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1
The language of mathematics and prompting
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1.1 The art of prompting
1.2 Black box warnings
1.3 Computer algebra (and python)
1.4 Numbers
1.5 Propositional logic
1.6 More on sets
1.7 Ordering numbers
1.8 Proof by induction
1.9 The concept of a function
2
Linear equations
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2.1 One linear equation with one unknown
2.2 Several linear equations with several unknowns
2.3 Gauss elimination
2.4 Polynomials
2.5 Applications of linear equations to polynomials
2.6 Shamir secret sharing
2.7 Fitting data
3
Matrices
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3.1 Matrices
3.2 Linear maps
3.3 Matrix multiplication
3.4 Matrix arithmetic
3.5 The inverse matrix
3.6 The transposed matrix
3.7 Symmetric matrices
4
What is optimization?
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4.1 What is an optimization problem?
4.2 General definition
4.3 Convex optimization
4.4 Linear optimization
4.5 Fourier-Motzkin elimination
4.6 Application in machine learning and data science
5
Euclidean vector spaces
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5.1 Vectors in the plane
5.2 Higher dimensions
5.3 The unreasonable effectiveness of the dot product
5.4 Pythagoras and the least squares method
5.5 The Cauchy-Schwarz inequality
5.6 Special subsets of euclidean spaces
5.7 Continuous functions
5.8 Important and special results for continuous functions
Introduction to Mathematics and Optimization
Niels Lauritzen