**1**The language of mathematics and prompting ❯- 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 ❯- 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 ❯- 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? ❯- 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 ❯- 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
**6**Convex functions ❯- 6.1 Strictly convex functions
- 6.2 Why are convex functions interesting?
- 6.3 Differentiable functions
- 6.4 Taylor polynomials
- 6.5 Differentiable convex functions
**7**Several variables ❯- 7.1 Introduction
- 7.2 Vector functions
- 7.3 Differentiability
- 7.4 Newton-Raphson in several variables!
- 7.5 Local extrema in several variables
- 7.6 The chain rule
- 7.7 Logistic regression
- 7.8 3Blue1Brown
- 7.9 Lagrange multipliers
- 7.10 Optimization using the interior and boundary of a subset
**8**The Hessian ❯