Whether you're a student, parent, or teacher, this book is your key to unlocking the aha! moments that make math truly click -- and make learning enjoyable.The book intentionally avoids mindless definitions and focuses on building a deep, natural intuition so you can integrate the ideas into your everyday thinking. Its explanations on the natural logarithm, imaginary numbers, exponents and the Pythagorean Theorem are among the most-visited in the world.The topics in Math, Better Explained include:1. Developing Math Intuition2. The Pythagorean Theorem3. Pythagorean Distance4. Radians and Degrees5. Imaginary Numbers6. Complex Arithmetic7. Exponential Functions & e8. The Natural Logarithm (ln)9. Interest Rates10. Understanding Exponents11. Euler’s Formula12. Introduction To CalculusThe book is written as the author wishes math was taught: with a friendly attitude, vivid illustrations and a focus on true understanding. Learn right, not rote!

    Topics covered in the book include the properties of arithmetic, exponents, primes and divisors, fractions, equations and inequalities, decimals, ratios and proportions, unit conversions and rates, percents, square roots, basic geometry (angles, perimeter, area, triangles, and quadrilaterals), statistics, counting and probability, and more! The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems. The solutions manual (sold separately) contains full solutions to all of the problems, not just answers. This book can serve as a complete Prealgebra course. This text is supplemented by free videos and a free learning system at the publisher's website.

    But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, cryptography, and quantum computing are usually considered too "advanced" to show to the typical student. The aim of this book is to bridge both gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non computer scientists and to computer scientists who finally want to understand what their formalisms are actually telling.This book gives a lucid and playful explanation of the field, starting with P and NP-completeness. The authors explain why the P vs. NP problem is so fundamental, and why it is so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing.At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduates and undergraduates, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.To request a copy of the Solutions Manual, visit: http: //global.oup.com/uk/academic/physics/ad...

    The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world. Until the first edition of this book appearing in 2006, it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO through 2009. This second edition contains 143 new problems, picking up where the 1959-2004 edition has left off.

    If we are unsure of the meaning or usage of a mathematical word, a quick internet search is invaluable. But what are we to do when confronted with some strange mathematical hieroglyph? What does one type into the search bar? This book is the answer! Our goal is to cover mathematical notation commonly used by engineers and scientists---notation a university student is likely to encounter. We make no attempt to teach the mathematics behind these symbols. Rather, our goal is to give reminders of what these symbols mean; from there, we can consult textbooks or resources on the web. The book is organized by mathematical topic, but multiple indices steer the reader to each symbol's explanation. We also show how to produce the symbols in LaTeX and give guidance on their mathematical usage.

    Gonick’s The Cartoon Guide to Calculus is a refreshingly humorous, remarkably thorough guide to general calculus that, like his earlier Cartoon Guide to Physics and Cartoon History of the Modern World, will prove a boon to students, educators, and eager learners everywhere.

    This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures.The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary onthe puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking throughmore difficult puzzles.

    The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Caratheodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Radamacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

    Indeed, they show that Sudoku puzzles and their variants are a gateway into mathematical thinking generally. Among many topics, the authors look at the notion of a Latin square--an object of long-standing interest to mathematicians--of which Sudoku squares are a special case; discuss how one finds interesting Sudoku puzzles; explore the connections between Sudoku, graph theory, and polynomials; and consider Sudoku extremes, including puzzles with the maximal number of vacant regions, with the minimal number of starting clues, and numerous others. The book concludes with a gallery of novel Sudoku variations--just pure solving fun! Most of the puzzles are original to this volume, and all solutions to the puzzles appear in the back of the book or in the text itself.A math book and a puzzle book, Taking Sudoku Seriously will change the way readers look at Sudoku and mathematics, serving both as an introduction to mathematics for puzzle fans and as an exploration of the intricacies of Sudoku for mathematics buffs.

