Selected for originality, general interest, or because they demonstrate valuable techniques, the problems are ideal as a supplement to courses in probability or statistics, or as stimulating recreation for the mathematically minded. Detailed solutions. Illustrated.

    In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

    Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated.Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center.Algorithms is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read. Tim Roughgarden Stanford University

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.Stone's book is renowned for its visually engaging style of presentation, which stems from teaching Bayes' rule to psychology students for over 10 years as a university lecturer.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

    The beginning chapters introduce basic chemical and biological concepts to provide students with the framework they need to comprehend physiological principles. The chapters that follow promote conceptual understanding rather than rote memorization of facts. Health applications are included throughout the book to heighten interest, deepen understanding of physiological concepts, and help students relate the material to their individual career goals. Every effort has been made to help students integrate related concepts and understand the relationships between anatomical structures and their functions.

    This book is focused on the details of data analysis that sometimes fall through the cracks in traditional statistics classes and textbooks. It is based in part on the authors blog posts, lecture materials, and tutorials. The author is one of the co-developers of the Johns Hopkins Specialization in Data Science the largest data science program in the world that has enrolled more than 1.76 million people. The book is useful as a companion to introductory courses in data science or data analysis. It is also a useful reference tool for people tasked with reading and critiquing data analyses. It is based on the authors popular open-source guides available through his Github account (https://github.com/jtleek). The paper is also available through Leanpub (https://leanpub.com/datastyle), if the book is purchased on that platform you are entitled to lifetime free updates.

    The new edition maintains the authors' innovative solutions to two central problems of the course: first, the text continues to focus on about 80 sites, giving students less encyclopedic detail but essential coverage of the discoveries that have produced the major insights into prehistory; second, it continues to be organized into essays on sites and concepts, allowing professors complete flexibility in organizing their courses.

    This edition also features the developments in Operations Research, such as metaheuristics, simulation, and spreadsheet modeling.

    This practical guide that covers all of the need to know topics in a very systematic way. For each machine learning approach, each step in the process is detailed, from preparing the data for analysis to evaluating the results. These steps will build the knowledge you need to apply them to your own data science tasks.Intended for those who want to learn how to use R's machine learning capabilities and gain insight from your data. Perhaps you already know a bit about machine learning, but have never used R; or perhaps you know a little R but are new to machine learning. In either case, this book will get you up and running quickly. It would be helpful to have a bit of familiarity with basic programming concepts, but no prior experience is required.

    Dealing with measure theory and Lebesque integration, this is an introductory graduate text.

    This book surveys the most important computer algorithms currently in use and provides a full treatment of data structures and algorithms for sorting, searching, graph processing, and string processing -- including fifty algorithms every programmer should know. In this edition, new Java implementations are written in an accessible modular programming style, where all of the code is exposed to the reader and ready to use.The algorithms in this book represent a body of knowledge developed over the last 50 years that has become indispensable, not just for professional programmers and computer science students but for any student with interests in science, mathematics, and engineering, not to mention students who use computation in the liberal arts.The companion web site, algs4.cs.princeton.edu contains An online synopsis Full Java implementations Test data Exercises and answers Dynamic visualizations Lecture slides Programming assignments with checklists Links to related material The MOOC related to this book is accessible via the "Online Course" link at algs4.cs.princeton.edu. The course offers more than 100 video lecture segments that are integrated with the text, extensive online assessments, and the large-scale discussion forums that have proven so valuable. Offered each fall and spring, this course regularly attracts tens of thousands of registrants.Robert Sedgewick and Kevin Wayne are developing a modern approach to disseminating knowledge that fully embraces technology, enabling people all around the world to discover new ways of learning and teaching. By integrating their textbook, online content, and MOOC, all at the state of the art, they have built a unique resource that greatly expands the breadth and depth of the educational experience.

    This comprehensive work covers both statistical and symbolic approaches to language processing; it shows how they can be applied to important tasks such as speech recognition, spelling and grammar correction, information extraction, search engines, machine translation, and the creation of spoken-language dialog agents. The following distinguishing features make the text both an introduction to the field and an advanced reference guide.- UNIFIED AND COMPREHENSIVE COVERAGE OF THE FIELDCovers the fundamental algorithms of each field, whether proposed for spoken or written language, whether logical or statistical in origin.- EMPHASIS ON WEB AND OTHER PRACTICAL APPLICATIONSGives readers an understanding of how language-related algorithms can be applied to important real-world problems.- EMPHASIS ON SCIENTIFIC EVALUATIONOffers a description of how systems are evaluated with each problem domain.- EMPERICIST/STATISTICAL/MACHINE LEARNING APPROACHES TO LANGUAGE PROCESSINGCovers all the new statistical approaches, while still completely covering the earlier more structured and rule-based methods.