Integers: Sets, Maps, and Principles

Related lectures (27)

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

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

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

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

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

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

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

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

Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

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

Covers the Diffie-Hellman key exchange protocol and the ElGamal public-key cryptosystem.

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

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

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

Introduces deterministic approaches to identify prime numbers and covers algorithms and modular arithmetic for prime number testing.

Explores the Chinese Remainders Theorem, RSA public-key cryptosystem, bijective properties, and key generation for encryption and decryption.

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

Covers function composition and integers, including properties and examples.

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

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