Neural networks are a key element of deep learning and artificial intelligence, which today is capable of some truly impressive feats. Yet too few really understand how neural networks actually work. This guide will take you on a fun and unhurried journey, starting from very simple ideas, and gradually building up an understanding of how neural networks work. You won't need any mathematics beyond secondary school, and an accessible introduction to calculus is also included. The ambition of this guide is to make neural networks as accessible as possible to as many readers as possible - there are enough texts for advanced readers already! You'll learn to code in Python and make your own neural network, teaching it to recognise human handwritten numbers, and performing as well as professionally developed networks. Part 1 is about ideas. We introduce the mathematical ideas underlying the neural networks, gently with lots of illustrations and examples. Part 2 is practical. We introduce the popular and easy to learn Python programming language, and gradually builds up a neural network which can learn to recognise human handwritten numbers, easily getting it to perform as well as networks made by professionals. Part 3 extends these ideas further. We push the performance of our neural network to an industry leading 98% using only simple ideas and code, test the network on your own handwriting, take a privileged peek inside the mysterious mind of a neural network, and even get it all working on a Raspberry Pi. All the code in this has been tested to work on a Raspberry Pi Zero.

    Python is easy to learn, and it's perfect for exploring topics like statistics, geometry, probability, and calculus. You’ll learn to write programs to find derivatives, solve equations graphically, manipulate algebraic expressions, even examine projectile motion.Rather than crank through tedious calculations by hand, you'll learn how to use Python functions and modules to handle the number crunching while you focus on the principles behind the math. Exercises throughout teach fundamental programming concepts, like using functions, handling user input, and reading and manipulating data. As you learn to think computationally, you'll discover new ways to explore and think about math, and gain valuable programming skills that you can use to continue your study of math and computer science.If you’re interested in math but have yet to dip into programming, you’ll find that Python makes it easy to go deeper into the subject—let Python handle the tedious work while you spend more time on the math.

    However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years. In particular, Bayesian methods have grown from a specialist niche to become mainstream, while graphical models have emerged as a general framework for describing and applying probabilistic models. Also, the practical applicability of Bayesian methods has been greatly enhanced through the development of a range of approximate inference algorithms such as variational Bayes and expectation propagation. Similarly, new models based on kernels have had a significant impact on both algorithms and applications. This new textbook reflects these recent developments while providing a comprehensive introduction to the fields of pattern recognition and machine learning. It is aimed at advanced undergraduates or first-year PhD students, as well as researchers and practitioners, and assumes no previous knowledge of pattern recognition or machine learning concepts. Knowledge of multivariate calculus and basic linear algebra is required, and some familiarity with probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory.

    Reflecting the need for even minor programming in today's model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work.The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation.By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling.Web ResourceThe book is accompanied by an R package (rethinking) that is available on the author's website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.

    Thoroughly updated to include Java 6, the Third Edition of Horstmann's bestselling text helps you absorb computing concepts and programming principles, develop strong problem-solving skills, and become a better programmer, all while exploring the elements of Java that are needed to write real-life programs. A top-notch introductory text for beginners, Big Java, Third Edition is also a thorough reference for students and professionals alike to Java technologies, Internet programming, database access, and many other areas of computer science.Features of the Third Edition: The 'Objects Gradual' approach leads you into object-oriented thinking step-by-step, from using classes, implementing simple methods, all the way to designing your own object-oriented programs. A strong emphasis on test-driven development encourages you to consider outcomes as you write programming code so you design better, more usable programs Helpful "Testing Track" introduces techniques and tools step by step, ensuring that you master one before moving on to the next New teaching and learning tools in WileyPLUS--including a unique assignment checker that enables you to test your programming problems online before you submit them for a grade Graphics topics are developed gradually throughout the text, conveniently highlighted in separate color-coded sections Updated coverage is fully compatible with Java 5 and includes a discussion of the latest Java 6 features

    The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)"No matter how gently one introduces students to the concept of Dirac's bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin)Reviews of the Second Edition:"This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. ... It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews)R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include:- Clear, accessible treatment of underlying mathematics- A review of Newtonian, Lagrangian, and Hamiltonian mechanics- Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates- Unsurpassed coverage of path integrals and their relevance in contemporary physicsThe requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book's self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