    Geometric algebra is an extension of linear algebra. It enhances the treatment of many linear algebra topics. And geometric algebra does much more. Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas. They provide a unified mathematical language for many areas of physics, computer science, and other fields. The book can be used for self study by those comfortable with the theorem/proof style of a mathematics text. This is a second printing, corrected and slightly revised. Visit the book's web site for more information: http: //faculty.luther.edu/ macdonal/laga I commend Alan Macdonald for his excellent book! His exposition is clean and spare. He has done a fine job of engineering a gradual transition from standard views of linear algebra to the perspective of geometric algebra. The book is sufficiently conventional to be adopted as a textbook by an adventurous teacher without getting flack from colleagues. Yet it leads to gems of geometric algebra that are likely to delight thoughtful students and surprise even the most experienced instructors. -- David Hestenes, Distinguished Research Professor, Arizona State University

    

    Hephaestus Books represents a new publishing paradigm, allowing disparate content sources to be curated into cohesive, relevant, and informative books. To date, this content has been curated from Wikipedia articles and images under Creative Commons licensing, although as Hephaestus Books continues to increase in scope and dimension, more licensed and public domain content is being added. We believe books such as this represent a new and exciting lexicon in the sharing of human knowledge. This particular book is a collaboration focused on Goosebumps.More info: Goosebumps is a series of children's horror fiction novels created and authored by R. L. Stine and published by Scholastic Publishing.

    It develops the skills and attitudes to tackle the future challenges of mathematics."-Sue O'Connell and John SanGiovanniIn today's math classroom, we want children to do more than just memorize math facts. We want them to understand the math facts they are being asked to memorize. Our goal is automaticity and understanding; without both, our children will never build the foundational skills needed to do more complex math. Both the Common Core State Standards and the NCTM Principles and Standards emphasize the importance of understanding the concepts of addition and subtraction. Sue O'Connell and John SanGiovanni provide insights into the teaching of basic math facts, including a multitude of instructional strategies, teacher tips, and classroom activities to help students master their facts while strengthening their understanding of numbers, patterns, and properties.Designed to be easily integrated into your existing math program, Mastering the Basic Math Facts: emphasizes the big ideas that provide a focus for math facts instruction broadens your repertoire of instructional strategies provides dozens of easy-to-implement activities to support varied levels of learners stimulates your reflection related to teaching math facts.Through investigations, discussions, visual models, children's literature, and hands-on explorations, students develop an understanding of the concepts of addition and subtraction, and through engaging, interactive practice achieve fluency with basic facts.Whether you're introducing your students to basic math facts, reviewing facts, or providing intervention for struggling students, this book will provide you with insights and activities to simplify this complex, but critical, component of math teaching.A teacher-friendly CD filled with customizable activities, templates, recording sheets, and teacher tools (hundred charts, multiplication tables, game templates, and assessment options) simplifies your planning and preparation. Over 450 pages of reproducible forms are included in English and Spanish translation.Study Guide included for Professional Learning Communities and Book Clubs.Discover more resources for developing mathematical thinking at Heinemann.com/Math

    A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory.Advanced undergraduate and graduate students in physics and applied mathematics will find clarity and insight into the subject in this textbook."

    

    Fisher shares his proven system of teaching that motivates students to learn and produces dramatic results. Using Mr. Fisher's method, students rapidly gain confidence and excitement that lead quickly to success. Each lesson includes an introduction to each topic that is clearly explained; a Helpful Hints section; examples with simple step-by-step solutions; written exercises; a short review section that ensures the student will remember what has been learned. No-Nonsense Algebra Chapter 1 - Necessary Tools for Algebra Chapter 2 - Solving Equations Chapter 3 - Graphing and Analyzing Linear Equations Chapter 4 - Solving and Graphing Inequalities Chapter 5 - Systems of Linear Equations and Inequalities Chapter 6 - Polynomials Chapter 7 - Rational Expressions (Algebraic Fractions) Chapter 8 - Radical Expressions and Geometry Chapter 9 - Quadratic Equations Chapter 10 - Algebra Word Problems Also includes chapter reviews, final exam, solutions for all problems, glossary, and resource center.

