Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

    Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.'W.W. Sawyer's deep understanding of how we learn and his lively, practical approach have made this an ideal introduction to mathematics for generations of readers. By starting at the level of simple arithmetic and algebra and then proceeding step by step through graphs, logarithms and trigonometry to calculus and the dizzying world of imaginary numbers, the book takes the mystery out of maths. Throughout, Sawyer reveals how theory is subordinate to the real-life applications of mathematics - the Pyramids were built on Euclidean principles three thousand years before Euclid formulated them - and celebrates the sheer intellectual stimulus of mathematics at its best.

    R has traditionally been difficult for non-statisticians to learn, and most R books assume far too much knowledge to be of help. R for Everyone is the solution. Drawing on his unsurpassed experience teaching new users, professional data scientist Jared P. Lander has written the perfect tutorial for anyone new to statistical programming and modeling. Organized to make learning easy and intuitive, this guide focuses on the 20 percent of R functionality you'll need to accomplish 80 percent of modern data tasks. Lander's self-contained chapters start with the absolute basics, offering extensive hands-on practice and sample code. You'll download and install R; navigate and use the R environment; master basic program control, data import, and manipulation; and walk through several essential tests. Then, building on this foundation, you'll construct several complete models, both linear and nonlinear, and use some data mining techniques. By the time you're done, you won't just know how to write R programs, you'll be ready to tackle the statistical problems you care about most. COVERAGE INCLUDES - Exploring R, RStudio, and R packages - Using R for math: variable types, vectors, calling functions, and more - Exploiting data structures, including data.frames, matrices, and lists - Creating attractive, intuitive statistical graphics - Writing user-defined functions - Controlling program flow with if, ifelse, and complex checks - Improving program efficiency with group manipulations - Combining and reshaping multiple datasets - Manipulating strings using R's facilities and regular expressions - Creating normal, binomial, and Poisson probability distributions - Programming basic statistics: mean, standard deviation, and t-tests - Building linear, generalized linear, and nonlinear models - Assessing the quality of models and variable selection - Preventing overfitting, using the Elastic Net and Bayesian methods - Analyzing univariate and multivariate time series data - Grouping data via K-means and hierarchical clustering - Preparing reports, slideshows, and web pages with knitr - Building reusable R packages with devtools and Rcpp - Getting involved with the R global community

    

    HEA guaranteed!

    The revised edition is updated with a greater focus on digital recording techniques, the most powerful tools available to the home recordist. There are chapters devoted to instrument recording, humanizing drum patterns, mixing with plug-ins and virtual consoles, and a new section on using digital audio skills. And since, many true "Guerrillas" still record to analog tape, we have retained the best of that world. This edition features many more graphics than in the original edition, further enforcing Guerrilla Home Recording's reputation as the most readable, user-frienly recording title on the market.

    Every integrated software development environment in the world--open-source, standards-based, and proprietary--now supports UML and, more importantly, the model-driven approach to software development. This makes learning the newest UML standard, UML 2.0, critical for all software developers--and there isn't a better choice than this clear, step-by-step guide to learning the language."--Richard Mark Soley, Chairman and CEO, OMGIf you're like most software developers, you're building systems that are increasingly complex. Whether you're creating a desktop application or an enterprise system, complexity is the big hairy monster you must manage.The Unified Modeling Language (UML) helps you manage this complexity. Whether you're looking to use UML as a blueprint language, a sketch tool, or as a programming language, this book will give you the need-to-know information on how to apply UML to your project. While there are plenty of books available that describe UML, Learning UML 2.0 will show you how to use it. Topics covered include:Capturing your system's requirements in your model to help you ensure that your designs meet your users' needsModeling the parts of your system and their relationshipsModeling how the parts of your system work together to meet your system's requirementsModeling how your system moves into the real world, capturing how your system will be deployedEngaging and accessible, this book shows you how to use UML to craft and communicate your project's design. Russ Miles and Kim Hamilton have written a pragmatic introduction to UML based on hard-earned practice, not theory. Regardless of the software process or methodology you use, this book is the one source you need to get up and running with UML 2.0.Russ Miles is a software engineer for General Dynamics UK, where he works with Java and Distributed Systems, although his passion at the moment is Aspect Orientation and, in particular, AspectJ. Kim Hamilton is a senior software engineer at Northrop Grumman, where she's designed and implemented a variety of systems including web applications and distributed systems, with frequent detours into algorithms development.

    HINTS SOLUTIONS of GRB PROBLEMS IN CALCULUS FOR JEE MAIN ADVANCED by Sameer Bansal

    This view was at the core of the compact between government and science that led to the golden age of scientific research after World War II—a compact that is currently under severe stress. In this book, Donald Stokes challenges Bush's view and maintains that we can only rebuild the relationship between government and the scientific community when we understand what is wrong with that view.Stokes begins with an analysis of the goals of understanding and use in scientific research. He recasts the widely accepted view of the tension between understanding and use, citing as a model case the fundamental yet use-inspired studies by which Louis Pasteur laid the foundations of microbiology a century ago. Pasteur worked in the era of the "second industrial revolution," when the relationship between basic science and technological change assumed its modern form. Over subsequent decades, technology has been increasingly science-based. But science has been increasingly technology-based--with the choice of problems and the conduct of research often inspired by societal needs. An example is the work of the quantum-effects physicists who are probing the phenomena revealed by the miniaturization of semiconductors from the time of the transistor's discovery after World War II.On this revised, interactive view of science and technology, Stokes builds a convincing case that by recognizing the importance of use-inspired basic research we can frame a new compact between science and government. His conclusions have major implications for both the scientific and policy communities and will be of great interest to those in the broader public who are troubled by the current role of basic science in American democracy.

    She easily connects to them through her conversational style, empathy, case studies and a strong belief in their power to succeed. She shares strategies for learning through graphics and activities that ensure their active engagement. She fully understands the importance of readability as she fills the text with questions. This book explodes with energy and passion and should be on every student's bookshelf. -Martha E. Casazza, Educational Consultant, TRPPAssociates, CLADEA Founding Fellow"Much can be gained from this book by both students and instructors in all fields. My biggest take-away is the author's insistence, 'Now hear this: All students are capable of excelling'. This book shows how."--Reflective TeachingMaybe this is a reflection on just how big of a nerd I am, but this is the book that I wish I had when I was in college, or even in high school, to understand that I could have a little bit more control over my brain, and harness [its] power in a good direction. It would be really good for a first-year student seminar, a class that focused on study skills, or a tutoring center.--Kathryn (Katie) Linder, Research Director for Ecampus, Oregon State University

    

    Escher -- goes to some of the strangest spots imaginable. It takes us to a place where the purely intellectual enters our daily world: where our outraged senses, overloaded with grocery bills, the price of gas, and what to eat for lunch, are expected to absorb really bizarre ideas. And no better guide to this weird universe exists than the brilliant thinker Clifford A. Pickover, the 21st century's answer to Buckminster Fuller. Come along as Pickover traces the origins of the Mobius strip from the mid-1800s, when the visionary scientist Dr. August Mobius became the first to describe the properties of one-sided surfaces, to the present, where it is an integral part of mathematics, magic, science, art, engineering, literature, and music. It has become a metaphor for change, strangeness, looping, and rejuvenation. Touching on everything from molecules and metal sculptures to postage stamps, architectural structures, and models of our entire universe, The Mobius Strip is lavishly illustrated and gives readers a glimpse into other worlds and new ways of thinking as Pickover reaches across cultures and dimensions.

    Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    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.

    Now more visual and even easier to use and understand, EasyWriter offers practical help with research and documentation and expanded coverage of academic writing for students in all disciplines.