Lectures related to Algebraic Structures and Integers

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

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

Covers selected topics in mathematics, including Taylor approximations and algebraic structures of Z and K[X].

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

Covers the properties of subtraction and the distributivity of multiplication.

Covers Shor's factoring algorithm, aiming to find integer factors efficiently using quantum computation.

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

Covers the analysis of worst time complexity for algorithms and time complexity with real numbers and integers.

Introduces Pollard's rho method for the discrete log problem and finding collisions efficiently in a cyclic group.