    The story of information begins in a time profoundly unlike our own, when every thought and utterance vanishes as soon as it is born. From the invention of scripts and alphabets to the long-misunderstood talking drums of Africa, Gleick tells the story of information technologies that changed the very nature of human consciousness. He provides portraits of the key figures contributing to the inexorable development of our modern understanding of information: Charles Babbage, the idiosyncratic inventor of the first great mechanical computer; Ada Byron, the brilliant and doomed daughter of the poet, who became the first true programmer; pivotal figures like Samuel Morse and Alan Turing; and Claude Shannon, the creator of information theory itself. And then the information age arrives. Citizens of this world become experts willy-nilly: aficionados of bits and bytes. And we sometimes feel we are drowning, swept by a deluge of signs and signals, news and images, blogs and tweets. The Information is the story of how we got here and where we are heading.

    The real response to the question should be, "Yes, you will, because algebra gives you power" - the power to help your children with their math homework, the power to manage your finances, the power to be successful in your career (especially if you have to manage the company budget). The list goes on. Algebra is a system of mathematical symbols and rules that are universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end to solve complex problems. There's no doubt that algebra can be easy to some while extremely challenging to others. For those of you who are challenged by working with numbers, Algebra I For Dummies can provide the help you need.This easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems. But rest assured, this book is not about memorizing a bunch of meaningless steps; you find out the whys behind algebra to increase your understanding of how algebra works.In Algebra I For Dummies, you'll discover the following topics and more:All about numbers - rational and irrational, variables, and positive and negative Figuring out fractions and decimals Explaining exponents and radicals Solving linear and quadratic equations Understanding formulas and solving story problems Having fun with graphs Top Ten lists on common algebraic errors, factoring tips, and divisibility rules. No matter if you're 16 years old or 60 years old; no matter if you're learning algebra for the first time or need a quick refresher course; no matter if you're cramming for an algebra test, helping your kid with his or her homework, or coming up with next year's company budget, Algebra I For Dummies can give you the tools you need to succeed.

    Politicians and marketers present shoddy evidence for dubious claims all the time. But smart people make mistakes too, and when it comes to statistics, plenty of otherwise great scientists--yes, even those published in peer-reviewed journals--are doing statistics wrong."Statistics Done Wrong" comes to the rescue with cautionary tales of all-too-common statistical fallacies. It'll help you see where and why researchers often go wrong and teach you the best practices for avoiding their mistakes.In this book, you'll learn: - Why "statistically significant" doesn't necessarily imply practical significance- Ideas behind hypothesis testing and regression analysis, and common misinterpretations of those ideas- How and how not to ask questions, design experiments, and work with data- Why many studies have too little data to detect what they're looking for-and, surprisingly, why this means published results are often overestimates- Why false positives are much more common than "significant at the 5% level" would suggestBy walking through colorful examples of statistics gone awry, the book offers approachable lessons on proper methodology, and each chapter ends with pro tips for practicing scientists and statisticians. No matter what your level of experience, "Statistics Done Wrong" will teach you how to be a better analyst, data scientist, or researcher.

    Authors Drew Conway and John Myles White help you understand machine learning and statistics tools through a series of hands-on case studies, instead of a traditional math-heavy presentation.Each chapter focuses on a specific problem in machine learning, such as classification, prediction, optimization, and recommendation. Using the R programming language, you'll learn how to analyze sample datasets and write simple machine learning algorithms. "Machine Learning for Hackers" is ideal for programmers from any background, including business, government, and academic research.Develop a naive Bayesian classifier to determine if an email is spam, based only on its textUse linear regression to predict the number of page views for the top 1,000 websitesLearn optimization techniques by attempting to break a simple letter cipherCompare and contrast U.S. Senators statistically, based on their voting recordsBuild a "whom to follow" recommendation system from Twitter data

    KEY TOPICS: The major changes of the revision are reorganization of chapter material and the addition of a much wider range of difficulties.

    The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra.

    This work includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.