*Selected Writings*

**Author**: Jonathan M. Borwein

**Publisher:** PSIpress

**ISBN:** 193563805X

**Category:** Experimental mathematics

**Page:** 297

**View:** 4097

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## Experimental and Computational Mathematics

A quiet revolution in mathematical computing and scientific visualization took place in the latter half of the 20th century. These developments have dramatically enhanced modes of mathematical insight and opportunities for "exploratory" computational experimentation. This volume collects the experimental and computational contributions of Jonathan and Peter Borwein over the past quarter century.
## Computational Logic

Proceedings of the NATO Advanced Study Institute on Computational Logic, held in Marktoberdorf, Germany, July 29 - August 10, 1997
## Mathematical Approaches to Biomolecular Structure and Dynamics

This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES TO BIOMOLECULAR STRUCTURE AND DYNAMICS is one of the two volumes based on the proceedings of the 1994 IMA Sum mer Program on "Molecular Biology" and comprises Weeks 3 and 4 of the four-week program. Weeks 1 and 2 appeared as Volume 81: Genetic Mapping and DNA Sequencing. We thank Jill P. Mesirov, Klaus Schulten, and De Witt Sumners for organizing Weeks 3 and 4 of the workshop and for editing the proceedings. We also take this opportunity to thank the National Institutes of Health (NIH) (National Center for Human Genome Research), the National Science Foundation (NSF) (Biological Instrumen tation and Resources), and the Department of Energy (DOE), whose fi nancial support made the summer program possible. A vner Friedman Robert Gulliver v PREFACE The revolutionary progress in molecular biology within the last 30 years opens the way to full understanding of the molecular structures and mech anisms of living organisms. Interdisciplinary research in mathematics and molecular biology is driven by ever growing experimental, theoretical and computational power. The mathematical sciences accompany and support much of the progress achieved by experiment and computation as well as provide insight into geometric and topological properties of biomolecular structure and processes. This volume consists of a representative sample of the papers presented during the last two weeks of the month-long Institute for Mathematics and Its Applications Summer 1994 Program in Molecular Biology.
## Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
## Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Random Structures and Algorithms. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Random Structures and Algorithms in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
## Multiscale Modeling of Cancer

Mathematical modeling, analysis and simulation are set to play crucial roles in explaining tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial scales. This book, the first to integrate state-of-the-art numerical techniques with experimental data, provides an in-depth assessment of tumor cell modeling at multiple scales. The first part of the text presents a detailed biological background with an examination of single-phase and multi-phase continuum tumor modeling, discrete cell modeling, and hybrid continuum-discrete modeling. In the final two chapters, the authors guide the reader through problem-based illustrations and case studies of brain and breast cancer, to demonstrate the future potential of modeling in cancer research. This book has wide interdisciplinary appeal and is a valuable resource for mathematical biologists, biomedical engineers and clinical cancer research communities wishing to understand this emerging field.
## Computer Mathematics

This volume covers some of the most recent and significant advances in computer mathematics. Researchers, engineers, academics and graduate students interested in doing mathematics using computers will find it good reading as well as a valuable reference.
## Computational and Analytical Mathematics

The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publications, Jonathan Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing, and continues to have an enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and Borwein is one of the 250 most cited mathematicians of the period 1980-1999. He has served the Canadian Mathematics Community through his presidency (2000–02) as well as his 15 years of editing the CMS book series. Jonathan Borwein’s vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scientific interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle. The workshops that were held over the years in Dr. Borwein’s honor attracted high-caliber scientists from a wide range of mathematical fields. This present volume is an outgrowth of the workshop on ‘Computational and Analytical Mathematics’ held in May 2011 in celebration of Dr. Borwein’s 60th Birthday. The collection contains various state-of-the-art research manuscripts and surveys presenting contributions that have risen from the conference, and is an excellent opportunity to survey state-of-the-art research and discuss promising research directions and approaches.
## Electrocatalysis: Computational, Experimental, and Industrial Aspects

