Contents: Jonathan\ Michael\ Borwein, The experimental mathematician: a computational guide to the mathematical unknown (1--3); Gert-Martin\ Greuel\ and Gerhard\ Pfister, Computer algebra and finite groups (4--14); Michael\ Joswig, Software integration and computer proofs (15--28); David\ Defour\ and Florent\ De Dinechin, Software carry-save for fast multiple-precision algorithms (29--39); J.-G.\ Dumas, T.\ Gautier, M.\ Giesbrecht, P.\ Giorgi, B.\ Hovinen, E.\ Kaltofen, B.\ D.\ Saunders, W.\ J.\ Turner\ and G.\ Villard, LinBox: a generic library for exact linear algebra (40--50); Ming\ Jiang\ and Ge\ Wang, Block-iterative algorithms for image reconstruction (51--60); C.-P.\ Jeannerod\ and G.\ Labahn, The SNAP package for arithmetic with numeric polynomials (61--71); Jieqing\ Tan\ and Shuo\ Tang, Algorithms of composite rational interpolation based on continued fractions (72--81); Sonoko\ Moriyama, Ayumu\ Nagai\ and Hiroshi\ Imai, Fast and space-efficient algorithms for deciding shellability of simplicial complexes of large size using $h$-assignments (82--92); Mingsheng\ Wang [Ming\ Sheng Wang\asup 2]\ and C.\ P.\ Kwong, Computing GCLF using syzygy algorithm (93--103). \par Yi\ Shang, Markus\ P. J. Fromherz\ and Lara\ S.\ Crawford, Efficient cooperative solvers for nonlinear continuous constraint problems (104--114); Zhikun\ She, Bican\ Xia\ and Zhiming\ Zheng, Pseudo-division machine. I. A model of symbolic computation (115--125); Dieter\ Hofbauer, Friedrich\ Otto, Christoph\ Kögl\ and Klaus\ E.\ Madlener, XSSR: an experimental system for string rewriting---decision problems, algorithms, and implementation (126--135); Mathias\ Schulze, The differential structure of the Brieskorn lattice (136--146); Masayuki\ Noro, An efficient modular algorithm for computing the global $b$-function (147--157); Yayoi\ Nakamura\ and Shinichi\ Tajima, A method for constructing holonomic systems for algebraic local cohomology classes with support on a zero dimensional variety (158--168); Anton\ Leykin, $D$-modules for Macaulay 2 (169--179); Thomas\ F.\ Banchoff, Computer graphics in mathematical research, from ICM 1978 to ICM 2002: a personal reflection (180--189); Anders\ Linnér, Generating optimal curves via the $\roman C^{++}$ standard library (190--200); M.\ V.\ Andreeva, I.\ A.\ Dynnikov\ and K.\ Polthier, A mathematical webservice for recognizing the unknot (201--207). \par Ulrich\ Kortenkamp\ and Jürgen\ Richter-Gebert, Making the move: the next version of Cinderella (208--216); Kazuhiro\ Yokoyama, Prime decomposition of polynomial ideals over finite fields (217--227); Anne\ Frühbis-Krüger, Partial standard bases for families (228--238); G.\ Dos Reis, B.\ Mourrain, Ph.\ Trébuchet\ and F.\ Rouillier, An environment for symbolic and numeric computation (239--249); Masanari\ Kida, Computing elliptic curves using KASH (250--260); M.\ Henningsen [Maike\ Henningsen], Computing the endomorphism type of ordinary elliptic curves over finite fields with KANT V4 (261--270); Ryouhei\ Takeuchi, On distribution of the group of rational points of reductions of an elliptic curve (271--280); Andreas\ Enge, Algorithmic constructions of elliptic curves with complex multiplication (281--282); Masakazu\ Kojima, Yang\ Dai, Katsuki\ Fujisawa, Sunyoung\ Kim\ and Akiko\ Takeda, Parallel implementation of polyhedral continuation methods for systems of polynomial equations (283--284); Sunyoung\ Kim\ and Masakazu\ Kojima, CMPSm: a continuation method for polynomial systems (MATLAB version) (285--295). \par Jesús A. De Loera, Generating functions that count $t$-designs with given automorphism group: algorithms and structure (296--306); Raymond\ Hemmecke, On the computation of Hilbert bases of cones (307--317); Doron\ Zeilberger, Encapsulate! (318); S.\ A.\ Abramov, K.\ O.\ Geddes\ and H.\ Q.\ Le, Computer algebra library for the construction of the minimal telescopers (319--329); Jörg\ Rambau, TOPCOM: triangulations of point configurations and oriented matroids (330--340); Izumi\ Miyamoto, Parallel backtrack computing of association schemes using classroom PC's (341--349); David\ Avis, Komei\ Fukuda\ and Stefano\ Picozzi, On canonical representations of convex polyhedra (350--360); Yong-Bin\ Li [Yong\ Bin\ Li], Jing-Zhong\ Zhang\ and Lu\ Yang, Decomposing polynomial systems into strong regular sets (361--371); Na\ Lei, Tie-Ru\ Wu\ and Guo-Chen\ Feng, Wu Wen-Tsün formulae for the blending of quadratic surfaces (372--378); Dongming\ Wang, Epsilon: a library of software tools for polynomial elimination (379--389). \par Massimo\ Caboara, Martin\ Kreuzer\ and Lorenzo\ Robbiano, Minimal sets of critical pairs (390--404); Stephen\ M.\ Watt, A study in the integration of computer algebra systems: memory management in a Maple-Aldor environment (405--410); Yongwei\ Wu, Weidong\ Liao, Dongdai\ Lin\ and Paul\ S.\ Wang, Local and remote user interface for ELIMINO through OMEI (411--420); Samuel\ S.\ Dooley, Programming the IBM MathML expression editor for interactive mathematical applications (421--431); Mike\ Dewar\ and David\ Carlisle, From mathematical servers to mathematical services (432--441); Olga\ Caprotti\ and Wolfgang\ Schreiner, Towards a mathematical services description language (442--452); K.\ O.\ Geddes\ and H.\ Q.\ Le, An algorithm to compute the minimal telescopers for rational functions (differential-integral case) (453--463); Zhi-Bin\ Li [Zhi\ Bin Li\asup 1], Yin-Ping\ Liu [Yinping\ Liu]\ and Ruo-Xia\ Yao, An automated algebraic method for finding exact solutions to nonlinear evolution equations (464--474); Andrey\ V.\ Banshchikov, Parametric analysis of systems of algebraic inequalities (475--484); Manuel\ Bronstein, $\Sigma^{it}$---an Aldor library for linear differential and difference equations (abstract) (485). \par Fritz\ Schwarz, ALLTYPES: an algebraic language and type system (486--500); Dongdai\ Lin, Zhimin\ Song\ and Paul\ S.\ Wang, Secure internet accessible mathematical computation framework (501--502); Sheqin\ Dong, Xianlong\ Hong, Song\ Chen\ and Shuo\ Zhou, Solution space smoothing for VLSI module placement: a computational study (503--504); T.\ Matsui, D.\ Kobayashi, M.\ Abe\ and K.\ Nakamula, SIMATH---recent developments in TMU (505--506); A.\ V.\ Flegontov, Structures of the polynomial types in problems of the invariant analysis and synthesis of differential equations (507--508). \par \{The papers will not be reviewed individually.\}