Lectures related to Invariance of Domain

Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Power of a Point in Geometry

Explores the power of a point outside a circle and its practical applications.

Geometry: Eulerian Circuits

Explores Eulerian circuits through the Königsberg bridges problem, leading to the development of graph theory and topology.

Open Balls and Topology in Euclidean Spaces

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

Circle Orthogonal & Poincaré Disk

Covers circle orthogonal and Poincaré disk concepts in geometry.

Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Structural Design: Concepts and Innovations

Explores fundamental aspects of structural design, emphasizing safety and comfort in buildings through factors like loads, supports, materials, and innovative designs.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

Inversion & Family of Orthogonal Circles

Explores inversion, orthogonal circles, unique projective, and non-constructible figures in geometry.

Topology & Modern Symmetry

Delves into topology, homomorphism, and their practical implications on CAD software.

Topology: Homeomorphisms

Covers the concept of homeomorphisms in topology, focusing on functions that preserve topological properties.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Structural Design Principles: Key Considerations and Examples

Covers the key principles of structural design and their implications for architects.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Recognizing a Quotient

Discusses the recognition of a quotient in topology and the properties of the quotient topology.

Structural Analysis: Reticulated Systems and Their Equilibrium

Covers the principles of structural analysis for reticulated systems, focusing on equilibrium, force diagrams, and the modeling of trusses and cables.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.