Series and Complex Numbers

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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.