Okay, interesting. I hope you start a blog or something on it to track your progress for the benefit of others.
At the end of the course, what will they be tested on? Does this course replace a precalc course? This will determine to an extent what you can do. When I taught http://www.usna.edu/Users/math/wdj/teach/sm450.html (python and some fairly advanced discrete math), I found that the Python was almost completely orthogonal to the math. Before teaching the course, I thought I could teach them both math and Python by doing math examples in Python. That worked for some very good students. For others, I had to teach them Python and teach them the math, and then carefully explain the example in Python. You asked for ideas, so here is one. Take the Fibonacci sequence, f0=1, f1=1,f2=2, f3=3, f4=5, .... It is easy to show (using binary trees) that the "stupid" way to compute fn using the most naive algorithm is extremely inefficient. However, if you use a trick with matrices and repeated squaring, fn can be computed in linear time! For your class this might take a week or two but you would have to go through lots of cool and useful ideas. The big payoff is that at the end, you get an algorithm which is very short and elegant but fast, and you have taught them a ton of useful tools. Some details are (among many other places) in the lecture notes posted to the 450 website above. On Mon, Jun 7, 2010 at 8:13 PM, michel paul <[email protected]> wrote: > On Mon, Jun 7, 2010 at 6:27 AM, David Joyner <[email protected]> wrote: >> >> >Are you going to teach programming (eg, Python) in this course? > > Exactly. We'll be using the Litvins' Math for the Digital Age and > Programming in Python, and I think we can work through that text in a > semester. Though it does touch on some precalc topics, it is not > specifically a precalc text, so we'll also draw from our regular text to > fill in the gaps. Then second semester we'll focus on the remaining precalc > topics not addressed in Digital Age. The kids should be proficient enough > at that point in using Sage to be able to write little papers about the math > we're studying. Each student will have an online Sage notebook account that > will serve as a portfolio of their work. > >> >> Seems like you are leaning towards discrete math+precalc topics. >> Is that correct? > > Our current precalc text, Demana Waits, does contain a chapter on discrete > math - basic combinatorics, sequences, series, binomial theorem, math > induction, etc., but again, it's towards the end of the text and is normally > done 2nd semester. I think a lot of those topics could easily be done first > semester and would have more relevance for learning programming. So I'm > going to change some things around and save the trig stuff and the analytic > geometry for 2nd semester. > > Eventually a computational discrete math course would also be a great thing > to create. There actually used to be a ProbStat/Finite math course at our > school, but it was tracked for the 'lower' math students, the ones 'not > headed for calculus', and I really disliked the illusion it created that > 'Finite was for dummies' or 'not real math'. > > -- > You received this message because you are subscribed to the Google Groups > "sage-edu" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/sage-edu?hl=en. > -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