    It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichm�ller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

    

    Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control

    Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincar� conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems.The essential introduction to discrete and computational geometryCovers traditional topics as well as new and advanced materialFeatures numerous full-color illustrations, exercises, and unsolved problemsSuitable for sophomores in mathematics, computer science, engineering, or physicsRigorous but accessibleAn online solutions manual is available (for teachers only).

    

    Mathematician Colin Pask gently introduces you to the main ideas of mathematics and painlessly demonstrates how they are expressed in terms of symbols. He teaches the reader not only why symbols are used, and how and why equations are constructed, but also exactly what is achieved by doing that. Through simple yet intriguing examples in number theory, Pask generates confidence in thinking mathematically and reveals the pleasure of seeing how mathematical patterns evolve and are explored.

    The book is divided into two parts. 11 chapters are dedicated to the development of theoretical tools for the structural analysis of networks, and 7 chapters are illustrating, in a critical way, applications of these tools to real-world scenarios. The first chapters provide detailed coverage of adjacency and metric and topological properties of networks, followed by chapters devoted to the analysis of individual fragments and fragment-based global invariants in complex networks. Chapters that analyse the concepts of communicability, centrality, bipartivity, expansibility and communities in networks follow. The second part of this book is devoted to the analysis of genetic, protein residue, protein-protein interaction, intercellular, ecological and socio-economic networks, including important breakthroughs as well as examples of the misuse of structural concepts.

    Hopkins presents the first in-depth study of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts, especially mathematical concepts and the process of mathematical abstraction that generates them, have been key to the development of phenomenology. Both Husserl and Klein independently came to the conclusion that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein came to their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

    Whether you need to retrieve hallowed memories or just want to familiarize yourself with the mathematics underlying this degree, this unique book offers a terrific return on investment.? --Peter Carr, PhD Global Head of Modeling, Morgan Stanley; Director of the Masters Program in Mathematical Finance, Courant Institute, NYU ``This is the book I always recommend to people who ask about their mathematics before doing an MFE, and a few people could do with reading it after as well." --Dominic Connor Director, P&D Quantitative Recruitment Every exercise from the Second Edition of the Math Primer (175 exercises in total) is solved in detail in this Solutions Manual. The Solutions Manual to the Second Edition of "A Primer for the Mathematics of Financial Engineering" offers the reader the opportunity to undertake a rigorous self-study of the mathematical topics presented in the Math Primer, with the goal of achieving a deeper understanding of the financial applications therein. The First Edition of the Solutions Manual proved to be an important resource for prospective financial engineering graduate students. Using the Solution Manual as a companion to the Math Primer is an efficient way to glean a more advanced perspective on financial engineering applications by studying the solutions of the many challenging exercises. Studying the material from the Math Primer in tandem with the Solutions Manual provides the solid mathematical background required for successful graduate studies.

    This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

    Rather than reading literally dozens of physics and mathematics texts, trying to assimilate the countless ideas, translate notations and perspectives, and see how it all fits together to get a holistic understanding, this series provides a detailed overview of the major mathematical and physical ideas in theoretical particle physics. Ultimately the ideas will be presented in a unified, consistent, holistic picture, where each topic is built firmly on what has come before, and all topics are related in a clear and intuitive way.This introductory text on quantum field theory and particle physics provides both a self-contained and complete introduction to not only the necessary physical ideas, but also a complete introduction to the necessary mathematical tools. Assuming minimal knowledge of undergraduate physics and mathematics, this book lays both the mathematical and physical groundwork with clear, intuitive explanations and plenty of examples. The book then continues with an exposition of the Standard Model of Particle Physics, the theory that currently seems to explain the universe apart from gravity. Furthermore, this book was written as a primer for the more advanced mathematical and physical ideas to come later in this series.

    More than 500 exoplanets are now known, and groups world-wide are actively involved in a broad range of observational and theoretical efforts. This book ties together these many avenues of investigation - from the perspectives of observation, technology and theory - to give a comprehensive, up-to-date review of the entire field. All areas of exoplanet investigation are covered, making it a unique and valuable guide for researchers in astronomy and planetary science, including those new to the field. It treats the many different techniques now available for exoplanet detection and characterization, the broad range of underlying physics, the overlap with related topics in solar system and Earth sciences, and the concepts underpinning future developments. It emphasizes the interconnection between the various fields and provides extensive references to more in-depth treatments and reviews. Figures from the book are available at: www.cambridge.org/9780521765596.

    Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.

    These hidden texts, slowly being retrieved and deciphered by scientists, show that Archimedes' thinking (2,200 years ago) was even ahead of Isaac Newton in the 17th century.Archimedes discovered the value of Pi, he developed the theory of specific gravity and made steps towards the development of calculus. Everything we know about him comes from three manuscripts, two of which have disappeared. The third, currently in the Walters Art Museum, is a palimpsest - the text has been scraped off, the book taken apart and its parchment re-used, in this case as a prayer book. William Noel, the project director, and Reviel Netz, a historian of ancient mathematics, tell the enthralling story of the survival of that prayer book from 1229 to the present, and examine the process of recovering the invaluable text underneath as well as investigating into why that text is so important.

    From this book, you will discover new and old mathematical theorems by folding paper and find out how to reason toward proofs. With the help of 200 color figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's Web site, http: //www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.

    Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schattschneider identifies some of the mathematical inspirations of M. C. Escher's art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more.In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed physicist and mathematician Freeman Dyson. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

    Seeking to address questions raised by critics, The Philosophy of Evidence-based Medicine challenges the over dependency of EBM on randomized controlled trials. This book also explores EBM methodology and its relationship with other approaches used in medicine.

    It is the definitive work on a scientific wave theory of human experience. Nature's law: The secret of the universe (Elliott Wave) is such an important, fascinating, even mind-bending work, that it should be read by and and every serious student of the market, be they fundamentalist or technician, dealing in stocks, bonds or commodities.

    

    While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic - as this handbook attests - is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. Chapter on the Port Royal contributions to probability theory and decision theoryServes as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights

    His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics.Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.

    This text provides a comprehensive, colorful, up to date, and accessible presentation of AI without sacrificing theoretical foundations. It includes numerous examples, applications, full color images, and human interest boxes to enhance student learning. Advanced topics cover neural nets, genetic algorithms, and complex board games. A companion DVD is included with resources, simulations, and figures from the book. Numerous instructors resources are available upon adoption."

    Holistic introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras.

    Statistical and Mathematical Methods in Horse Racing" thoroughly discusses the mathematical and statistical methods in handicapping and betting techniques. Differentiations, combinatorics, normal distribution, kernel smoothing and other mathematical and statistical tools are introduced. The jargons and equations are kept to a minimum so that it is easy to understand for most readers. More than 20 professional programs are freely available to download, which can allow readers to easily apply the methodology introduced in the book.This book can be divided into three main parts: horse handicapping (Chapters 2-6), wagering (Chapters 7-9) and theories in practices (Chapters 10-11). Chapter 1 will explain why long term gains are possible in horse racing. About horse handicapping, we will start with analysing racing forms in Chapter 2. Other handicapping factors such as weight carried, jockeys, trainers and pedigrees will be discussed in Chapter 3. Some advanced statistical methods, such as chi-square test and kernel smoothing, will be introduced in Chapter 4 to further analyse those handicapping factors discussed in previous chapters. The following two chapters are about probability estimations. In Chapter 5, normal distribution and multinominal logistic regression are introduced in estimating winning probability of each race horse. In Chapter 6, we will talk about some methods in misconceptions in estimating placed probability.Two main concepts in wagering, Kelly criterion and hedging, will be discussed in Chapters 7 and 8. To hit exotic pools, those theories in combinatorics in Chapter 9 will definitely help the readers. The author will share his experiences in betting syndicate in Chapter 10, and tell you how to be a successful professional horseplayer in the last Chapter.Some readers may find the mathematics in this book difficult, but the free program will take your pain away and do all the calculations. You can simply apply all the professional formulae by no more than a click, and pick your horses like an expert analyst.As an awardee in Asian-Pacific Mathematics Olympiad, the author abandoned his career as an actuary and became a key member in a gambling syndicate. This book was reprinted in the 4th edition in Hong Kong, ranked #2 in the best-selling chart in the international Chinese weekly Yazhou Zhoukan, and now available worldwide.

