### Highlighted pages

- The idea of the divergence of a vector field

Intuitive introduction to the divergence of a vector field. Interactive graphics illustrate basic concepts. - 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. - 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. - Parametrization of a line

Introduction to how one can parametrize a line. Interactive graphics illustrate basic concepts. - The idea behind Green's theorem

Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field.

### Recent news

Redesigned for small screens

by Duane Q. Nykamp on May 31, 2012Interactive Gallery of Quadric Surfaces

by Duane Q. Nykamp on March 14, 2012- More recent news

### Recent pages

- Basic Programming
*Added July 26, 2016* - Plotting Graphs
*Added July 26, 2016* - Vector Creation
*Added July 26, 2016* - More new items

### Highlighted applets

The angles of a stick figure form a nine-dimensional vector determining the stick figure's configuration.

Illustration of a linear transformation mapping the unit cube to a parallelepiped while reversing orientation.

### 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.