Integers: Sets, Maps, and Principles

This lecture covers the fundamental concepts related to integers, including sets operations, injective and surjective maps, natural numbers, well-ordering principle, induction principle, divisors, prime numbers, Euclid's lemma, greatest common divisor, least common multiple, long division theorem, and the Euclidean algorithm. The instructor explains the uniqueness of prime factorization, the fundamental theorem of arithmetic, and Bézout's theorem. The lecture also introduces the Euler's totient function and its application in finding the number of positive integers coprime to a given integer.