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Gems in Experimental Mathematics

Edited by: Tewodros Amdeberhan Tulane University, New Orleans, LA
Luis A. Medina University of Puerto Rico, San Juan, PR
Victor H. Moll Tulane University, New Orleans, LA
Available Formats:
Softcover ISBN: 978-0-8218-4869-2
Product Code: CONM/517
List Price: $117.00 MAA Member Price:$105.30
AMS Member Price: $93.60 Electronic ISBN: 978-0-8218-8196-5 Product Code: CONM/517.E List Price:$115.00
MAA Member Price: $103.50 AMS Member Price:$92.00
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List Price: $175.50 MAA Member Price:$157.95
AMS Member Price: $140.40 Click above image for expanded view Gems in Experimental Mathematics Edited by: Tewodros Amdeberhan Tulane University, New Orleans, LA Luis A. Medina University of Puerto Rico, San Juan, PR Victor H. Moll Tulane University, New Orleans, LA Available Formats:  Softcover ISBN: 978-0-8218-4869-2 Product Code: CONM/517  List Price:$117.00 MAA Member Price: $105.30 AMS Member Price:$93.60
 Electronic ISBN: 978-0-8218-8196-5 Product Code: CONM/517.E
 List Price: $115.00 MAA Member Price:$103.50 AMS Member Price: $92.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$175.50 MAA Member Price: $157.95 AMS Member Price:$140.40
• Book Details

Contemporary Mathematics
Volume: 5172010; 413 pp
MSC: 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.

Graduate students and research mathematicians interested in computational aspects of mathematics.

• Articles
• Gert Almkvist - The art of finding Calabi-Yau differential equations. Dedicated to the 90-th 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 ]
• O-Yeat 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 log-rational 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 Ramanujan-type 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 $a^n-1$ and $b^n-1$ and the Ailon-Rudnick 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 García-Puente, 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 Picard-Fuchs differential equations for Calabi-Yau threefolds [ MR 2731075 ]

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 5172010; 413 pp
MSC: 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.

Graduate students and research mathematicians interested in computational aspects of mathematics.

• Articles
• Gert Almkvist - The art of finding Calabi-Yau differential equations. Dedicated to the 90-th 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 ]
• O-Yeat 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 log-rational 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 Ramanujan-type 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 $a^n-1$ and $b^n-1$ and the Ailon-Rudnick 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 García-Puente, 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 Picard-Fuchs differential equations for Calabi-Yau threefolds [ MR 2731075 ]
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.