These are the proceedings of the conference "Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics" held at the Department of Mathematics, University of Florida, Gainesville, from November 11 to 13, 1999. The main emphasis of the conference was Com­ puter Algebra (i. e. symbolic computation) and how it related to the fields of Number Theory, Special Functions, Physics and Combinatorics. A subject that is common to all of these fields is q-series. We brought together those who do symbolic computation with q-series and those who need q-series in­ cluding workers in Physics and Combinatorics. The goal of the conference was to inform mathematicians and physicists who use q-series of the latest developments in the field of q-series and especially how symbolic computa­ tion has aided these developments. Over 60 people were invited to participate in the conference. We ended up having 45 participants at the conference, including six one hour plenary speakers and 28 half hour speakers. There were talks in all the areas we were hoping for. There were three software demonstrations.

Gaussian hypergeometric series and combinatorial congruences.- A double bounded key identity for Göllnitz's (BIG) partition theorem.- Engel expansions of q-series by computer algebra.- Sums of squares and the preservation of modularity under congruence restrictions.- On the transformation formula for the Dedekind eta-function.- Experiments and discoveries in q-trigonometry.- Algebraic consequences of Jacobi's two- and four-square theorems.- The Borweins' cubic theta functions and q-elliptic functions.- Some Eisenstein series identities associated with the Borwein functions.- Hankel determinants of Eisenstein series.- Jacobi's identity and two K3-surfaces.- q-Random matrix ensembles.- Differential endomorphisms for modular forms.- On the asymptotics of Takeuchi numbers.- Fine-Tuning Zeilberger's Algorithm: The Methods of Automatic Filtering and Creative Substituting.- Gaussian integrals and the Rogers-Ramanujan identities.- Some remarks on a product expansion: an unexplored partition function.