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Ten Problems in Experimental Mathematics

Description: This article was stimulated by the recent SIAM ''100 DigitChallenge'' of Nick Trefethen, beautifully described in a recent book. Indeed, these ten numeric challenge problems are also listed in a recent book by two of present authors, where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent was to present ten problems that are characteristic of the sorts of problems that commonly arise in ''experimental mathematics''. The challenge in each case is to obtain a high precision numeric evaluation of the quantity, and then, if possible, to obtain a symbolic answer, ideally one with proof. Our goal in this article is to provide solutions to these ten problems, and in the process present a concise account of how one combines symbolic and numeric computation, which may be termed ''hybrid computation'', in the process of mathematical discovery.
Date: September 30, 2004
Creator: Bailey, David H.; Borwein, Jonathan M.; Kapoor, Vishaal & Weisstein, Eric
Partner: UNT Libraries Government Documents Department

Experimental Mathematics and Mathematical Physics

Description: One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
Date: June 26, 2009
Creator: Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David & Zudilin, Wadim
Partner: UNT Libraries Government Documents Department

Experimental Mathematics and Computational Statistics

Description: The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of 'experimental mathematics'. These includes both applications of experimental mathematics in statistics, as well as statistical methods applied to computational mathematics.
Date: April 30, 2009
Creator: Bailey, David H. & Borwein, Jonathan M.
Partner: UNT Libraries Government Documents Department

National Mathematics Advisory Panel

Description: The U.S. Department of Education, in partnership with the Conference Board of Mathematical Sciences, hosted the first National Math Panel Forum on October 6-7, 2008. This page documents the Forum activities, which brought together various organizations and other interested parties.
Date: 2008
Creator: National Mathematics Advisory Panel
Partner: UNT Libraries Government Documents Department

MATHEMATICS OF INTERMITTENT IRRADIATION

Description: Initiation of reactions by intermittent irradiation is frequently encountered in physical, chemical, and biological systems. Mathematicai expressions for transient and steady state concentrations of reactive species in these systems are useful for predicting performance and for research purposes. A general method of formulation of the intermittent irradiation problem is presented herein, and illustrative solutions are obtained for radioactive decay chains and for the rotating sector method. 20 references. (auth)
Date: October 1, 1962
Creator: Hill, F.B.
Partner: UNT Libraries Government Documents Department

Mathematics and string theory

Description: The continuation of the collaboration with Liu and Lian on the calculation of the II A model opened up the possibility to understand calculations for higher genus curves also; many detailed calculations were carried out. They provided evidence that the method is powerful enough to calculate GW invariants in many cases. Local mirror symmetry was worked out with Chiang, Klemm, and Zaslow; it is consistent with physics intuition. Work was carried out to advance the ideas of Stroninger-Yau-Zaslow's geometric version of mirror symmetry in terms of special Lagragian torus fibration. Several papers were written on understanding such duality; it fits well with the predictions, and the ideas are still being studied.
Date: November 25, 2002
Creator: Yau, Shing-Tung
Partner: UNT Libraries Government Documents Department

Applied mathematics of chaotic systems

Description: This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The objectives of the project were to develop new mathematical techniques for describing chaotic systems and for reexpressing them in forms that can be solved analytically and computationally. The authors focused on global bifurcation analysis of rigid body motion in an ideal incompressible fluid and on an analytical technique for the exact solution of nonlinear cellular automata. For rigid-body motion, they investigated a new completely integrable partial differential equation (PDE) representing model motion of fronts in nematic crystals and studied perturbations of the integrable PDE. For cellular automata with multiple domain structures, the work has included: (1) identification of the associated set of conserved quantities for each type of domain; (2) use of the conserved quantities to construct isomorphism between the nonlinear system and a linear template; and (3) use of exact solvability methods to characterize detailed structure of equilibrium states and to derive bounds for maximal transience times.
Date: July 1, 1996
Creator: Jen, E.; Alber, M.; Camassa, R.; Choi, W.; Crutchfield, J.; Holm, D. et al.
Partner: UNT Libraries Government Documents Department

[Physics-Mathematics Building, Exterior]

Description: Photograph of the Physics-Mathematics Building, a three-story brick building that was built in 1959. In 1977, it became known as the Physics Building. Small trees can be seen on the buildings' lawn. The number 2 has been written in the bottom left of the image.
Date: unknown
Location Info:
Partner: UNT Libraries Special Collections

[Physics-Mathematics Building]

Description: Photograph of the Physics-Mathematics Building, a three-story brick building that was built in 1959. In 1977, it became known as the Physics Building. Small trees can be seen on the buildings' lawn.
Date: unknown
Location Info:
Partner: UNT Libraries Special Collections

[Mathematics and string theory]

Description: Work on this grant was centered on connections between non- commutative geometry and physics. Topics covered included: cyclic cohomology, non-commutative manifolds, index theory, reflection positivity, space quantization, quantum groups, number theory, etc.
Date: January 1, 1993
Creator: Jaffe, A. & Yau, Shing-Tung.
Partner: UNT Libraries Government Documents Department

(Mathematics and string theory)

Description: Over the past year our research activities concentrated around: (1) non-commutative differential geometry and its connections with quantum physics and (2) 2-dimensional(super) conformal quantum field theories and related non-linear {sigma}-models. This paper discusses these topics.
Date: January 1, 1992
Partner: UNT Libraries Government Documents Department

[TAMS Permission Form]

Description: Permission form for parents of students at the Texas Academy of Mathematics and Science covering off-campus travel, dating, and off-campus activities.
Date: 1988
Creator: Texas Academy of Mathematics and Science
Partner: Texas Academy of Mathematics and Science