Lectures related to Surfaces: The Torus

Space Identification: SO(3)

Explores the identification of the space SO(3) and the topology of SS-space of R₃(R).

Graph and Diagonal

Discusses the graph of a relation and the concept of separation.

Differential Equations: Mathematical Complements

Covers the definition of differential equations and their relation to functions and derivatives.

Topology of Riemann Surfaces

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

Implicit Functions Theorem

Explores the implicit functions theorem and the equation of the tangent plane in a graph.

Optimization Problems: Algebra and Trinomial Equations

Explores optimization problems in algebra and trinomial equations, focusing on maximizing area with fixed perimeters.

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

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Consequences of TBS

Explores the consequences of the Total Bell System (TBS) in a commutative body.

Introduction to Category Theory: Examples

Introduces the theory of categories through examples and discusses the product of categories.

Properties of X/G

Explores the properties of the quotient space X/G when X is compact and sometimes separated.

Belief Propagation: Key Methods and Analysis

Covers Belief Propagation, a key method for both analysis and algorithm.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Analytic Continuation of Zeta Function

Explores the analytic continuation of the zeta function and its relation to holomorphic functions and natural numbers.

Separation Criterion in Recollement

Focuses on a criterion for separability in recollement, demonstrating iron properties and applications in various cases.

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Sets and Functions

Introduces binary relations, functions, and various types of relations in sets.

Material and Energy Balances

Explores material and energy balances in chemical engineering for process optimization and design.

Advanced Physics I

Covers velocity, acceleration, dynamics, moments of inertia, and kinetic energy storage systems.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.