Lectures related to Algebra: Integer Numbers and Principles

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

Covers function composition and integers, including properties and examples.

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

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

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

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

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

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

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

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Covers the basics of proofs, defining sets, and applications between sets.

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

Covers the Euclidean algorithm for GCD calculation and algorithmic complexity analysis.

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

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

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

Introduces fundamental concepts of linear algebra, focusing on sets and operations.

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.