(2002). The Curious History of Faa di Bruno's Formula. The American Mathematical Monthly: Vol. 109, No. 3, pp. 217-234.

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The Curious History of Faà di Bruno's Formula

This article explores the rich heritage of the boundary element method (BEM) by examining its mathematical foundation from the potential theory, boundary value problems, Green's functions, Green's identities, to Fredholm integral equations. The 18th to 20th century mathematicians, whose contributions were key to the theoretical development, are honored with short biographies. The origin of the numerical implementation of boundary integral equations can be traced to the 1960s, when the electronic computers had become available. The full emergence of the numerical technique known as the boundary element method occurred in the late 1970s. This article reviews the early history of the boundary element method up to the late 1970s.

https://www.olemiss.edu/sciencenet/benet/05eabeb.pdf

Heritage and early history of the boundary element method

Preface. Probability and Finance as a Game. PROBABILITY WITHOUT MEASURE. The Historical Context. The Bounded Strong Law of Large Numbers. Kolmogorov's Strong Law of Large Numbers. The Law of the Iterated Logarithm. The Weak Laws. Lindeberg's Theorem. The Generality of Probability Games. FINANCE WITHOUT PROBABILITY. Game-Theoretic Probability in Finance. Games for Pricing Options in Discrete Time. Games for Pricing Options in Continuous Time. The Generality of Game-Theoretic Pricing. Games for American Options. Games for Diffusion Processes. The Game-Theoretic Efficient-Market Hypothesis. References. Photograph Credits. Notation. Index.

Probability and Finance: It's Only a Game!

Modern interest in modal logic began with this seminal work by the American C.I. Lewis. As well as developing a theory of strict implication based on criticism of Russell and Whitebread's concept of implication, it contains historical information on the history and application of algebra to developments in symbolic logic.

A Survey of Symbolic Logic.

Paper 17: David H. Bailey and Jonathan M. Borwein, “Pi and its friends,” and “Normality: A stubborn question,” from Mathematics by Experiment: Plausible Reasoning in the 21st Century, A. K. Peters, Natick, MA, 2nd edition, 2008. Reproduced with permission of AK Peters.

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Mathematics by experiment : plausible reasoning in the 21st century

Geometries and Topology Mechanics and Mechanical Engineering Physics, Mathematical Physics, and Electrical Engineering Probability, Statistics, and the Social Sciences Higher Education and Institutions Mathematics and Culture.

Companion encyclopedia of the history and philosophy of the mathematical sciences

While many books have been written about Bertrand Russell's philosophy and some on his logic, I Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A N Whitehead in their Principia mathematica (1910-1913) ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schroeder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Goedel A strong American theme runs though the story, beginning with the mathematician E H Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GoedeI Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since

The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel

The development of the foundations of mathematical analysis from Euler to Riemann

The mathematics of the past: distinguishing its history from our heritage

Only for you today! Discover your favourite the search for mathematical roots 187

Ivor Grattan-Guinness

Papers

Companion encyclopedia of the history and philosophy of the mathematical sciences

The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel

The development of the foundations of mathematical analysis from Euler to Riemann

The mathematics of the past: distinguishing its history from our heritage

The Search for Mathematical Roots, 1870-1940