Lectures related to Linear Recurrence Relations

Advanced Counting: Linear Homogeneous Recurrence Relations and Generating Functions

Explores solving linear homogeneous recurrence relations and generating functions for sequence formulas.

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Correlations of the Liouville function

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

Linear Algebra: Abstract Concepts

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

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Cyclic Subspace Decomposition

Explores minimal annihilating polynomials and cyclic invariant subspaces, showcasing their practical applications through matrix computations.

Stein Algorithm: Polynomial Identity Testing

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

Fibonacci numbers and the golden ratio

Explores the Fibonacci sequence, identities, golden ratio, and explicit formulas.

Eigenvalues and Minimal Polynomial

Explores eigenvalues and minimal polynomial, emphasizing their importance in linear algebra.

Sequences: Induction Method

Covers sequences, induction method, Fibonacci, Bernoulli's inequality, and binomial formula.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Division Polynomials: Theorems and Applications

Explores division polynomials, theorems, spectral values, and minimal polynomials in endomorphisms and vector spaces.

Real Analysis: Sequences and Limits

Covers real sequences, induction, limits, and convergence in mathematical analysis.

Integration of CnR Class Functions

Explains the integration of Taylor series for CnR class functions.

Minimal Polynomials: Uniqueness and Division

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Polynomial Identity Testing

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

Polynomials: Operations and Properties

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

Normal Ordered Product And Wick Theorem

Covers normal ordered product, Wick's theorem, creation and destruction fields, and efficient computation methodology.

System Equivalence

Explores system equivalence, state-space representation, transfer functions, and Euclidean rings, emphasizing unimodular matrices and their properties.

Complex Roots and Polynomials

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