Lectures related to Number Theory: Operations and Equivalence

Covers the construction of integers through equivalence relations and their properties in mathematics.

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

Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.

Covers basic properties of natural numbers, including order relations and inverses.

Covers the basics of group theory, including definitions, examples, and isometries.

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

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Explores division in rational numbers and the extension of addition from integers.

Explores division and multiplication in rational numbers, emphasizing the concept of multiplying by the inverse.

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

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

Covers the concept of total order relation and properties of real numbers.

Covers the extension of addition and multiplication operations in rational numbers.

Covers the rules of calculation for powers, roots, and more, focusing on positive numbers and integers.

Covers addition properties and operations in the set of integers Z.

Covers fundamental concepts related to integers, including properties of well-ordered sets and the principle of induction.

Explains the importance of parentheses in simplifying mathematical operations and notations.

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

Covers commutative groups and their significance in cryptography.

Covers function composition and integers, including properties and examples.