Math Insight

Highlighted pages

  • The components of the curl
    Illustration of the meaning behind the components of the curl.
  • 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.
  • An introduction to conservative vector fields
    An introduction to the concept of path-independent or conservative vector fields, illustrated by interactive graphics.
  • 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.
  • Level sets
    A introduction to level sets. Illustrates level curves and level surfaces with interactive graphics.

Recent pages

Highlighted applets

Undamped pendulum
Applet: Undamped pendulum
The dynamics of an undamped pendulum illustrate a two-dimensional state space of a continuous 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.