Last Update: June 15, 2007.
We will first learn Maple, and how to program in it. This semester the focus will be on Wilf-Zeilberger theory and the so-called Holonomic ansatz.
There are no prerequisites, and no previous programming knowledge is assumed. People with no Maple background will be tutored. The final projects for this class may lead to journal publications.
One of the greatest tools for Experimental Math is Neil Sloane's Amazing Sequence Database, maintained by Neil, who donates so much of his free time so that the whole mathematical world can benefit. You can help out by going to the recent additions, and editing any of the still unedited sequences. For more details E-mail Neil Sloane (njas at research dot att dot com).
Hint: Let x= [op(L),op(L), op(L), ...]. Then x satisfies x=[op(L),x]. Use CFtoNu to evaluate [op(L),x] symolically, and use Maple's solve to find its positive root.
Hint: Let y= [op(S),op(L),op(L), op(L), ...]. Then y satisfies y=[op(S),x]. Use CFtoNu and the previous program.
For example, Celine1((n+k)!/n!/k!,n,k,N,K,1); should return NK-K-N .
Lara talked about using Maple in Calculus. See
p_0(n)a(n)+p_1(n) a(n-1)+ ... + p_L(n)a(n-L)=0
for some positive integer L (the order) and polynomials p_0(n), ..., p_L(n). Write a program Pfinite.txt, that does the analog for P-finite sequences what Cfinite.txt does for C-finite sequences.
(Hint: if a sequence of polynomials Pn(x) has the generating function G(x,t)=Sum(Pn(x)*t^n,n=0..infinity), then Pn(x) is the contour integral (up to a const. multiple), w.r.t. t, of G(x,t)/t^(n+1)).
It was a beautiful day, and the computer room was unbearable, so we went outside and worked on the beginning of a software development project that the whole class would participate in. It is to create and solve KAKURU puzzles.
Lara is the boss. Eric, Baxter, and Aek are the sub-bosses. Aek's team consists of Ke, Humberto and Mangesh. Eric's team consists of Justin, Mike, and Emilie. Baxter's team consists of Paul and Jason. I hope to post a working Maple program next Monday.
KAKURO: The Whole Class's Group effort!