This comprehensive, detailed reference provides readers with both a working knowledge of Mathematica in general and a detailed knowledge of the key aspects needed to create the fastest, shortest, and most elegant implementations possible. It gives users a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The three volumes - Programming, Graphics, and Mathematics - each with a CD, total 3,000 pages and contain more than 15,000 Mathematica inputs, over 1,500 graphics, 4,000+ references, and more than 500 exercises. This second volume covers 2 and 3D graphics, providing a detailed treatment of creating images from graphic primitives such as points, lines, and polygons. It also shows how to graphically display functions that are given either analytically or in discrete form and a number of images from the Mathamatica graphics gallery. The use of Mathematicas graphics capabilities provides a very efficient and instructive way to learn how to deal with the structures arising in solving complicated problems.

William Thurston (1946–2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of areas of mathematics, from foliations, contact structures, and Teichmüller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. In What's Next?, many of today's leading mathematicians describe recent advances and future directions inspired by Thurston's transformative ideas. This book brings together papers delivered by his colleagues and former students at "What's Next? The Mathematical Legacy of Bill Thurston," a conference held in June 2014 at Cornell University. It discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. Incisive and wide-ranging, the book explores how he introduced new ways of thinking about and doing mathematics—innovations that have had a profound and lasting impact on the mathematical community as a whole—and also features two papers based on Thurston's unfinished work in dynamics.

Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.

This text demonstrates the process of comprehensive applied mathematical modeling through the introduction of various case studies. The case studies are arranged in increasing order of complexity based on the mathematical methods required to analyze the models. The development of these methods is also included, providing a self-contained presentation. To reinforce and supplement the material introduced, original problem sets are offered involving case studies closely related to the ones presented. With this style, the text’s perspective, scope, and completeness of the subject matter are considered unique. Having grown out of four self-contained courses taught by the authors, this text will be of use in a two-semester sequence for advanced undergraduate and beginning graduate students, requiring rudimentary knowledge of advanced calculus and differential equations, along with a basic understanding of some simple physical and biological scientific principles.

Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics 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 General and Specialized Mathematics Research: 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/.

Why narrative is essential to mathematics Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier—"Don't disturb my circles"—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more. In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.

This book is devoted to modeling of multi-level complex systems, a challenging domain for engineers, researchers and entrepreneurs, confronted with the transition from learning and adaptability to evolvability and autonomy for technologies, devices and problem solving methods. Chapter 1 introduces the multi-scale and multi-level systems and highlights their presence in different domains of science and technology. Methodologies as, random systems, non-Archimedean analysis, category theory and specific techniques as model categorification and integrative closure, are presented in chapter 2. Chapters 3 and 4 describe polystochastic models, PSM, and their developments. Categorical formulation of integrative closure offers the general PSM framework which serves as a flexible guideline for a large variety of multi-level modeling problems. Focusing on chemical engineering, pharmaceutical and environmental case studies, the chapters 5 to 8 analyze mixing, turbulent dispersion and entropy production for multi-scale systems. Taking inspiration from systems sciences, chapters 9 to 11 highlight multi-level modeling potentialities in formal concept analysis, existential graphs and evolvable designs of experiments. Case studies refer to separation flow-sheets, pharmaceutical pipeline, drug design and development, reliability management systems, security and failure analysis. Perspectives and integrative points of view are discussed in chapter 12. Autonomous and viable systems, multi-agents, organic and autonomic computing, multi-level informational systems, are revealed as promising domains for future applications. Written for: engineers, researchers, entrepreneurs and students in chemical, pharmaceutical, environmental and systems sciences engineering, and for applied mathematicians.