Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.
Explores the historical development of approximating ellipses with ovals and the challenges in machining trajectories.
Explores Fubini's theorem in multiple dimensions, demonstrating integration over rectangles and closed unit balls with practical examples.
Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.
Covers the concept of barycentric coordinates and includes quizzes for practice.
Delves into Moller-Plesset Perturbation Theory, discussing energy corrections and wavefunction expansion in quantum chemistry.
Introduces sets, Cartesian product, order importance, and relations on sets.
Explains the construction of basis functions in the Finite Element Method, focusing on local to global mapping and numerical accuracy.
Explains root system classification and fundamental regions in Coxeter groups.
