These sections together make an appropriate one-term advanced/graduate level course (mathematical prerequisites: vector analysis and simple partial-differential equations). The book is printed to make it easy for readers to identify these sections.• The remaining Track 2 material provides a wealth of advanced topics instructors can draw from to flesh out a two-term course, with Track 1 sections serving as prerequisites.

    The book s two-part coverage organizes topics under basic theory, and assembles an arsenal of approximation schemes with illustrative applications. For physicists and engineers. "

    

    The Cleveland Cavaliers' star has appeared on the cover of Sports Illustrated, has had his high school jersey retired, and signed a $90 million contract with Nike. His future is truly bright.

    Aczel turns his sights on probability theory -- the branch of mathematics that measures the likelihood of a random event. He explains probability in clear, layman's terms, and shows its practical applications. What is commonly called luck has mathematical roots and in Chance, you'll learn to increase your odds of success in everything from true love to the stock market. For thousands of years, the twin forces of chance and mischance have beguiled humanity like none other. Why does fortune smile on some people, and smirk on others? What is luck, and why does it so often visit the undeserving? How can we predict the random events happening around us? Even better, how can we manipulate them? In this delightful and lucid voyage through the realm of the random, Dr. Aczel once again makes higher mathematics intelligible to us.

    Now that machine learning is thriving, even programmers who know close to nothing about this technology can use simple, efficient tools to implement programs capable of learning from data. This practical book shows you how.By using concrete examples, minimal theory, and two production-ready Python frameworks—Scikit-Learn and TensorFlow—author Aurélien Géron helps you gain an intuitive understanding of the concepts and tools for building intelligent systems. You’ll learn how to use a range of techniques, starting with simple Linear Regression and progressing to Deep Neural Networks. If you have some programming experience and you’re ready to code a machine learning project, this guide is for you.This hands-on book shows you how to use:Scikit-Learn, an accessible framework that implements many algorithms efficiently and serves as a great machine learning entry pointTensorFlow, a more complex library for distributed numerical computation, ideal for training and running very large neural networksPractical code examples that you can apply without learning excessive machine learning theory or algorithm details

    It is designed as a reference for students in the physical sciences and engineering.

    However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice-freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You'll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you've mastered these techniques, you'll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes - Learning the Bayesian "state of mind" and its practical implications - Understanding how computers perform Bayesian inference - Using the PyMC Python library to program Bayesian analyses - Building and debugging models with PyMC - Testing your model's "goodness of fit" - Opening the "black box" of the Markov Chain Monte Carlo algorithm to see how and why it works - Leveraging the power of the "Law of Large Numbers" - Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning - Using loss functions to measure an estimate's weaknesses based on your goals and desired outcomes - Selecting appropriate priors and understanding how their influence changes with dataset size - Overcoming the "exploration versus exploitation" dilemma: deciding when "pretty good" is good enough - Using Bayesian inference to improve A/B testing - Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.

    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.

    . . a most valuable contribution." — Douglas R. Hofstadter, author of Gödel, Escher, BachThe foundations of game theory were laid by John von Neumann, who in 1928 proved the basic minimax theorem, and with the 1944 publication of the Theory of Games and Economic Behavior, the field was established. Since then, game theory has become an enormously important discipline because of its novel mathematical properties and its many applications to social, economic, and political problems.Game theory has been used to make investment decisions, pick jurors, commit tanks to battle, allocate business expenses equitably — even to measure a senator's power, among many other uses. In this revised edition of his highly regarded work, Morton Davis begins with an overview of game theory, then discusses the two-person zero-sum game with equilibrium points; the general, two-person zero-sum game; utility theory; the two-person, non-zero-sum game; and the n-person game.A number of problems are posed at the start of each chapter and readers are given a chance to solve them before moving on. (Unlike most mathematical problems, many problems in game theory are easily understood by the lay reader.) At the end of the chapter, where solutions are discussed, readers can compare their "common sense" solutions with those of the author. Brimming with applications to an enormous variety of everyday situations, this book offers readers a fascinating, accessible introduction to one of the most fruitful and interesting intellectual systems of our time.

    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

    Begun in 1982, the Algebra Project is transforming math education in twenty-five cities. Founded on the belief that math-science literacy is a prerequisite for full citizenship in society, the Project works with entire communities-parents, teachers, and especially students-to create a culture of literacy around algebra, a crucial stepping-stone to college math and opportunity.Telling the story of this remarkable program, Robert Moses draws on lessons from the 1960s Southern voter registration he famously helped organize: 'Everyone said sharecroppers didn't want to vote. It wasn't until we got them demanding to vote that we got attention. Today, when kids are falling wholesale through the cracks, people say they don't want to learn. We have to get the kids themselves to demand what everyone says they don't want.'We see the Algebra Project organizing community by community. Older kids serve as coaches for younger students and build a self-sustained tradition of leadership. Teachers use innovative techniques. And we see the remarkable success stories of schools like the predominately poor Hart School in Bessemer, Alabama, which outscored the city's middle-class flagship school in just three years.Radical Equations provides a model for anyone looking for a community-based solution to the problems of our disadvantaged schools.

    

    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.

    'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science.