The owners of this site have written several reference books on computational mathematics, some of which have material useful for financial mathematics. We feature some of these books here:
- Exploratory experimentation in mathematics: Selected Works.
This book collects sixteen articles written by Bailey and Borwein (either together or separately) and with
- Experimental and computational mathematics: Selected writings. This volume collects the experimental and computational contributions of Jonathan and Peter Borwein over the past quarter century.
- The Computer as Crucible: An Introduction to Experimental
Keith Devlin and Jonathan Borwein have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics.
- Experimentelle Mathematik: Eine beispielorientierte Einführung. (German translation of The Computer as Crucible: An Introduction to Experimental Mathematics).
- The Computer as Crucible. (Japanese translation of The Computer as Crucible).
- Mathematics by Experiment: Plausible Reasoning in the 21st Century (Second Edition).
"Experimental mathematics" means using advanced computing technologyas a "laboratory" for mathematical research. This book, by well-known mathematicians Bailey and Borwein, presents the rationale and historical context of experimental mathematics, and includes a series of examples that best portray the experimental methodology, together with some of the numerical techniques used in this research. Numerous historical and biographical notes are also included.
- Experimentation in Mathematics: Computational Paths to Discovery.
Following the lead of the first volume, this book gives numerous additional case studies of experimental mathematics in action, ranging from sequences, series, products, integrals, Fourier series, zeta functions, partitions, primes and polynomials. Some advanced numerical techniques are also presented.
- Experiments in Mathematics. This is a CD-ROM with a hyperlinked, searchable PDF files of the above two books. This is the first time a major work of mathematics has appeared in this format.
- Experimental Mathematics in Action. This new book, published in May 2007 by AK Peters, is the companion volume to the
MAA Short Course conducted at the San Antonio AMS-MAA meeting in Jan 2006. Each chapter presents some case studies of experimental mathematics being used in real problems of mathematical research, both pure and applied:
AK Peters |
- Jonathan M. Borwein, "A Philosophical Introduction".
- David H. Bailey, "Algorithms I"
- David H. Bailey, "Algorithms II"
- Russell Luke, "Inverse Scattering"
- Roland Girgensohn, "Strange Functions"
- Neil Calkin, "Factoring Integers"
- Victor Moll, "Integrals"
- Jonathan M. Borwein, "A Computational Conclusion"
- Mathematics and the Aesthetic: New Approaches to an Ancient Affinity. This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating.
- Convex Analysis and Nonlinear Optimization: Theory and Examples. Optimization is a rich and thriving mathematical discipline, with applications in many fields, including mathematical finance. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises.
- Techniques of Variational Analysis. The book presents a nice treatment of variational analysis and their application in many fields of mathematics. It includes many exercises and examples.