Sousa discusses the cognitive mechanisms for learning mathematics and the environmental and developmental factors that contribute to mathematics difficulties. This award-winning text examines:Children's innate number sense and how the brain develops an understanding of number relationships Rationales for modifying lessons to meet the developmental learning stages of young children, preadolescents, and adolescents How to plan lessons in PreK-12 mathematics Implications of current research for planning mathematics lessons, including discoveries about memory systems and lesson timing Methods to help elementary and secondary school teachers detect mathematics difficulties Clear connections to the NCTM standards and curriculum focal points

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    In 1935, aged 22, he developed the mathematical theory upon which all subsequent stored-program digital computers are modeled.At the outbreak of hostilities with Germany in September 1939, he joined the Government Codebreaking team at Bletchley Park, Buckinghamshire and played a crucial role in deciphering Engima, the code used by the German armed forces to protect their radio communications. Turing's work on the versionof Enigma used by the German navy was vital to the battle for supremacy in the North Atlantic. He also contributed to the attack on the cyphers known as Fish, which were used by the German High Command for the encryption of signals during the latter part of the war. His contribution helped toshorten the war in Europe by an estimated two years.After the war, his theoretical work led to the development of Britain's first computers at the National Physical Laboratory and the Royal Society Computing Machine Laboratory at Manchester University.Turing was also a founding father of modern cognitive science, theorizing that the cortex at birth is an unorganized machine which through training becomes organized into a universal machine or something like it. He went on to develop the use of computers to model biological growth, launchingthe discipline now referred to as Artificial Life.The papers in this book are the key works for understanding Turing's phenomenal contribution across all these fields. The collection includes Turing's declassified wartime Treatise on the Enigma; letters from Turing to Churchill and to codebreakers; lectures, papers, and broadcasts which opened upthe concept of AI and its implications; and the paper which formed the genesis of the investigation of Artifical Life.

    Based on a course of lectures delivered by the author at Columbia University, the text is elementary in treatment and remarkable for its clarity and organization. Although it is assumed that the reader is familiar with the fundamental facts of thermometry and calorimetry, no advanced mathematics beyond calculus is assumed.Partial contents: thermodynamic systems, the first law of thermodynamics (application, adiabatic transformations), the second law of thermodynamics (Carnot cycle, absolute thermodynamic temperature, thermal engines), the entropy (properties of cycles, entropy of a system whose states can be represented on a (V, p) diagram, Clapeyron and Van der Waals equations), thermodynamic potentials (free energy, thermodynamic potential at constant pressure, the phase rule, thermodynamics of the reversible electric cell), gaseous reactions (chemical equilibria in gases, Van't Hoff reaction box, another proof of the equation of gaseous equilibria, principle of Le Chatelier), the thermodynamics of dilute solutions (osmotic pressure, chemical equilibria in solutions, the distribution of a solute between 2 phases vapor pressure, boiling and freezing points), the entropy constant (Nernst's theorem, thermal ionization of a gas, thermionic effect, etc.).

    John Taylor has brought to his new book, Classical Mechanics, all of the clarity and insight that made his introduction to Error Analysis a best-selling text.

    With amusing examples from film, TV, and history, learn how physics affects everything in your surroundings--without the use of mind-bending math or the need for a particle accelerator. With E=MC2, you'll learn: When forces balance: Simple answers to questions such as, "Why do balloons rise while apples fall?" The Good, the Bad, and the Impossible: Why The Good, the Bad, and the Ugly is full of absurdities. (For someone whose characters often uphold the law, Clint Eastwood certainly defies the laws of physics in this film.) AC/DC: but only AC really rocks: Alternating current (AC) is much more complicated than direct current (DC). The voltage is constantly moving between positive and negative; the current therefore flows one way, and then the other (rocking back and forth). Why do I feel this warm glow?: The theory behind how the first stars were born General Relativity and GPS: The strange result of gravity on time is well proven. Compared to the interminable time you experience while stuck in a traffic jam, time literally runs faster (because gravity is weaker) in the orbiting GPS satellites that help your GPS system get its fix. At the speed of light: A refresher on the theory of relativity and an understanding of why--a hundred years later--Einstein's physics still points the way in cutting-edge research. Yu again: In the martial arts movie Crouching Tiger, Hidden Dragon, the rebellious young heroine, Jen Yu, blocks an attacker with her hand without standing or bracing herself. All the while, she holds a cup of tea in her other hand and doesn't spill a drop. Find out why kinetic energy and scalar quantity make her move impossible. It's physics for the rest of us. So why not come along for the ride? Advance at the speed of light through the fundamental laws of physics as they were discovered, proven wrong, and revolutionized. Make this and all of the Blackboard Books(tm) a permanent fixture on your shelf, and you'll have instant access to a breadth of knowledge. Whether you need homework help or want to win that trivia game, this series is the trusted source for fun facts.

