Lectures related to Euclidean Spaces: Properties and Concepts

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Topology: Exploring Cohomology and Quotient Spaces

Covers the basics of topology, focusing on cohomology and quotient spaces, emphasizing their definitions and properties through examples and exercises.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Matrices and Orthogonal Transformations

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Hilbert Spaces: Orthonormal Systems

Explores Hilbert spaces, orthonormal systems, and the Bessel inequality, emphasizing their properties and significance.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Sequences and Convergence: Understanding Mathematical Foundations

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