Illustration of the Cartesian coordinates of a movable three-dimensional point
Highlighted pages
- 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. - 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. - Developing an initial model to describe bacteria growth
By analyzing some data and hypothesizing rules for cell division, we develop a discrete dynamical system for the growth of a population of bacteria. - 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 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.
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
Illustration of the Cartesian coordinates of a movable three-dimensional point
Animation of the mapping of rectangle by a nonlinear change of variables.
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.