### Highlighted pages

- An introduction to the directional derivative and the gradient

Interactive graphics about a mountain range illustrate the concepts behind the directional derivative and the gradient of scalar-valued functions of two variables. - Introduction to differentiability in higher dimensions

An introduction to the basic concept of the differentiability of a function of multiple variables. Discussion centers around the existence of a tangent plane to a function of two variables. - Subtleties of differentiability in higher dimensions

A description of some of the tricky ways where a function of multiple variables can fail to be differentiable. Example two variable functions are illustrated with interactive graphics. - Introduction to the multivariable chain rule

Introduction to the multivariable chain rule. The basic concepts are illustrated through a simple example. - Parametrization of a line

Introduction to how one can parametrize a line. Interactive graphics illustrate basic concepts.

### Recent pages

- A birth-death process
*Added April 13, 2022* - A stochastic process introduction
*Added April 13, 2022* - An introduction to neural coding and decoding
*Added April 3, 2022* - More new items

### Highlighted applets

Illustration of how the polar coordinate transformation maps a rectangle onto on the Cartesian plane and changes area.

A bacteria population that doubles every time step illustrates a discrete dynamical system.

### Welcome to Math Insight

The Math Insight web site is a collection of pages and applets designed to shed light on concepts underlying a few topics in mathematics. The focus is on qualitative description rather than getting all technical details precise. Many of the pages were designed to be read even before students attend lecture on the topic, so they are intended to be somewhat readable introductions to the basic ideas.

You can browse the pages organized into threads, which are sequences through a subset of pages organized by particular topics. An index can help you find pages discussing a particular term. You can also search through the pages, applets, and image captions. A few pages allow you to change the notation system used to render the mathematics.

We hope Math Insight can help you understand key mathematical concepts. We welcome comments on how we can improve it.