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Table of Contents
- 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.
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
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
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