Home/Learning resources

- Introduction
- Python
- Error & Big-O
- Floating Point
- Rounding & Cancellation
- Taylor Series
- Randomness & Monte Carlo Methods
- Vectors, Matrices & Norms
- Linear System of Equations
- Conditioning
- Sparse Matrices
- Eigenvalues
- Markov Chains
- Nonlinear System of Equations
- Optimization
- Singular Value Decomposition
- Linear Least Squares
- Principal Component Analysis

Our comprehensive set of learning materials sorted by topic. For each topic you'll find up to
three
types of resources. **Notes** is our course textbook, providing in-depth factual knowledge. Each
section starts with a set of learning objectives. These are designed to help guide your learning,
but they
do not limit what you are supposed to know. **Colab** hosts coding examples demonstrating the
topic's
applications. Alternatively you can view the code repo here. **Lecture
Slides** provide the material used during lectures.

Find out what you are going to learn in this Numerical Methods course.

Python is a powerful, yet simple programming language with a rich library of numerical analysis tools such as Numpy. Python will be a core part of this course

When approximating values, we want to control and bound our errors.

Representing real numbers is one of the most fundamental units of data in computer systems

Floating point operations have finite precision, but we can learn how to predict, control and/or avoid them.

Taylor Series is a method of expanding a function into an infinite sum of its derivatives.

When mathematically approximating a value becomes too difficult, sometimes the best way is to simulate it with raw compute power

The most fundamental form of data in linear algebra.

Many problems can be represented as a linear system of equations.

How much the error of a function's output changes with respect to change in its input

A special set of scalars associated with a linear system of equations

A stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event

A system of two or more equations in two or more variables containing at least one equation that is not linear

Continuously improving a function through its parameters.

All matrix transformations can be described as a rotation, a stretching, and another rotation.

Approximates the solution to a linear system of equations. Often used when a true solution does not exist.

A technique used to emphasize variation and bring out strong patterns in a dataset