Arithmetic Fundamentals: Equivalence and Irreducibility

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

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

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

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

Covers Lenstra's Algorithm for integer factorization, which efficiently computes prime factors of an integer.

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

Covers integers, rationals, logic, proof techniques, functions, and relations using examples and truth tables.

Explores reciprocity, equivalence, and proof techniques in linear algebra, emphasizing logical reasoning and mathematical rigor.

Covers prime numbers, unique decomposition of natural numbers into prime factors, and practical implications for calculations.

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