Electrocatalysis applications are employed in a large number of industries worldwide, ranging from old technologies such as galvanoplasty to the most up-to-date deployments involving ultracapacitators. Recognizing electrocatalysis as a useful interfacial approach to a dynamic interdisciplinary science, Electrocatalysis: Computational, Experimental, and Industrial Aspects focuses on important developments in the field that are the most relevant to new technologies. Gathering the experiences of a collection of experts who have worked on the basic principles of electrocatalysis as it applies to theoretical physics and theoretical chemistry, the book gives readers a clear view of the problems inside electrocatalytic reactions, presenting both the limitations of electrocatalysis in the laboratory along with its possibilities in industry. Topics discussed include: The current uses of electrocatalysis Future perspectives on the field Surface physical properties and surface relaxation on noble and non-noble surfaces The quantum nature of the electron transfer Müller-Calandra, Srinivasan-Gileadi, and instantaneous nucleation-growth overlap models The production, storage, use, and delivery of hydrogen in industrial electrochemistry Theoretical approaches to current distribution on rough surfaces The use of microradiology to study electrodeposition Principles of electrochemical engineering, fuel cell reactors, and electrocatalytic reactor design Electrocatalysis of electroless plating Fundamental aspects of the corrosion of metals The book reviews four main electrochemical processes (hydrogen production, oxygen electrochemistry, energy conversion/production, and fine electroplating). Surface modified non-noble metal substrates and natural minerals as well as noble mineral catalysts are considered. The text goes beyond other books, which merely focus on progress in the application of surface science and ultra high vacuum techniques to electrochemistry. Instead, this volume offers potential industrial applications of these findings, making it a unique reference for professionals and academia alike.
## Organic Mathematics

This volume is the hardcopy version of the electronic manuscript, Proceedings of the Organic Mathematics Workshop held at Simon Fraser University in December 1995 (www.cecm.sfu.ca/organics). The book provides a fixed, easily referenced, and permanent version of what is otherwise an evolving document. Contained in this work is a collection of articles on experimental and computational mathematics contributed by leading mathematicians around the world. The papers span a variety of mathematical fields - from juggling to differential equations to prime number theory. The book also contains biographies and photos of the contributing mathematicians and an in-depth characterization of organic mathematics.
## Introduction to Computational Science and Mathematics

Mathematics of Computing -- Numerical Analysis.
## Proof and Other Dilemmas

For the majority of the twentieth century, philosophers of mathematics focused their attention on foundational questions. However, in the last quarter of the century they began to return to basics, and two new schools of thought were created: social constructivism and structuralism. The advent of the computer also led to proofs and development of mathematics assisted by computer, and to questions concerning the role of the computer in mathematics. This book of sixteen original essays is the first to explore this range of new developments in the philosophy of mathematics, in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers have not yet discussed. The other half, written by philosophers of mathematics, summarise the discussion in that community during the last 35 years. A connection is made in each case to issues relevant to the teaching of mathematics.
## Mathematical Theory of Statistics

## Experimentelle Mathematik

Papier und Bleistift wurden lange als die einzigen Hilfsmittel der Mathematiker betrachtet (einige würden hier auch noch den Papierkorb dazuzählen). Wie in vielen anderen Gebieten auch, hat allerdings in den letzten Jahren der Einsatz von Computern in der Mathematik stark zugenommen und somit die Rolle des Experiments in der Mathematik erweitert und legitimiert. Wie können Mathematiker den Computer als Werkzeug benutzen? Und kann er vielleicht nicht nur als Werkzeug, sondern sogar als Mitarbeiter eingesetzt werden? Keith Devlin und Jonathan Borwein, zwei bekannte Mathematiker mit Expertise in unterschiedlichen mathematischen Spezialgebieten, aber mit einem gemeinsamen Interesse am Experimentieren in der Mathematik, haben sich für diese Einführung in die experimentelle Mathematik zusammengetan. Sie behandeln eine Vielfalt an Themen und Beispielen, um dem Leser einen guten Einblick in die aktuelle Entwicklung dieses rasch wachsenden neuen Gebietes zu geben. Die Darstellung ist klar und übersichtlich; die Erläuterungen sind durch historische Fakten und Geschichten von Mathematikern und deren Begegnungen mit dem Gebiet der experimentellen Mathematik angereichert. Stimme zur Originalausgabe: “Das Buch wird für jeden Leser für Interesse sein, der anhand Kostproben kennen lernen möchte, wie man mathematische Problem mit einem Computer löst. Es macht nichts, wenn die Leser nicht viele mathematische Kenntnisse mitbringen: Sie können das Wesentliche des Buchs verstehen und Spaß dabei haben, einige Fragestellungen experimentell zu erforschen.“ Valentina Dagienë, Zentralblatt MATH
## Experimental and Computational Techniques in Soft Condensed Matter Physics

Soft condensed matter physics relies on a fundamental understanding at the interface between physics, chemistry, biology, and engineering for a host of materials and circumstances that are related to, but outside, the traditional definition of condensed matter physics. Featuring contributions from leading researchers in the field, this book uniquely discusses both the contemporary experimental and computational manifestations of soft condensed matter systems. From particle tracking and image analysis, novel materials and computational methods, to confocal microscopy and bacterial assays, this book will equip the reader for collaborative and interdisciplinary research efforts relating to a range of modern problems in nonlinear and non-equilibrium systems. It will enable both graduate students and experienced researchers to supplement a more traditional understanding of thermodynamics and statistical systems with knowledge of the techniques used in contemporary investigations. Color versions of a selection of the figures are available at www.cambridge.org/9780521115902.
## Computational and Experimental Biomedical Sciences: Methods and Applications

