Handbook of Visual, Experimental and Computational Mathematics by Sriraman, Bharath;

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This Handbook examines the interaction of visual, computational and experimental approaches in modern mathematics through its interaction with data. Experimental mathematics made the first bold foray into using computational techniques to solve theoretical problems via data saturation and visualizations. Since computing power and powerful algorithms have changed the landscape of visualizing and doing mathematics, different sections of the book provide an access to data driven scenarios in contemporary society. These include data driven modeling in mathematical epidemiology; visualization of information patterns; climate science and ecology. Other sections include chapters which provide visualizations of abstract (theoretical) mathematics; and the application of mathematics in areas such as sports analytics. In this Handbook, the interaction of visualization, computation and experimental mathematics is covered with forays into problems at the intersection of biology, sports, epidemiology, physics, information theory and mathematics both pure and applied. The book is of interest to graduate students of mathematics, computer science, information theory and the sciences as well as university professors of these topics.

Editorial Advisory Board

Alexander Schliep, Brandenburg Technical University Cottbus-Senftenberg, Germany
Andreas Daniel Matt, IMAGINARY gGmbH, Berlin, Germany
Antonio Araujo, Universidade Aberta, Portugal
Benjamin Itza-Ortiz, Universidad Autónoma del Estado de Hidalgo, Mexico
Harry R. Lewis, Harvard University, USA
Hyungrul Baik, KAIST, South Korea
Scott Lindstrom, Curtin University, Australia
Urban Larsson, IIT-B, Mumbai India
Vanja Dukic, University of Colorado-Boulder, USA
Xin-She Yang, Middlesex University London, England

Testimonials

The Handbook of Visual, Experiment and Computational Mathematics is a tremendous resource for both researchers and teachers. The variety of applications demonstrates how mathematics is done in this age of collaboration and computation, and the thoughtful and well-prepared graphics illustrate the theoretical principles from various subfields of mathematics. It is worth noting that many students are among the authors, and teachers looking for student projects, from undergraduate research to graduate dissertations, will find that the chapters encourage further exploration and alternate approaches.

• Rick Cleary, Weissman Professor of Business Analytics, Babson College

The Handbook of Visual, Experimental, and Computational Mathematics—Bridges through Data offers a timely and compelling view of how modern mathematics is practiced at the intersection of computation, visualization, and data. Spanning topics from abstract theoretical mathematics to pressing real-world applications, the volume highlights a unifying theme: data is not merely an input, but a bridge connecting theory, computation, and visualization.

The sports analytics section exemplifies the book’s breadth and approach. Sports provide a natural laboratory for data-driven mathematics, where predictive modeling, visualization, machine learning, and linear algebra converge on questions of performance, strategy, and decision-making. The wide-ranging chapters illustrate how mathematical structure, statistical reasoning, and thoughtful visualization can yield insights that are both practically relevant and mathematically rich.

Beyond sports, the handbook spans fields including epidemiology, life sciences, climate science and ecology, information theory, and pure mathematics. Taken as a whole, it offers a rich collection of examples demonstrating how mathematical thinking informs data-driven inquiry in contemporary society.

• Tim Chartier, Joseph R. Morton Professor of Mathematics and Computer Science, Davidson College

This comprehensive volume spotlights the critical roles that visual, computational, and experimental methodologies play in contemporary mathematics. The Handbook’s scope is impressive, with topics ranging from the applied to the abstract—from the spread of influenza to groups of orientation-preserving isometries of hyperbolic 3-space. This text is an essential resource for students and researchers seeking to understand how data is analyzed and communicated.

• Dr. Jessica Katherine Sklar. Pacific Lutheran University

The Handbook of Visual, Experimental, and Computational Mathematics will be a valuable resource for students and instructors alike. The book provides an engaging introduction to a wide variety of mathematical topics, through the lenses of computation and experimentation. The diversity of important mathematical topics brought together in this book is impressive. They include number theory, topology, neural networks, sports analytics, biology, and a multitude of others. Excellent exposition, including historical development of some of the topics, adds to the book's value. I am excited to share this unique resource with students, especially those in my Math and the Creative Process course.

• Ellen Eischen : William R. Kenan, Jr. Visiting Professor for Distinguished Teaching, Keller Center, Princeton University; Professor of Mathematics, University of Oregon

Tartalomjegyzék:

Introduction to Experimental Mathematics.- Computational Aspects of Totally Disconnected Locally Compact Groups.- Experimental Mathematics and the Post-secondary Visualization Toolbox: Mathematics, History, and the Visual.- Data-Informed Modeling of the Formation, Persistence, and Evolution of Social Norms and Conventions.- Visualization of Convergence Behavior of a Generalized Newton Method and Levenberg–Marquardt Algorithm.- Working Out Counterexamples in Convex Geometry.- Computational Mathematics and Music: Optimising Frequency Modulation.- Instance Space Analysis for Visualization of Algorithmic Trust.- Computational Convex Analysis.