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+# Mathematics
+
+This is my attempt at digitalizing (and translating) my math notes from uni. It's not finished yet, I'll update it bit by bit when I feel like it
+
+The topics covered in this script will be:
+1. Fundamentals and Notation  
+   1.1 Logic  
+   1.2 Sets and Functions  
+   1.3 Numbers
+
+2. Analysis: Part 1  
+   2.1 Elementary Inequalities  
+   2.2 Sequences and Limits  
+   2.3 Convergence of Series
+
+3. Linear Algebra  
+   3.1 Vector spaces  
+   3.2 Matrices and Gaussian elimination  
+   3.3 The Determinant  
+   3.4 Scalar Product  
+   3.5 Eigenvalue problems
+
+4. Analysis: Part 2  
+   4.1 Limits of Functions  
+   4.2 Differential Calculus
+
+5. Topology in Metric spaces  
+   5.1 Metric and Normed spaces  
+   5.2 Sequences, Series and Limits  
+   5.3 Open and Closed Sets  
+   5.4 ????  
+   5.5 Continuiuty  
+   5.6 Convergence of Function Sequences
+
+6. Differential Calculus for Functions with multiple Variables  
+   6.1 Partial and Total Differentiability  
+   6.2 Higher Derivatives  
+   6.3 Function Sequences and Differentiability  
+   6.4 The Banach Fixed-Point Theorem and the Implicit Function Theorem
+
+7. Measures and Integrals  
+   7.1 Contents and Measures  
+   7.2 Integrals  
+   7.3 Integrals over the real numbers  
+   7.4 ????  
+   7.5 Product Measures and the Fubini Theorem  
+   7.6 The Transformation Theorem
+
+8. Ordinary Differential Equations  
+   8.1 Solution Methods  
+   8.2 The Picard-Lindelöf Theorem  
+   8.3 Linear Differential Equation Systems
+
+9. Integration over Submanifolds  
+   9.1 Line Integrals  
+   9.2 Surface Integrals  
+   9.3 Ingegral Theorems
+
+10. Elements of Complex Analysis  
+   10.1 Complex Differentiability  
+   10.2 Complex Line Integrals  
+   10.3 Identity Theorems and Analytic Continuation  
+   10.4 Laurent Series  
+   10.5 Residue Theorem  
+   10.6 Application: Potential Theory
+
+11. Fourier Transform and Basics of Distribution Theory  
+   11.1 Fourier Transform on L¹(ℝᵈ)  
+   11.2 Fourier Transform on L²(ℝᵈ)  
+   11.3 Tempered Distributions
+
+12. Operator Theory  
+   12.1 Linear Operators  
+   12.2 Dual Spaces  
+   12.3 Hilbert Spaces  
+   12.4 Orthonormal Sets  
+   12.5 Adjoint Operators
+
+13. Spectral Theory  
+   13.1 Spectral Theory of Bounded Linear Operators
+   13.2 Spectral Representation of Bounded Self-Adjoint Operators I
+   13.3 Spectral Representation of Bounded Self-Adjoint Operators II
+   13.4 Compact Linear Operators
+   13.5 Unbounded Linear Operators
+   13.6 Spectral Representation of Unbounded Self-Adjoint Operaotrs
+
+14. Curves in ℝ³
+15. Differentiable Manifolds