### Highlighted pages

- An introduction to parametrized curves

An introduction to how a vector-valued function of a single variable can be viewed as parametrizing a curve. Interactive graphics illustrate the way in which the function maps an interval onto a curve. - The idea behind Stokes' theorem

Introduction to Stokes' theorem, based on the intuition of microscopic and macroscopic circulation of a vector field and illustrated by interactive graphics. - The idea behind Green's theorem

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

Introduction to the cross product with a focus on its basic properties. Includes an interactive graphic to illustrate these properties of the cross product. - Subtleties about divergence

Counterexamples illustrating how the divergence of a vector field may differ from the intuitive appearance of the expansion 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

- The standard unit vectors

The standard unit vectors are the vectors of length one that point along the positive coordinates axes.*Added March 15, 2014* - The zero vector

The zero vector is the unique vector having zero length. The direction of the zero vector is undefined.*Added March 15, 2014* - The right hand rule for determining orientations in three dimensions
*Added March 15, 2014* - More new items

### Highlighted applets

Changing a surface doesn't change the surface integral of the curl of a vector field as long as the boundary remains fixed.

Demonstration of the effect of applying a function repeatedly to a given starting value.

### 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.