Illustration of a linear transformation mapping the unit cube to a parallelepiped while reversing orientation.
Highlighted pages
- 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. - 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. - Introduction to the multivariable chain rule
Introduction to the multivariable chain rule. The basic concepts are illustrated through a simple example. - 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. - 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.
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 a linear transformation mapping the unit cube to a parallelepiped while reversing orientation.
The level curves of an elliptic paraboloid are shown as the intersection of a horizontal plane with the graph.
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.