This book contains the full papers presented at ICCEBS 2013 – the 1st International Conference on Computational and Experimental Biomedical Sciences, which was organized in Azores, in October 2013. The included papers present and discuss new trends in those fields, using several methods and techniques, including active shape models, constitutive models, isogeometric elements, genetic algorithms, level sets, material models, neural networks, optimization and the finite element method, in order to address more efficiently different and timely applications involving biofluids, computer simulation, computational biomechanics, image based diagnosis, image processing and analysis, image segmentation, image registration, scaffolds, simulation and surgical planning. The main audience for this book consists of researchers, Ph.D students and graduate students with multidisciplinary interests related to the areas of artificial intelligence, bioengineering, biology, biomechanics, computational fluid dynamics, computational mechanics, computational vision, histology, human motion, imagiology, applied mathematics, medical image, medicine, orthopaedics, rehabilitation, speech production and tissue engineering.
## Experimental Mathematics with Maple

As discrete mathematics rapidly becomes a required element of undergraduate mathematics programs, algebraic software systems replace compiled languages and are now most often the computational tool of choice. Newcomers to university level mathematics, therefore, must not only grasp the fundamentals of discrete mathematics, they must also learn to use an algebraic manipulator and develop skills in abstract reasoning. Experimental Mathematics with MAPLE uniquely responds to these needs. Following an emerging trend in research, it places abstraction and axiomatization at the end of a learning process that begins with computer experimentation. It introduces the foundations of discrete mathematics and, assuming no previous knowledge of computing, gradually develops basic computational skills using the latest version of the powerful MAPLE® software. The author's approach is to expose readers to a large number of concrete computational examples and encourage them to isolate the general from the particular, to synthesize computational results, formulate conjectures, and attempt rigorous proofs. Using this approach, Experimental Mathematics with MAPLE enables readers to build a foundation in discrete mathematics, gain valuable experience with algebraic computing, and develop a familiarity with basic abstract concepts, notation, and jargon. Its engaging style, numerous exercises and examples, and Internet posting of selected solutions and MAPLE worksheets make this text ideal for use both in the classroom and for self-study.
## Constructive, Experimental, and Nonlinear Analysis

This volume presents twenty original refereed papers on different aspects of modern analysis, including analytic and computational number theory, symbolic and numerical computation, theoretical and computational optimization, and recent development in nonsmooth and functional analysis with applications to control theory. These papers originated largely from a conference held in conjunction with a 1999 Doctorate Honoris Causa awarded to Jonathan Borwein at Limoges. As such they reflect the areas in which Dr. Borwein has worked. In addition to providing a snapshot of research in the field of modern analysis, the papers suggest some of the directions this research is following at the beginning of the millennium.
## Systems Biology Approaches to Understanding the Cause and Treatment of Heart, Lung, Blood, and Sleep Disorders

Development of powerful new high- throughput technologies for probing the transcriptome, proteome and metabolome is driving the rapid acquisition of information on the function of molecular systems. The importance of these achievements cannot be understated – they have transformed the nature of both biology and medicine. Despite this dramatic progress, one of the greatest challenges that continues to confront modern biology is to understand how behavior at the level of genome, proteome and metabolome determines physiological function at the level of cell, tissue and organ in both health and disease. Because of the inherent complexity of biological systems, the development, analysis, and validation of integrative computational models based directly on experimental data is necessary to achieve this understanding. This approach, known as systems biology, integrates computational and experimental approaches through iterative development of mathematical models and experimental validation and testing. The combination of these approaches allows for a mechanistic understanding of the function of complex biological systems in health and their dysfunction in disease. The National Heart, Lung, and Blood Institute (NHLBI) has recognized the importance of the systems biology approach for understanding normal physiology and perturbations associated with heart, lung, blood, and sleep diseases and disorders. In 2006, NHLBI announced the Exploratory Program in Systems Biology, followed in 2010 by the NHLBI Systems Biology Collaborations. The goal of these programs is to support collaborative teams of investigators in using experimental and computational strategies to integrate the component parts of biological networks and pathways into computational models that are based firmly on and validated using experimental data. These validated models are then applied to gain insights into the mechanisms of altered system function in disease, to generate novel hypotheses regarding these mechanisms that can be tested experimentally, and to then use the results of experiments to refine the models. The purpose of this Research Topic is to present the range of innovative, new approaches being developed by investigators working in areas of systems biology that couple experimental and modeling studies to understand the cause and possible treatment of heart, lung, blood and sleep diseases and disorders. This Research Topic will be of great interest to the cardiovascular research community as well as to the general community of systems biologists.

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