Lectures related to Monodromy Conjecture

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Recurrence Exercise Correction

Covers the correction of an additional exercise on recurrence, demonstrating the step-by-step process.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Improper Integrals: Fundamental Concepts and Examples

Covers improper integrals, their definitions, properties, and examples in two and three dimensions.

Spectral Gap in Markov Chains

Explores the spectral gap in Markov chains and its impact on convergence speed.

Logarithmic Functions: Properties and Convergence

Covers properties of logarithmic functions, series convergence, and the Riemann integral.

Limits of Sequences

Covers the concept of limits of sequences, including definitions, examples, boundedness, and more.

Compact Sets and Convergence

Explains compact sets, convergence, and absolute convergence in real analysis.

Spectral Gap and Mixing Time

Explores spectral gap and mixing time in Markov chains, including their definitions and behavior.

Convergence of Random Walks

Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Eigenvalues and Fibonacci Sequence

Covers eigenvalues, eigenvectors, and the Fibonacci sequence, exploring their mathematical properties and practical applications.

Calculus Foundations: Taylor Series and Integrals

Introduces calculus concepts, focusing on Taylor series and integrals, including their applications and significance in mathematical analysis.

Cauchy-Folgen: Induction

Covers Cauchy sequences, induction, recursive sequences, and convergence in mathematical analysis.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Numerical Analysis: Implicit Schemes

Covers implicit schemes in numerical analysis for solving partial differential equations.

Rigorous Proof of Differential Equations

Covers the rigorous proof of differential equations, emphasizing accuracy and precision.

Generalized Integrals and Convergence Criteria

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.