Math Insight

Highlighted pages

  • 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.
  • 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.
  • Level sets
    A introduction to level sets. Illustrates level curves and level surfaces with 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.
  • 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.

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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.