Lectures related to Series and Complex Numbers

Complex Numbers: Operations and Representations

Explores complex numbers, their operations, and representations in Cartesian and polar forms.

Complex Numbers: Definitions and Applications

Explores complex numbers, arguments, modules, and polynomial equations with complex coefficients.

Python Modules and Pandas

Introduces Python modules, scoping, lambdas, and pandas for data manipulation and analysis.

Riemann Sums and Definite Integrals

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Elementary Properties of Complex Numbers

Covers the elementary properties of complex numbers through examples and discusses the regions of the complex plane.

Analysis I: Functions of a Variable

Introduces fundamental concepts of Analysis I, focusing on functions of a variable and numerical sequences.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Analysis I Exam 2022

Covers the correction of a mock exam for Analysis I, focusing on sequences, series, and limits.

Complex Numbers: Module and Conjugate

Covers the manipulation of algebraic laws on complex numbers.

Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Modules and Namespaces

Explores Python modules, program hierarchy, module importing, and namespaces, including variables and scopes within functions.

Free Resolution of Modules

Covers free resolution of modules and projective modules in module theory.

Tensor Product: Bilinear Maps

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Module Theory: Chain Conditions

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

Linear Algebra: Modules and Endomorphisms

Explores modules, endomorphisms, and linear applications in algebra, including A-modules and commutative rings.

Algebraic Structures: Modules and Morphisms

Explores modules, sub-modules, and morphisms in algebraic structures.

Homomorphisms and Projective Resolutions

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Complex Numbers: Sequences, Series in C, exp, sin, cos

Covers complex numbers, sequences, series, and exponential, sine, and cosine functions in the complex plane.

Complex Numbers: Definitions and Properties

Covers the definitions and properties of complex numbers, including the field of complex numbers, the conjugate, the real and imaginary parts, algebraic form, modulus, and argument.