Primes in Arithmetic Progression

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Number Theory: Prime Numbers and Modular Arithmetic

Explores prime numbers, modular arithmetic, Wilson's theorem, and complexity analysis.

Primes: Fundamental Theorem and Sieve of Eratosthenes

Explores primes, the Fundamental Theorem of Arithmetic, trial division, the Sieve of Eratosthenes, and Euclid's Theorem.

Local Rings and Minimal Primes

Explores local rings, Noetherian rings, and minimal primes in the context of integral domains.

Class Number Formula

Explores the Class Number Formula in number theory, focusing on Lemmas, Proofs, and a significant theorem.

Complex Numbers: Gauss Numbers

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

Primes and Coprime

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

Number Theory: Modular Exponentiation Examples

Covers examples of modular exponentiation, complexities, Lame's Theorem, Collatz Conjecture, and prime numbers.

Course Overview: Teaser on Course Contents

Offers an overview of propositional and predicate logic, sets, functions, relations, algorithms, Swiss cities, sorting tables, Covid infections, poker hands, and prime numbers.

Characters and Dirichlet's Theorem

Introduces characters over a finite abelian group and explains the proof of the infinitude of primes in arithmetic progressions.

Frobenius Theorems in Number Theory

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.