To install Cygwin from a Math server Archive:

Open this using a browser: http://math.ucdenver.edu/downloads/cygwin/setup.exe
This will install and run a program which downloads and installs cygwin.
Instructions for running this installer follow:

Click Next after each of the following steps.
0. Read Introduction
1. Select "Download from internet"
2. Set Local Package Directory to /cygwin
3. Select "Direct Connection"
4. Enter "http://math.ucdenver.edu/downloads/cygwin" as the User URL and Add
   (Make sure http://math.ucdenver.edu is selected)
5. Choose what you want to install by clicking on the + and up-down-circle icons
   (wait a few seconds after each click as it takes a while to respond)
6. Wait for download and install to complete