    This completely updated edition brings you all the latest information about LaTeX and the vast range of add-on packages now available--over 200 are covered! Full of new tips and tricks for using LaTeX in both traditional and modern typesetting, this book will also show you how to customize layout features to your own needs--from phrases and paragraphs to headings, lists, and pages. Inside, you will find: Expert advice on using LaTeX's basic formatting tools to create all types of publications--from memos to encyclopedias In-depth coverage of important extension packages for tabular and technical typesetting, floats and captions, multicolumn layouts--including reference guides and discussions of the underlying typographic and TeXnical concepts Detailed techniques for generating and typesetting contents lists, bibliographies, indexes, etc. Tips and tricks for LaTeX programmers and systems support New to this edition: Nearly 1,000 fully tested examples that illustrate the text and solve typographical and technical problems--all ready to run! An additional chapter on citations and bibliographies Expanded material on the setup and use of fonts to access a huge collection of glyphs, and to typeset text from a wide range of languages and cultures Major new packages for graphics, "verbatim" listings, floats, and page layout Full coverage of the latest packages for all types ofdocuments--mathematical, multilingual, and many more Detailed help on all error messages, including those troublesome low-level TeX errors Like its predecessor, The LaTeX Companion, Second Edition, is an indispensable reference for anyone wishing to use LaTeX productively. The accompanying CD-ROM contains a complete plug-and-play LaTeX installation, including all the packages and examples featured in the book.

    Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. This book can be used for readers who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.

    This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

     They are also used in countless industries such as medicine, manufacturing and finance to help companies make better decisions and reduce risk. Whether coded or scratched out by hand, both algorithms are powerful tools that can make a significant impact. This book is a visual introduction for beginners that unpacks the fundamentals of decision trees and random forests. If you want to dig into the basics with a visual twist plus create your own machine learning algorithms in Python, this book is for you.

    Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

    Hamilton was reshaping the image of the vampire with her own take on the vampire mythos in her Anita Blake, Vampire Hunter fantasy novel series. While Hamilton's work draws on traditional vampire and fairy lore, her interpretation of these subjects brought new dimensions to the genres, influencing the direction of urban fantasy over the past two decades.Reading Laurell K. Hamilton focuses upon Hamilton's two bestselling series, the Anita Blake, Vampire Hunter series and the Merry Gentry series. The volume is intended as a resource for leaders of book clubs or discussion groups, containing chapters that examine Hamilton's role in the current vampire literature craze, the themes and characters in her work, and responses to Hamilton on the Internet. The book also provides a brief overview of Hamilton's life.

    It offers a comprehensive and accessible treatment of the theory of algorithms and complexity—the elegant body of concepts and methods developed by computer scientists over the past 30 years for studying the performance and limitations of computer algorithms. The book is self-contained in that it develops all necessary mathematical prerequisites from such diverse fields such as computability, logic, number theory and probability.

    New co-authors--Irl Bivens and Stephen Davis--from Davidson College; both distinguished educators and writers.* More emphasis on graphing calculators in exercises and examples, including CAS capabilities of graphing calculators.* More problems using tabular data and more emphasis on mathematical modeling.