Lectures related to Complex Roots: Conjugate Pairs and Quadratic Equations

Explores polynomials with real coefficients, complex roots, and sequences' properties.

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

The Fundamental Theorem of Algebra

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

Complex Polynomials and Factorization

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

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Factorisation: Polynomials and Theorem

Covers irreducible polynomials, fundamental theorem of algebra, and factorization in complex and real polynomials.

Untitled

Quadratic Forms: Definitions, Examples

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

Linear Algebra: Quadratic Forms and Matrix Diagonalization

Discusses quadratic forms, matrix diagonalization, and their applications in optimization problems.

Linear Combinations and Vector Spaces

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

Polynomials Vector Space

Covers the properties of polynomials vector space and subspaces.

Factorisation: Real Coefficients Examples

Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.

Linear Transformations: Polynomials and Bases

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Complex Numbers: Roots and Polynomials

Covers the properties of complex numbers, including finding roots and factorizing polynomials.

Complex Numbers: Operations and Applications

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

Attack on RSA using LLL

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

Linear Algebra: Abstract Concepts

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Coppersmith's Method: Small Roots of Polynomials Mod N

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

Orthogonal/Orthonormal Bases and Polynomials

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Integral Techniques: Rational Functions

Explores integrating rational functions using decomposition and division techniques with step-by-step examples.