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Book DetailsContemporary MathematicsVolume: 517; 2010; 413 ppMSC: Primary 05; 11; 14; 15; 37;
These proceedings reflect the special session on Experimental Mathematics held January 5, 2009, at the Joint Mathematics Meetings in Washington, DC as well as some papers specially solicited for this volume.
Experimental Mathematics is a recently structured field of Mathematics that uses the computer and advanced computing technology as a tool to perform experiments. These include the analysis of examples, testing of new ideas, and the search of patterns to suggest results and to complement existing analytical rigor.
The development of a broad spectrum of mathematical software products, such as Mathematica® and Maple™, has allowed mathematicians of diverse backgrounds and interests to use the computer as an essential tool as part of their daily work environment.
This volume reflects a wide range of topics related to the young field of Experimental Mathematics. The use of computation varies from aiming to exclude human input in the solution of a problem to traditional mathematical questions for which computation is a prominent tool.ReadershipGraduate students and research mathematicians interested in computational aspects of mathematics.

Table of Contents

Articles

Gert Almkvist  The art of finding CalabiYau differential equations. Dedicated to the 90th birthday of Lars Gärding [ MR 2731057 ]

Tewodros Amdeberhan  A note on a question due to A. Garsia [ MR 2731058 ]

David H. Bailey and Jonathan M. Borwein  Experimental computation with oscillatory integrals [ MR 2731059 ]

David H. Bailey, Jonathan M. Borwein, David Broadhurst and Wadim Zudilin  Experimental mathematics and mathematical physics [ MR 2731060 ]

Stefan T. Boettner  An extension of the parallel Risch algorithm [ MR 2731061 ]

Robert P. Boyer and William M. Y. Goh  Appell polynomials and their zero attractors [ MR 2731062 ]

OYeat Chan and Dante Manna  Congruences for Stirling numbers of the second kind [ MR 2731094 ]

Mark W. Coffey  Expressions for harmonic number exponential generating functions [ MR 2731093 ]

Richard E. Crandall  Theory of logrational integrals [ MR 2731092 ]

Stavros Garoufalidis and Xinyu Sun  A new algorithm for the recursion of hypergeometric multisums with improved universal denominator [ MR 2731091 ]

Ivan Gonzalez, Victor H. Moll and Armin Straub  The method of brackets. Part 2: examples and applications [ MR 2731090 ]

Jesús Guillera  History of the formulas and algorithms for $\pi $ [ MR 2731089 ]

Jesús Guillera  A matrix form of Ramanujantype series for $1/\pi $ [ MR 2731088 ]

Karen Kohl and Flavia Stan  An algorithmic approach to the Mellin transform method [ MR 2731087 ]

Christoph Koutschan  Eliminating human insight: an algorithmic proof of Stembridge’s TSPP theorem [ MR 2731086 ]

Michel L. Lapidus and Robert G. Niemeyer  Towards the Koch snowflake fractal billiard: computer experiments and mathematical conjectures [ MR 2731085 ]

Luis A. Medina and Doron Zeilberger  An experimental mathematics perspective on the old, and still open, question of when to stop? [ MR 2731084 ]

Michael J. Mossinghoff  The distance to an irreducible polynomial [ MR 2731083 ]

Sam Northshield  Square roots of $2\times 2$ matrices [ MR 2731082 ]

Olivier Oloa  On a series of Ramanujan [ MR 2731081 ]

Paul Raff and Doron Zeilberger  Finite analogs of Szemerédi’s theorem [ MR 2731080 ]

Andrew V. Sills  Towards an automation of the circle method [ MR 2731079 ]

Joseph H. Silverman  The greatest common divisor of $a^n1$ and $b^n1$ and the AilonRudnick conjecture [ MR 2731078 ]

Jonathan Sondow and Kyle Schalm  Which partial sums of the Taylor series for $e$ are convergents to $e$? (and a link to the primes 2, 5, 13, 37, 463). Part II [ MR 2731077 ]

Christopher Hillar, Luis GarcíaPuente, Abraham Martín del Campo, James Ruffo, Zach Teitler, Stephen L. Johnson and Frank Sottile  Experimentation at the frontiers of reality in Schubert calculus [ MR 2731076 ]

Yifan Yang and Wadim Zudilin  On ${\rm Sp}_4$ modularity of PicardFuchs differential equations for CalabiYau threefolds [ MR 2731075 ]


