The Bright Side of Mathematics Courses

Manifolds

Explore key concepts in topology and geometry, including Hausdorff spaces, quotient spaces, and smooth structures, to gain a comprehensive understanding of manifolds.

• YouTube
• 2 hours 30 minutes
• On-Demand
• Free Video

Linear Algebra

Explore vectors, linear combinations, and subspaces in ℝ² and ℝⁿ. Gain a solid foundation in key linear algebra concepts through clear explanations and practical examples.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

Complex Analysis

Explore complex analysis fundamentals, including differentiability, holomorphic functions, Cauchy-Riemann equations, power series, and complex integration, enhancing mathematical understanding.

• YouTube
• 3 hours 30 minutes
• On-Demand
• Free Video

Linear Algebra

Comprehensive exploration of advanced linear algebra concepts, including matrix operations, complex numbers, decompositions, and Jordan Normal Form, with practical examples and calculations.

• YouTube
• 2 hours 30 minutes
• On-Demand
• Free Video

Distribution Theory

Explore the foundations of distribution theory, covering key concepts from delta functions to coordinate transformations in mathematical analysis.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

Probability Theory

Comprehensive exploration of probability theory, covering key concepts from basic measures to advanced topics like random variables and distribution functions.

• YouTube
• 2 hours 30 minutes
• On-Demand
• Free Video

Real Analysis

Comprehensive exploration of real analysis, covering sequences, limits, series, functions, continuity, differentiation, integration, and fundamental theorems of calculus.

• YouTube
• 10 hours
• On-Demand
• Free Video

Start Learning Mathematics

Comprehensive introduction to mathematical foundations, covering logic, set theory, number systems, real numbers, and complex numbers with a focus on rigorous definitions and proofs.

• YouTube
• 4 hours 30 minutes
• On-Demand
• Free Video

Functional Analysis

Comprehensive exploration of functional analysis, covering metric spaces, Banach spaces, Hilbert spaces, operators, and spectral theory, with detailed examples and key theorems.

• YouTube
• 4 hours 30 minutes
• On-Demand
• Free Video

Measure Theory

Comprehensive exploration of measure theory, covering sigma algebras, Lebesgue measures, integrals, convergence theorems, and advanced concepts like product measures and Fubini's theorem.

• YouTube
• 5 hours
• On-Demand
• Free Video

Mehrdimensionale Integration

Umfassende Einführung in mehrdimensionale Integration, einschließlich Satz von Fubini, Transformationsformel, Symmetrieargumente und Anwendungen in der Vektoranalysis. Praktische Übungen zur Berechnung von Flächen und Volumina.

• YouTube
• 3 hours 30 minutes
• On-Demand
• Free Video

Vektoranalysis

Umfassende Einführung in die Vektoranalysis: Von Kurven und Flächen bis zu Integralsätzen. Praktische Übungen vertiefen das Verständnis komplexer mathematischer Konzepte.

• YouTube
• 6 hours
• On-Demand
• Free Video

Mathematik für Ingenieure 3

Umfassende Einführung in mehrdimensionale Integration und Vektoranalysis für Ingenieure, mit Fokus auf praktische Anwendungen und Problemlösungen in der höheren Mathematik.

• YouTube
• 21 hours
• On-Demand
• Free Video

Determinanten

Umfassende Einführung in Determinanten: Definition, Berechnung in 2D, Volumeninterpretation, Leibniz-Formel und Laplace-Entwicklung mit praktischen Beispielen.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

Linear Algebra

Umfassende Einführung in die lineare Algebra mit Schwerpunkt auf Matrizen, Determinanten, Eigenwerte und komplexe Zahlen. Praktische Anwendungen und Übungen vertiefen das Verständnis.

• YouTube
• 20 hours
• On-Demand
• Free Video