Date  Worksheet  Description  
10/17/99  zdemo1.mws  Zeilberger's Algorithm  
10/17/99  gosperdemo.mws  Gosper Sum demo  
10/25/99  koepf4.7.mws  Showing sums are equal, without being able to evaluate the sums in closed form  
10/27/99  sum2int1.mws  Creative Telescoping for multisums/integrals
(Zeilberger's DOUBLE_SUM_SINGLE_INTEGRAL) 

10/27/99  int3.mws  Creative Telescoping for a triple integral
(Zeilberger's TRIPLE_INTEGRAL) 

10/27/99  demo1.nb
(Mathematica) 
Demo of Kurt Wegschaider's MultiSum  
10/29/99  WZdemo.mws  WZ method demo  
11/1/99  extendedalg.mws  Koepf's "Extended Gosper" algorithm  
11/2/99  oredemo1.mws  Ore Algebras, NonCommutative Division and Euclidean Algorithm
(intro to Chyzak's software) 

11/8/99  hyperdemo.mws  Polynomial/Hypergeometric solutions of recurrences  
11/11/99  resultant_lcm.mws  LCM, GCD of commutative and noncommutative polynomials using resultants  
11/17/99  dfin_closure.mws  Sum/product/... of Dfinite functions is Dfinite  
12/2/99  celine_gb.mws  Sums via noncommutative Grobner bases  
12/2/99  gbsample1.mws  Using commutative Grobner bases to solve a system of polynomial equations via elimination ideals 
Date
Assigned 
Assignment
(PDF) 
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.
Recurrences. 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. Dfinite functions. Grobner bases. 
12/10/99  Homework 9  MWS PDF  Guessing sequences (Sloane, Gfun, Rate) 