Lectures related to Completing the Square in Quadratic Polynomials

Covers polynomial factorization examples and polynomial division in complex numbers.

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

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Covers the fundamental theorem of algebra, explaining how every polynomial has complex roots.

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Covers the theory and implementation of RST regulators, focusing on factorization of zeros and matrix writing.

Covers the Quadratic Sieve method for integer factorization, emphasizing the importance of choosing the right parameters for efficient factorization.

Covers the design of polynomial regulators using the RST method.

Explores quadratic trinomials, absolute values, Vieta's formulas, and graphical representation of equations.

Covers the integration of simple elements using various techniques to solve integration problems.

Explores the Weierstrass Preparation Theorem for entire functions and the construction of root sequences.

Covers Simpson's rule for numerical integration and its accuracy for polynomial functions.

Covers integration on H_pxH and arithmetic topics, focusing on the Hensel Lemma and the process of finding R and S such that R.S-P=0.

Covers the concepts of compression and prediction using prefix-free codes and distributions.

Explores complex number properties, roots, and polynomial equations in the complex plane.

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

By the instructor Malo Jézéquel explores Möbius transformations and bounded distortion in SL(2, R).

Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.

Covers the determinant of a matrix, factorization, and linear equations with infinite solutions.

Explores groups and numbers, emphasizing the hidden subgroup problem and its complexities in classic and quantum algorithms.