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Lecture
Complex Numbers: Operations and Properties
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Related lectures (34)
Complex Numbers: Definition
Covers the construction and properties of complex numbers, introducing the new constant 'i'.
Fundamental Theorem of Algebra
Covers the Fundamental Theorem of Algebra, complex sequences, convergence, and continuity of functions.
Lie Algebra: Group Theory
Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.
Complex Numbers: Introduction and Properties
Introduces complex numbers to solve unsolvable equations, exploring their properties and relationship with real numbers.
Complex Numbers: Module and Conjugate
Covers the manipulation of algebraic laws on complex numbers.
Mathematics: Analysis and Algebra Overview
Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.
Complement: Monotone Class Theorem
Explains the independence of events and sets in an algebraic context.
Complex Numbers: Roots and Polynomials
Covers the properties of complex numbers, including finding roots and factorizing polynomials.
Definition of Complex Numbers Field
MOOC: Analysis I
MOOC: Analysis I (part 2) : Introduction to complex numbers
Introduces complex numbers and defines their field, emphasizing properties and operations.
Complex exponentials: Oscillations and advantages
Explores the use of complex exponentials to simplify trigonometry and algebra in digital systems.
Geometric Examples
MOOC: Linear Algebra (Part 2)
Explores geometric examples related to linear applications in algebra.
Pushouts in Group Theory: Universal Properties Explained
Covers the construction and universal properties of pushouts in group theory.
Complex Roots: Conjugate Pairs and Quadratic Equations
Explores complex roots, conjugate pairs, and quadratic equations solving strategies.
Analyse I: Summary
Covers real numbers, complex numbers, numerical sequences, series, real functions, function limits, derivatives, Taylor series, integrals, and growth rates of functions.
Group Theory Basics
Covers the basics of group theory, including elements, associativity, identity, inverses, and closure.
Ideals and Representations
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Covers ideals, representations, modules, and maximal ideals in associative algebras.
Representation Theory: Algebras and Homomorphisms
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Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.
Schur's Lemma and Representations
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Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.
Group Algebra: Maschke's Theorem
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Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Complex Numbers: Polar Form
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Covers the polar form of complex numbers and its applications in mathematical calculations.
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