The Bright Side of Mathematics Courses

Manifolds

Syllabus: Manifolds - Part 1 - Introduction and Topology. Manifolds - Part 2 - Interior, Exterior, Boundary, Closure. Manifolds - Part 3 - Hausdorff Spaces. Manifolds - Part 4 - Quotient Spaces. Manifolds - Part 5 - Projective Space. Manifolds - Part 6 -…

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• 2-3 hours worth of material
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• Free Online Course

Linear Algebra

Syllabus: Linear Algebra - Part 1 - Introduction. Linear Algebra - Part 2 - Vectors in ℝ². Linear Algebra - Part 3 - Linear Combinations and Inner Product in ℝ². Linear Algebra - Part 4 - Lines in ℝ². Linear Algebra - Part 5 - Vector Space ℝⁿ. Linear Alg…

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• 1-2 hours worth of material
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• Free Online Course

Complex Analysis

Syllabus: Complex Analysis - Part 1 - Introduction. Complex Analysis - Part 2 - Complex Differentiability. Complex Analysis - Part 3 - Complex Derivative and Examples. Complex Analysis - Part 4 - Holomorphic and Entire Functions. Complex Analysis - Part…

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• 3-4 hours worth of material
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• Free Online Course

Linear algebra (English)

Syllabus: Calculating the kernel of a matrix - An example. Polar form of complex numbers - How to calculate?. Change of basis - transformation matrices. Calculating dimension and basis of range and kernel. LU decomposition - An Example. PLU decomposition…

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• 2-3 hours worth of material
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Distribution theory

Syllabus: Distributions Part 1: Motivation and delta function. Distributions Part 2: Test functions. Distributions Part 3: Convergence for test functions. Distributions Part 4: Space of distributions. Distributions Part 5: Regular Distributions. Distribu…

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• 1-2 hours worth of material
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Probability Theory

Syllabus: Probability Theory - Part 1 - Introduction. Probability Theory - Part 2 - Probability Measures. Probability Theory - Part 3 - Discrete vs. Continuous Case. Probability Theory - Part 4 - Binomial Distribution. Probability Theory - Part 5 - Produ…

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• 2-3 hours worth of material
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Real Analysis

Syllabus: Real Analysis - Part 1 - Introduction.Real Analysis - Part 2 - Sequences and limits.Real Analysis - Part 3 - Bounded sequences and unique limits.Real Analysis - Part 4 - Theorem on limits.Real Analysis - Part 5 - Sandwich theorem.Real Analysis…

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• 10 hours worth of material
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• Free Online Course

Start Learning Mathematics

Syllabus: Start Learning Mathematics. Start Learning Logic - Part 1 - Logical Statements, Negation and Conjunction. Start Learning Logic - Part 2 - Disjunction, Tautology and Logical Equivalence. Start Learning Logic - Part 3 - Conditional, Biconditional…

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• 4-5 hours worth of material
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• Free Online Course

Functional analysis

Syllabus: Functional Analysis - Part 1 - Metric Space.Functional Analysis - Part 2 - Examples for metrics.Functional Analysis - Part 3 - Open and closed sets.Functional Analysis - Part 4 - Sequences, limits and closed sets.Functional Analysis - Part 5 -…

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• 4-5 hours worth of material
• On-Demand
• Free Online Course

Measure Theory

This course covers Sigma algebra, Borel Sigma algebra, measure, Lebesgue integral, Monotone convergence theorem, Fatou's Lemma, Carathéodory's extension theorem, Lebesgue-Stieltjes measures, Radon-Nikodym

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• 5 hours worth of material
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• Free Online Course

Mehrdimensionale Integration

Syllabus: Mehrdimensionale Integration Teil 1 (Satz von Fubini). Mehrdimensionale Integration Teil 2 (Aufgabe 1 - Satz von Fubini). Mehrdimensionale Integration Teil 3 (Substitution, Transformationsformel). Mehrdimensionale Integration Teil 4 ( Aufgabe 2…

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• 3-4 hours worth of material
• On-Demand
• Free Online Course

Vektoranalysis

Syllabus: Vektoranalysis Teil 1 (Wege, parametrisierte Kurven, Bogenlänge, Tangentialvektor, Normalenvektor). Vektoranalysis Teil 2 (Aufgabe 10 - Wege). Vektoranalysis Teil 3 (Aufgabe 11 - Wege). Vektoranalysis Teil 4 (Aufgabe 12 - Bogenlänge). Vektorana…

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• 6 hours worth of material
• On-Demand
• Free Online Course

Mathematik für Ingenieure 3

Syllabus: Mehrdimensionale Integration Teil 1 (Satz von Fubini).Mehrdimensionale Integration Teil 2 (Aufgabe 1 - Satz von Fubini).Mehrdimensionale Integration Teil 3 (Substitution, Transformationsformel).Mehrdimensionale Integration Teil 4 ( Aufgabe 2a -…

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• 21 hours worth of material
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• Free Online Course

Determinanten

Syllabus: Determinanten - Ein Überblick. Determinanten - Teil1 - Determinante in 2 Dimensionen. Determinanten - Teil2 - Determinante als Volumenmaß (Leibniz-Formel). Determinanten - Teil3 - Laplace'sche Entwicklungsformel. Determinante - Entwicklungssatz…

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• 1-2 hours worth of material
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Linear Algebra

Syllabus: Jordan-Normalform Teil 1.Jordan-Normalform Teil 2.Jordan-Normalform Teil 3.Jordan-Normalform Teil 4 (Transformationsmatrix aufstellen).Bestimmung von Eigenwerten und Eigenvektoren einer Matrix.LR-Zerlegung - Beispielrechnung.Determinantenformel…

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• 20 hours worth of material
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• Free Online Course