Math Insight

Highlighted pages

  • 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.
  • 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.
  • 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 idea of the divergence of a vector field
    Intuitive introduction to the divergence of a vector field. Interactive graphics illustrate basic concepts.
  • Level sets
    A introduction to level sets. Illustrates level curves and level surfaces with interactive graphics.

Recent news

Recent pages

Highlighted applets

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

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.