According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

    The rest is known as dark matter and dark energy, because their precise identities are unknown. "The Cosmic Cocktail" is the inside story of the epic quest to solve one of the most compelling enigmas of modern science--what is the universe made of?--told by one of today's foremost pioneers in the study of dark matter.Blending cutting-edge science with her own behind-the-scenes insights as a leading researcher in the field, acclaimed theoretical physicist Katherine Freese recounts the hunt for dark matter, from the discoveries of visionary scientists like Fritz Zwicky--the Swiss astronomer who coined the term "dark matter" in 1933--to the deluge of data today from underground laboratories, satellites in space, and the Large Hadron Collider. Theorists contend that dark matter consists of fundamental particles known as WIMPs, or weakly interacting massive particles. Billions of them pass through our bodies every second without us even realizing it, yet their gravitational pull is capable of whirling stars and gas at breakneck speeds around the centers of galaxies, and bending light from distant bright objects. Freese describes the larger-than-life characters and clashing personalities behind the race to identify these elusive particles.Many cosmologists believe we are on the verge of solving the mystery. "The Cosmic Cocktail" provides the foundation needed to fully fathom this epochal moment in humankind's quest to understand the universe.

    Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled Calculus Required.) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors), to show how the computer is used, and to introduce applications of linear algebra in a one-semester course.

    There are deep connections between stars and atoms, between the cosmos and the microworld. Just six numbers, imprinted in the "big bang," determine the essential features of our entire physical world. Moreover, cosmic evolution is astonishingly sensitive to the values of these numbers. If any one of them were "untuned," there could be no stars and no life. This realization offers a radically new perspective on our universe, our place in it, and the nature of physical laws.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    In the quantum realm, objects can be in two places at once. It's a place where time travel is not only possible, but necessary. It's a place where cause and effect can happen in reverse and observing something changes its state. From parallel universes to antimatter, quantum mechanics has revealed that when you get right down to it, the laws of nature are insane. The scientist J. B. S. Haldane once said, 'Reality is not only stranger than we imagine . . . it's stranger than we can imagine.' Never is this more true than with quantum mechanics; our best, most recent attempt to make sense of the fundamental laws of nature.Fundamental is a comprehensive beginner's guide to quantum mechanics, explaining not only the weirdness of the subject but the experiments that proved it to be true. Using a humorous and light-hearted approach, Fundamental tells the story of how the most brilliant minds in science grappled with seemingly impossible ideas and gave us everything from microchips to particle accelerators. Fundamental gives clear explanations of all the quantum phenomena known to modern science, without requiring an understanding of complex mathematics; tells the eccentric stories of the scientists who made these shattering discoveries and what they used them for; explains how quantum field theory (a topic not covered in detail by any other popular-science book) gave rise to particle physics and why the Higgs boson isn't the end of the story.

    QFT is the only physics theory that makes sense and that dispels or resolves the paradoxes of relativity and quantum mechanics that have confused and mystified so many people.

    As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

    In this amazingly comprehensible history of the universe, Simon Singh decodes the mystery behind the Big Bang theory, lading us through the development of one of the most extraordinary, important, and awe-inspiring theories in science.

    In this book, a wealth of exercises are provided throughout each section, designed to reinforce learning and the logical comprehension of topics. The use of real data is incorporated much more extensively than in any other book on the market. Consist of strong coverage of computer-based methods, especially in the coverage of analysis of variance and regression. This text stresses mastery of methods most often used in medical research, with specific reference to actual medical literature and actual medical research. The approach minimizes mathematical formulation, yet gives complete explanations of all important concepts. Every new concept is systematically developed through completely worked-out examples from current medical research problems. Computer output is used to illustrate concepts when appropriate.

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    This brief, accessible introduction describes some of the most interesting research in the field and also enables readers to implement and experiment with genetic algorithms on their own. It focuses in depth on a small set of important and interesting topics--particularly in machine learning, scientific modeling, and artificial life--and reviews a broad span of research, including the work of Mitchell and her colleagues.The descriptions of applications and modeling projects stretch beyond the strict boundaries of computer science to include dynamical systems theory, game theory, molecular biology, ecology, evolutionary biology, and population genetics, underscoring the exciting general purpose nature of genetic algorithms as search methods that can be employed across disciplines.An Introduction to Genetic Algorithms is accessible to students and researchers in any scientific discipline. It includes many thought and computer exercises that build on and reinforce the reader's understanding of the text. The first chapter introduces genetic algorithms and their terminology and describes two provocative applications in detail. The second and third chapters look at the use of genetic algorithms in machine learning (computer programs, data analysis and prediction, neural networks) and in scientific models (interactions among learning, evolution, and culture; sexual selection; ecosystems; evolutionary activity). Several approaches to the theory of genetic algorithms are discussed in depth in the fourth chapter. The fifth chapter takes up implementation, and the last chapter poses some currently unanswered questions and surveys prospects for the future of evolutionary computation.

    This book introduces you to R, RStudio, and the tidyverse, a collection of R packages designed to work together to make data science fast, fluent, and fun. Suitable for readers with no previous programming experience, R for Data Science is designed to get you doing data science as quickly as possible. Authors Hadley Wickham and Garrett Grolemund guide you through the steps of importing, wrangling, exploring, and modeling your data and communicating the results. You’ll get a complete, big-picture understanding of the data science cycle, along with basic tools you need to manage the details. Each section of the book is paired with exercises to help you practice what you’ve learned along the way. You’ll learn how to: Wrangle—transform your datasets into a form convenient for analysis Program—learn powerful R tools for solving data problems with greater clarity and ease Explore—examine your data, generate hypotheses, and quickly test them Model—provide a low-dimensional summary that captures true "signals" in your dataset Communicate—learn R Markdown for integrating prose, code, and results

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    This work has played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of the classical ideas of space, time and locality. This book contains all of John Bell's published and unpublished papers on the conceptual and philosophical problems of quantum mechanics.