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These proceedings reflect the special session on Experimental Mathematics held January 5, 2009, at the Joint Mathematics Meetings in Washington, DC as well as some papers specially solicited for this volume.
Experimental Mathematics is a recently structured field of Mathematics that uses the computer and advanced computing technology as a tool to perform experiments. These include the analysis of examples, testing of new ideas, and the search of patterns to suggest results and to complement existing analytical rigor.
The development of a broad spectrum of mathematical software products, such as Mathematica® and Maple™, has allowed mathematicians of diverse backgrounds and interests to use the computer as an essential tool as part of their daily work environment.
This volume reflects a wide range of topics related to the young field of Experimental Mathematics. The use of computation varies from aiming to exclude human input in the solution of a problem to traditional mathematical questions for which computation is a prominent tool.
Graduate students and research mathematicians interested in computational aspects of mathematics.

Articles

Gert Almkvist  The art of finding CalabiYau differential equations. Dedicated to the 90th birthday of Lars Gärding [ MR 2731057 ]

Tewodros Amdeberhan  A note on a question due to A. Garsia [ MR 2731058 ]

David H. Bailey and Jonathan M. Borwein  Experimental computation with oscillatory integrals [ MR 2731059 ]

David H. Bailey, Jonathan M. Borwein, David Broadhurst and Wadim Zudilin  Experimental mathematics and mathematical physics [ MR 2731060 ]

Stefan T. Boettner  An extension of the parallel Risch algorithm [ MR 2731061 ]

Robert P. Boyer and William M. Y. Goh  Appell polynomials and their zero attractors [ MR 2731062 ]

OYeat Chan and Dante Manna  Congruences for Stirling numbers of the second kind [ MR 2731094 ]

Mark W. Coffey  Expressions for harmonic number exponential generating functions [ MR 2731093 ]

Richard E. Crandall  Theory of logrational integrals [ MR 2731092 ]

Stavros Garoufalidis and Xinyu Sun  A new algorithm for the recursion of hypergeometric multisums with improved universal denominator [ MR 2731091 ]

Ivan Gonzalez, Victor H. Moll and Armin Straub  The method of brackets. Part 2: examples and applications [ MR 2731090 ]

Jesús Guillera  History of the formulas and algorithms for $\pi $ [ MR 2731089 ]

Jesús Guillera  A matrix form of Ramanujantype series for $1/\pi $ [ MR 2731088 ]

Karen Kohl and Flavia Stan  An algorithmic approach to the Mellin transform method [ MR 2731087 ]

Christoph Koutschan  Eliminating human insight: an algorithmic proof of Stembridge’s TSPP theorem [ MR 2731086 ]

Michel L. Lapidus and Robert G. Niemeyer  Towards the Koch snowflake fractal billiard: computer experiments and mathematical conjectures [ MR 2731085 ]

Luis A. Medina and Doron Zeilberger  An experimental mathematics perspective on the old, and still open, question of when to stop? [ MR 2731084 ]

Michael J. Mossinghoff  The distance to an irreducible polynomial [ MR 2731083 ]

Sam Northshield  Square roots of $2\times 2$ matrices [ MR 2731082 ]

Olivier Oloa  On a series of Ramanujan [ MR 2731081 ]

Paul Raff and Doron Zeilberger  Finite analogs of Szemerédi’s theorem [ MR 2731080 ]

Andrew V. Sills  Towards an automation of the circle method [ MR 2731079 ]

Joseph H. Silverman  The greatest common divisor of $a^n1$ and $b^n1$ and the AilonRudnick conjecture [ MR 2731078 ]

Jonathan Sondow and Kyle Schalm  Which partial sums of the Taylor series for $e$ are convergents to $e$? (and a link to the primes 2, 5, 13, 37, 463). Part II [ MR 2731077 ]

Christopher Hillar, Luis GarcíaPuente, Abraham Martín del Campo, James Ruffo, Zach Teitler, Stephen L. Johnson and Frank Sottile  Experimentation at the frontiers of reality in Schubert calculus [ MR 2731076 ]

Yifan Yang and Wadim Zudilin  On ${\rm Sp}_4$ modularity of PicardFuchs differential equations for CalabiYau threefolds [ MR 2731075 ]