Math 262A, Fall 1999
Homework and handouts

6/27/01: When the class was taught, everyone had accounts on a computer where all the software and worksheets were installed.  You should be able to view the PDF images of the worksheets even if you do not have Maple or the various packages written for it.  No attempt has been made to update the worksheets to current versions of Maple or the various packages.  If you want to modify or execute the worksheets, you will have to get Maple and download and install the relevant packages.  The majority of the worksheets require Koepf's software, and many of the homework worksheets contain solutions originally provided on Koepf's website.

Class handouts

Date Worksheet   Description
10/17/99 zdemo1.mws PDF Zeilberger's Algorithm
10/17/99 gosperdemo.mws PDF Gosper Sum demo
10/25/99 koepf4.7.mws PDF Showing sums are equal, without being able to evaluate the sums in closed form
10/27/99 sum2int1.mws PDF Creative Telescoping for multisums/integrals
10/27/99 int3.mws PDF Creative Telescoping for a triple integral
(Zeilberger's TRIPLE_INTEGRAL)
10/27/99 demo1.nb
  Demo of Kurt Wegschaider's MultiSum
10/29/99 WZdemo.mws PDF WZ method demo
11/1/99 extendedalg.mws PDF Koepf's "Extended Gosper" algorithm
11/2/99 oredemo1.mws PDF Ore Algebras, Non-Commutative Division and Euclidean Algorithm
(intro to Chyzak's software)
11/8/99 hyperdemo.mws PDF Polynomial/Hypergeometric solutions of recurrences
11/11/99 resultant_lcm.mws PDF LCM, GCD of commutative and noncommutative polynomials using resultants
11/17/99 dfin_closure.mws PDF Sum/product/... of D-finite functions is D-finite
12/2/99 celine_gb.mws PDF Sums via noncommutative Grobner bases
12/2/99 gbsample1.mws PDF Using commutative Grobner bases to solve a system of polynomial equations via elimination ideals


Answer key Description
10/6/99 Homework 1 Part 1 PDF
Part 2 MWS  PDF
Hypergeometric series notation
10/13/99 Homework 2 Part 1 PDF
Part 2 MWS  PDF
Proving simple hypergeometric identities by hand.
Sister Celine's Method.
10/22/99 Homework 3 Part 1 PDF
Part 2 MWS  PDF
Gosper's Algorithm
10/29/99 Homework 4 Part 1 MWS  PDF
Part 2 MWS  PDF
Zeilberger's Algorithm
(Zeilberger's EKHAD)
11/5/99 Homework 5 MWS  PDF WZ method.
Extensions of the algorithms.
11/12/99 Homework 6 Part 1 PDF
Part 2 MWS  PDF
Petkovsek's Algorithm.
Classical methods of solving recurrence equations: Reduction of Order.
11/19/99 Homework 7 Part 1 PDF
Part 2 MWS  PDF
GCD, LCM of recurrences.
More classical methods of solving recurrence equations: Wronskians, Resultants, Taylor series.
11/24/99 Homework 8 Part 1 PDF
Part 2 MWS  PDF
Factorization of operators.
Ore algebras.
D-finite functions.
Grobner bases.
12/10/99 Homework 9 MWS  PDF Guessing sequences (Sloane, Gfun, Rate)