Lectures related to Analytic Continuation of Zeta Function

Differential Equations: Mathematical Complements

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

Optimization Problems: Algebra and Trinomial Equations

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

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

Analytic Continuation and Uniqueness of Holomorphic Functions

Covers the concept of analytic continuation and the uniqueness of holomorphic functions, including the extension of holomorphic functions and the properties of entire and meromorphic functions.

Implicit Functions Theorem

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

Graph and Diagonal

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

Riemann Zeta Function

Covers the definition and properties of the Riemann Zeta function, including convergence and singularities.

Surfaces: The Torus

Explores the definition of surfaces, focusing on the torus and its construction through various examples and morphic images.

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

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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.

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

Belief Propagation: Key Methods and Analysis

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

Space Identification: SO(3)

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

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

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

Functional Equation of Zeta

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Holomorphic Functions: Cauchy-Riemann Equations and Applications

Discusses holomorphic functions, focusing on the Cauchy-Riemann equations and their applications in complex analysis.