Lectures related to Constructive analysis

Crystallography: Describing Periodic Structures

Covers crystallography, lattice structures, vectors, and diffraction patterns.

Lagrange Theorem: Applications and Proofs

Covers the application and proof of the Lagrange theorem in group theory.

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

Logical Structure: Choice and Bar Induction Principles

Covers the logical structure of principles equivalent to choice and bar induction, focusing on generalized dependent choice and its implications in mathematics.

Local Lipschitz Functions

Explores locally Lipschitz functions, discussing differentiability, unique solutions, and function reduction.

Generalized Integral: Comparison Criteria and Taylor Series

Explores series convergence criteria, generalized integrals, and Taylor series applications.

Architectural Narratives: Designing Crematoria and Their Contexts

Covers the architectural design of crematoria, focusing on their contextual and emotional significance.

Logical Formulas and Types: Understanding the Kerry Howard Isomorphism

Explores the Kerry Howard Isomorphism, translating logical propositions into types and terms, with a focus on proof by induction and exam preparation.

Derivability and Continuity

Explores continuity, derivability, and linear approximation in mathematical analysis.

Open Balls and Topology in Euclidean Spaces

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Implicit Functions Theorem

Explores the Implicit Functions Theorem and properties of hypersurfaces and matrices.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Injectivity: Sufficient Conditions

Explores the conditions for injectivity in mathematical functions, with detailed examples and proofs.

Cauchy-Folgen: Induction

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

Convergence of Sequences in Multivariable Analysis

Covers the convergence of sequences in multivariable analysis, including definitions, properties, and examples in higher dimensions.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Comparison Criterion: Convergence and Divergence

Explores the comparison criterion for series convergence and divergence, with proofs and examples.

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.