The Calculus Tutorial Page from Harvey Mudd College.
The Taylor Series entry from Wolfram MathWorld.
There are many options available for doing the kind of calculations and graphical analyses that we use in this course. I have the most experience with R and Matlab, though I use Mathematica some as well.
The R Project for Statistical Computing. R is a statistical programming language with fantastic graphics. R makes it easy to do all the matrix calculations we use. Best of all, it's free!
Matlab. In my experience, Matlab is the best platform for doing matrix calculations and numerically solving differential equations. It also makes very nice graphics, though I prefer the graphics in R. De gustibus non dispudantum est. While I have certainly never done a rigorous survey, my sense is that most people working on life history theory use Matlab. Matlab is (expensive) commercial software. However, Stanford maintains a site license and there is a very affordable student version available at the bookstore.
Mathematica. Mathematica's specialty is symbolic calculation. It can be very handy for things like checking your algebra. The graphics are nice, but I prefer those of the previous two applications. Because of its excellence in symbolic calculation, Mathematica can seem a little temperamental for beginners. Mathematica is also (expensive) commercial software. However, Stanford maintains a site license and there is a very affordable student version available at the bookstore.
Maple. Maple is another package for doing symbolic mathematical calculations. Alan Rogers uses Maple and has some excellent notes available on his website using the software for evolutionary ecology. My sense is that most mathematical epidemiologists use Maple (again, based on primarily anecdotal evidence).
The place to start is the R-Project home page. CRAN is where you download R and get all the packages and other goodies.
Sometimes searching for help on R can be difficult because the letter "R" can be found on many pages. Rseek can help you search the internets for all that R goodness and wisdom.
R for MacOS Developer's Page. Bleeding-edge builds.
A tool that I find absolutely critical is ESS ("Emacs Speaks Statistics"). ESS is an add-on package for emacs text editors such as GNU Emacs and XEmacs. I could wax poetic about the benefits of using ESS. The main cost is that you have to use/know Emacs, a text editor that can seem a little strange to the unitiated. If you plan to do serious quantitative work, you should learn to use some sort of text editor. The way I see it, it might as well be some flavor of Emacs 'cause then you get to use ESS.
The specific implementation of Emacs that I use is called Aquamacs. Aquamacs is a form of Emacs that is seemlessly integrated with the Aqua graphics system for MacOS. It also comes bundled with lots of useful packages like ESS and AUCTeX
Wikipedia has a handy comparison of text editors here
RStudio is a nice integrated development environment for R.
There is a page that handily collects all the unicode geometric symbols. This is made all the cooler by Ben Bolker's description of how to use these symbols here!
There is a very thorough tutorial available on the main R site.
Stanford's own Dan McFarland has a series of R tutorials, specifically focused on social network analysis.
John Fox has his syllabus for his ICPSR Introduction to R class posted here.
Kieran Healy's Plain Person's Guide to Plain Text Social Science (which is also available as a single pdf file). There is a lot of wisdom here that applies to our class!
R Markdown Tutorial from RStudio.
Nice intro to R Markdown from the Coding Club. Last Modified: 01.12.18