Lectures related to Complexity of Algorithms: Big-O

Covers the Big-O notation to analyze algorithm efficiency and provides examples of polynomial and factorial function estimates.

Covers algorithmic complexity and travel time analysis, focusing on measuring the time taken by algorithms and evaluating their performance.

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Explains Big-O notation for algorithm complexity and polynomial growth rates.

Covers proofs of Big-O using witnesses and rules to analyze algorithm complexity.

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

Explores finite dimensional spaces, covering extraction process, bases generation, and space completion.

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Explores algorithm correctness, worst-case complexity analysis, and efficiency comparison based on input size.

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Explores algorithmic complexity, comparing growth rates using Theta notation and characterizing different complexity classes.

Analyzes the growth of functions to understand algorithm complexity and efficiency.

Covers Coppersmith's method for finding small roots of polynomials modulo N efficiently.

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Explores the process of division euclidienne in polynomials, emphasizing the importance of polynomial degrees during operations.

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

Explores polynomial operations, properties, and subspaces in vector spaces.

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.