This book provides a modern introduction to the main principles that are foundational to thermal physics, thermodynamics and statistical mechanics. The key concepts are carefully presented in a clear way, and new ideas are illustrated with copious worked examples as well as a description of the historical background to their discovery. Applications are presented to subjects as diverse as stellar astrophysics, information and communication theory, condensed matter physics and climate change. Each chapter concludes with detailed exercises.

    Never again will you order the Poisson Distribution in a French restaurant!This updated version features all new material.

    Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.

    Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.

    These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning.

    Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

    Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.

    Love is.Currently in its eighteenth printing in Japan, this best-selling novel is available in English at last. Combining mathematical rigor with light romance, Math Girls is a unique introduction to advanced mathematics, delivered through the eyes of three students as they learn to deal with problems seldom found in textbooks. Math Girls has something for everyone, from advanced high school students to math majors and educators.

    Its world-class authors provide guidance on all aspects of Bayesian data analysis and include examples of real statistical analyses, based on their own research, that demonstrate how to solve complicated problems. Changes in the new edition include:Stronger focus on MCMC Revision of the computational advice in Part III New chapters on nonlinear models and decision analysis Several additional applied examples from the authors' recent research Additional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and more Reorganization of chapters 6 and 7 on model checking and data collectionBayesian computation is currently at a stage where there are many reasonable ways to compute any given posterior distribution. However, the best approach is not always clear ahead of time. Reflecting this, the new edition offers a more pluralistic presentation, giving advice on performing computations from many perspectives while making clear the importance of being aware that there are different ways to implement any given iterative simulation computation. The new approach, additional examples, and updated information make Bayesian Data Analysis an excellent introductory text and a reference that working scientists will use throughout their professional life.

    In this book, you’ll learn how many of the most fundamental data science tools and algorithms work by implementing them from scratch. If you have an aptitude for mathematics and some programming skills, author Joel Grus will help you get comfortable with the math and statistics at the core of data science, and with hacking skills you need to get started as a data scientist. Today’s messy glut of data holds answers to questions no one’s even thought to ask. This book provides you with the know-how to dig those answers out. Get a crash course in Python Learn the basics of linear algebra, statistics, and probability—and understand how and when they're used in data science Collect, explore, clean, munge, and manipulate data Dive into the fundamentals of machine learning Implement models such as k-nearest Neighbors, Naive Bayes, linear and logistic regression, decision trees, neural networks, and clustering Explore recommender systems, natural language processing, network analysis, MapReduce, and databases

    Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.

    Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning.The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models.Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

    In the modern experimentalist paradigm, these techniques address clear causal questions such as: Do smaller classes increase learning? Should wife batterers be arrested? How much does education raise wages? Mostly Harmless Econometrics shows how the basic tools of applied econometrics allow the data to speak.In addition to econometric essentials, Mostly Harmless Econometrics covers important new extensions--regression-discontinuity designs and quantile regression--as well as how to get standard errors right. Joshua Angrist and Jorn-Steffen Pischke explain why fancier econometric techniques are typically unnecessary and even dangerous. The applied econometric methods emphasized in this book are easy to use and relevant for many areas of contemporary social science.An irreverent review of econometric essentials A focus on tools that applied researchers use most Chapters on regression-discontinuity designs, quantile regression, and standard errors Many empirical examples A clear and concise resource with wide applications