Day 1: Mathematics for AI

There are two parts to Day 1: Fundamentals of Linear Algebra (morning) and Fundamentals of Calculus (afternoon). In Linear Algebra, we cover vectors and their linear combinations, the dot product, systems of linear equations and orthogonal projections onto a line or onto a plane. In Calculus, we review elementary functions and their composition, the notion of derivative, as well as rules of differentiation, and linear and quadratic approximations of a function at a point. We wrap up with the discussion of the behavior of the function from its derivative.

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Fundamentals of Linear Algebra for AI Fundamentals of Linear Algebra for AI

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Problem Set Fundamentals of Linear Algebra for AI

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Fundamentals of Calculus Fundamentals of Calculus

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Problem Set Fundamentals of Calculus

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Linear Algebra Class Notes Linear Algebra

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Problem Set Notes Linear Algebra

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Problem Set Solution Linear Algebra

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Calculus Lecture Notes Fundamentals of Calculus

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Problem Set Notes Fundamentals of Calculus

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Problem Set Solution Fundamentals of Calculus

Linear Regression Code Objective
Linear Regression Code Functions Linear Algebra

Fast Track: Linear Algebra Source Objective
Vectors and Their Linear Combinations Vectors 1 Vectors and Their Linear Combinations
The Dot Product Dot Product The Dot Product
Solving Problems with Vectors Vectors 2 Solving Problems with Vectors
A System of Linear Equations, $Ax=b$, and Its Matrix $A$ System of Linear Equations A System of Linear Equations, $Ax=b$, and Its Matrix $A$
Matrix Multiplication in Multiple Ways Matrix Multiplication Matrix Multiplication in Multiple Ways
Vector Spaces with Examples Vector Space Vector Spaces with Examples
Projecting onto a Line Projections 1 Projecting onto a Line
Projecting onto a Plane Projections 2 Projecting onto a Plane

Fast Track: Calculus Source Objective
Real Functions of Real Variables Functions 1 Real Functions of Real Variables
Compositions of Functions Functions 2 Compositions of Functions
Elementary Functions Functions 3 Elementary Functions
Limits Limits Limits
Derivative Derivatives Derivative
Rules of Differentiation Differentiation Rules of Differentiation
Behavior of a Real Function of a Real Variable from Its Derivative Derivatives Behavior of a Real Function of a Real Variable from Its Derivative

Additional Material Source Objective
Functions of Two or More Variables Functions Functions of Two or More Variables
Limits Limits Limits
Partial Derivatives Partial Derivatives Partial Derivatives
A Special Plane Special Plane A Special Plane
Differentiability Differentiability Differentiability
The Gradient Gradient 1 The Gradient
The Directional Derivative Directional Derivative The Directional Derivative
The Gradient: Geometric Insight Gradient 2 The Gradient: Geometric Insight
The Hessian Matrix Hessian The Hessian Matrix
Quadratic Approximation Quadratic Approximation Quadratic Approximation
Critical Points and Extrema Critical Points Critical Points and Extrema
Exercises Exercises Exercises