For anyone considering attending a future session of the Santa Fe Institute's (http://www.santafe.edu/) Complex Systems Summer School, below are some of the skills I suggest you'd want to brush up on in order to get off to a good start (and enjoy!) your time here. I've tried to be unbiased in these suggestions - some are areas where I was well-prepared but in others not so much. An important preface is to recognize the truly inter-disciplinary backgrounds of the participants - they come from health care, applied math, politics, ecology, economics, engineering, anthropology, etc. Comments below apply in this general context.
Calculus - This is a must have. Only about 1 in 20 in the class are from a math discipline but almost everyone has very solid, working, skills at the college calculus level. Almost every lecture and most discussion groups will use integrals, derivatives, limits, series, etc. and often extensively. Conversations very often evolve in slides and on the white board as a series of equations so it is important to be able to follow along in the mechanics... vague recollections of the general ideas from college (20 years ago in my case) would leave you lost. In working groups and on your project(s) you'll be at a noticeable disadvantage to your peers without these skills. The time I spent reviewing, and working the problems, from a college-level textbook (thru Calculus III) was time very well spent.
Reading and Writing and Speaking - There are 100s of pages to read....but not 1000s of pages. Some of the reading comes from journals but most of it is at the Science or Technology Review level. Every lecture has slides so there is plenty of PowerPoint stuff floating around....but the decks are very informationally dense... it can take a good chunk out of an hour to work thru the charts, tables, and discussion points on one slide. There are lots of charts and you have to keep track of frequent changes in axis, scales, representation, etc. Everyone has to do a paper individually (sometimes) or in a group (more often). You can see the website for examples of past papers - they don't have to be ready for peer-review in a professional publication but many of the participants will use the paper as a draft section of their dissertation or do a re-write for publication. Good grammar in professional writing and good habits for writing papers (e.g. citations) are important. Presentation skills are less important than questioning and listening skills - both for classes and group work. More emphasis on good questions than glib answers. More emphasis on sets of ideas that are well thought out and enduring than momentarily clever.
Matrices - Most of the lectures will use this. Every school lab computer has MatLab on it and many of the students bring their own copy (I did) - valuable for working on projects and to work out stuff during lecture. Ordinary sums and multiplications are most important. Ability to work with Eigen-stuff is pretty important - not a "must have" but they get used often in the lecture material. Every once in awhile someone will get into something more exotic (some special matrix or theory) but that stuff isn't really essential to doing the work. As popular as MatLab is, it is important to be able to do this by hand in order to follow the lectures, stuff that gets worked out on the board, and to work in the discussion/project groups. I lucked out here in that I've been using AHP for a few years now but only recently got a copy of ExpertChoice and so was still pretty fresh at doing some of this by hand.
Programming - No one in my class was a programmer or software engineer but almost everyone has solid programming skills - often in multiple tools/languages. Programming ability is just necessary to communicate ideas or to get the work done. "Programming" includes using scripting tools for stats packages or MatLab. Java is probably best since most of the modeling/simulation tools have a Java interface (e.g. Repast) and the participants are split between Windows and Mac (no C# available). You could get by, and do some good work, with really good VBA for Excel. Some of the tools introduced by the staff use languages that no one will know so everyone starts off on the same level there....but it will be valuable to be able to take a 1 hour intro and then self-teach in a few days to a skill level that contributes to your project.
Other Math Skills - Some familiarity with common equations of motion, acceleration, etc. is nice to have - they get used pretty often as reference points or metaphors and even in conversations with nothing to do about physics, math, etc. Non-linear dynamics is one of the kick-off topics and is a big theme for all of the lecture material - if you show up good at this you will be very popular for discussion/project groups. Pretty important to have at least a minimal recollection of the differences between ordinary differential equations and partial differential equations - ability to do the mechanics would be a nice. A working ability of statistics and probability is important - standard deviations, time series, correlation, etc. If you can't do the work well and fast "by hand", you can get by (I did) by being really solid using the stats functions in Excel. Ability to use one of the major stats packages is a "nice to have". - Brian