### Highlighted pages

- The idea of the curl of a vector field

Intuitive introduction to the curl of a vector field. Interactive graphics illustrate basic concepts. - 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. - A line or a plane or a point?

Examples showing how the graph of an equation depends on the underlying dimension, becoming a line or a point or a plane. - Spherical coordinates

Illustration of spherical coordinates with interactive graphics. - Level sets

A introduction to level sets. Illustrates level curves and level surfaces with interactive graphics.

### 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

Illustration of spherical coordinates illustrating the effect of changing each of the three spherical coordinates on the location of a point.

The level curves of an elliptic paraboloid are shown as the intersection of a horizontal plane with the graph.

### 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.