Animation of the mapping of rectangle by a nonlinear change of variables.
Highlighted pages
- 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. - Parametrized curve and derivative as location and velocity
Description of a parametrization of a curve as the position of a particle and the derivative as the particle's velocity. Illustrated with animated graphics. - 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. - The idea of the curl of a vector field
Intuitive introduction to the curl of a vector field. Interactive graphics illustrate basic concepts.
Recent pages
- A birth-death process
Added April 13, 2022 - A stochastic process introduction
Added April 13, 2022 - An introduction to neural coding and decoding
Added April 3, 2022 - More new items
Highlighted applets
Animation of the mapping of rectangle by a nonlinear change of variables.
Illustration of magnetic bead moving along a helix with tangent vector and vector corresponding to a magnetic field.
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.