rings

Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.

Integers: Sets, Maps, and Principles

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

Number Theory: Greatest Common Divisor and Prime Factorization

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

Number Theory: Fundamental Concepts

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

Number Theory: GCD and LCM

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

Number Theory: GCD and LCM

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

Number Theory: History and Concepts

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

Prime Numbers and Primality Testing

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

Shor's Factoring Algorithm

Covers Shor's factoring algorithm, aiming to find integer factors efficiently using quantum computation.

Integers: Well Ordering and Induction

Explores well ordering, induction, Euclidean division, and prime factorization in integers.

Shor's algorithm: factoring integers

Covers the basics of Shor's algorithm for factoring integers and the steps involved in the quantum algorithm.

Cartesian Product and Induction

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

Integer Factorization: Methods and Algorithms

Explores methods and algorithms for integer factorization, including testing for B smoothness and computing small primes.

Prime Numbers: Finding and Testing

Covers the definition of a function to determine if a given number is prime.

Number Theory: Division, Remainder, Congruence

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

Number Theory: Operations and Equivalence

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

Factoring Polynomials: Complexity and Algorithms

Delves into the complexity of factoring polynomials and the implications for security.