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Forbidden Configurations in Discrete Geometry
This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.
Media Theory
This book presents a mathematical structure modeling a physical or biological system that can be in any of a number of states. Each state is characterized by a set of binary features, and differs from some other neighbor state or states by just one of those features. The book considers the evolution of such a system over time and analyzes such a structure from algebraic and probabilistic (stochastic) standpoints.
Algorithms and Data Structures
This book constitutes the refereed proceedings of the 11th Algorithms and Data Structures Symposium, WADS 2009, held in Banff, Canada, in August 2009. The Algorithms and Data Structures Symposium - WADS (formerly "Workshop on Algorithms and Data Structures") is intended as a forum for researchers in the area of design and analysis of algorithms and data structures. The 49 revised full papers presented in this volume were carefully reviewed and selected from 126 submissions. The papers present original research on algorithms and data structures in all areas, including bioinformatics, combinatorics, computational geometry, databases, graphics, and parallel and distributed computing.
Range
'A goldmine of surprising insights. Makes you smarter with every page' - James Clear, author of Atomic Habits The essential guide to improving your performance, and a powerful argument for how to succeed in any field: develop broad interests and skills while everyone around you is rushing to specialize. The instant Sunday Times bestseller From the ‘10,000 hours rule’ to the power of tiger parenting, we have been taught that success in any field requires early specialization and many hours of deliberate practice. If you only dabble or delay, you'll never catch up with those who got a head start. This is completely wrong. In this landmark book, David Epstein shows you that the way to succe...
Data Structures
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Geometry Junkyard
Presents a collection of resources on geometry topics, including Usenet clippings, lecture notes, research excerpts, papers, abstracts, problems, and other items. Contains lesson plans and teaching materials and pointers to software and animations.
Algorithms and Data Structures
This book constitutes the refereed proceedings of the 16th International Symposium on Algorithms and Data Structures, WADS, 2019, held in Edmonton, AB, Canada, in August 2019. The 42 full papers presented together with 3 invited lectures, we carefully reviewed and selected from a total of 88 submissions. They present original research on the theory and application of algorithms and data structures in many areas, including combinatorics, computational geometry, databases, graphics, and parallel and distributed computing.
Learning Spaces
Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes. Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At the heart of ALEKS is an artificial intelligence engine that assesses each student individually and continously. The book is of interest to mathematically oriented readers in education, computer science, engineering, and combinatorics at research and graduate levels. Numerous examples and exercises are included, together with an extensive bibliography.
Conway's Game of Life
Dead cells with three live neighbors are born, while live cells with fewer than two or more than three live neighbors die. These simple rules define Conway's Game of Life, which exhibits complex and unpredictable behavior that has been studied for over 50 years. This book provides a thorough introduction to the Game of Life, the mathematics behind it, and the methods used to construct many of its most interesting patterns. It emphasizes conceptual techniques for constructing patterns that evolve in unusual ways, and guides the reader through the thought processes and ideas that are needed to combine various building blocks into more interesting composite patterns. While this book largely follows the history of the Game of Life, that is not its primary purpose. Rather, it is a by-product of the fact that most recently discovered patterns build upon patterns and techniques that were developed earlier. The goal of this book is to demystify the Game of Life by breaking down the complex patterns that have been developed in it into bite-size chunks that can be understood individually. Free (watermarked) PDF and associated pattern files available for download from conwaylife.com/book
