# Learning resources

#### Online course material

Our comprehensive set of learning materials sorted by topic. For each topic you'll find a variety of resources. Notes is our course textbook, providing in-depth factual knowledge. They are designed to guide your learning, but they do not limit what you are supposed to know. Slides contain all the course material and they are used as template for the pre-recorded videos. Review contain a list of questions to help you reviewing what you learned in each topic. IPython has a collection of Jupyter notebooks with examples and coding implementation for each topic. For each one of the topics below, you have a collection of PrairieLearn assignments to support your learning: lectures, homework, machine problems group activities.

Since we provide a variety of learning resources, we do not require a textbook for the course. However, in case you need extra reading material, we suggest "Numerical Mathematics and Computing" by Cheney and Kinkaid or "Scientific Computing: An Introductory Survey" by Michael Heath.

## Introduction

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

## Python

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.

## Error & Big-O

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

## Floating Point

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

## Rounding & Cancellation

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

## Taylor Series

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

## Randomness & Monte Carlo Methods

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

## Vectors, Matrices & Norms

The most fundamental form of data in linear algebra.

## Linear System of Equations

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

## Conditioning

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

## Sparse Matrices

Representing large systems with many zeros

## Eigenvalues

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

## Markov Chains

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

## Finite Difference Methods

A numerical approximation for derivatives

## Nonlinear System of Equations

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

## Optimization

Continuously improving a function through its parameters.

## Singular Value Decomposition

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

## Linear Least Squares

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

## Principal Component Analysis

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