### Highlighted pages

- An introduction to parametrized curves

An introduction to how a vector-valued function of a single variable can be viewed as parametrizing a curve. Interactive graphics illustrate the way in which the function maps an interval onto a curve. - Parametrization of a line

Introduction to how one can parametrize a line. Interactive graphics illustrate basic concepts. - 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. - 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 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.

### 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

The dynamics of an undamped pendulum illustrate a two-dimensional state space of a continuous dynamical system.

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.