    But this book is much more than a series of formulas and calculations; the emphasis is on how to think about and use bond math.Author Donald J. Smith, a professor at Boston University and an experienced executive trainer, covers in detail money market rates, periodicity conversions, bond yields to maturity and horizon yields, the implied probability of default, after-tax rates of return, implied forward and spot rates, and duration and convexity. These calculations are used on traditional fixed-rate and zero-coupon bonds, as well as floating-rate notes, inflation-indexed securities, and interest rate swaps.Puts bond math in perspective through discussions of bond portfolios and investment strategies. Critiques the Bloomberg Yield Analysis (YA) page, indicating which numbers provide reliable information for making decisions about bonds, which are meaningless data, and which can be very misleading to investors Filled with thought-provoking insights and practical advice, this book puts the intricacies of bond math into a clear and logical order.

    Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision, helping students develop the ability to think abstractly as they study each topic. In doing so, the book provides students with a strong foundation both for computer science and for other upper-level mathematics courses.

    Experience Kalman filter with hands-on examples to grasp the essence. A book long awaited by anyone who could not dare to put their first step into Kalman filter. The author presents Kalman filter and other useful filters without complicated mathematical derivation and proof but with hands-on examples in MATLAB that will guide you step-by-step. The book starts with recursive filter and basics of Kalman filter, and gradually expands to application for nonlinear systems through extended and unscented Kalman filters. Also, some topics on frequency analysis including complementary filter are covered. Each chapter is balanced with theoretical background for absolute beginners and practical MATLAB examples to experience the principles explained. Once grabbing the book, you will notice it is not fearful but even enjoyable to learn Kalman filter.

    

    This is done in the perspective of unifying phenomena, of bringing different conceptual universes into dialog. The analysis of the role of 'order' and of symmetries in the foundations of mathematics is linked to the main invariants and principles, among which the geodesic principle (a consequence of symmetries), which govern and confer unity to the various physical theories. Moreover, we attempt to understand causal structures, a central element of physical intelligibility, in terms of symmetries and their breakings. The importance of the mathematical tool is also highlighted, enabling us to grasp the differences in the models for physics and biology which are proposed by continuous and discrete mathematics, such as computational simulations. A distinction between principles of (conceptual) construction and principles of proofs, both in physics and in mathematics, guides this part of the work. As for biology, being particularly difficult and not as thoroughly examined at a theoretical level, we propose a unification by 'concepts', an attempt which should always precede mathematisation. This constitutes an outline for unification also basing itself upon the highlighting of conceptual differences, of complex points of passage, of technical irreducibilities of one field to another. Indeed, a monist point of view such as ours should not make us blind: we, the living objects, are surely just big bags of molecules or, at least, this is our main metaphysical assumption.

    

    We wish to introduce the student to applications andaspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises we wish to show to the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes apart where relevant facts from topology, functional analysis and Lebesgue integration are reviewed."

    It also covers classical methods for obtaining the analytical solution of differential equations and Laplace transforms. In addition, the authors discuss how these equations describe mathematical systems and how to use software to solve sets of equations where analytical solutions cannot be obtained.Using simple physics, the book introduces dynamic modeling, the definition of differential equations, two simple methods for obtaining their analytical solution, and a method to follow when modeling. It then presents classical methods for solving differential equations, discusses the engineering importance of the roots of a characteristic equation, and describes the response of first- and second-order differential equations. A study of the Laplace transform method follows with explanations of the transfer function and the power of Laplace transform for obtaining the analytical solution of coupled differential equations.The next several chapters present the modeling of translational and rotational mechanical systems, fluid systems, thermal systems, and electrical systems. The final chapter explores many simulation examples using a typical software package for the solution of the models developed in previous chapters.Providing the necessary tools to apply differential equations in engineering and science, this text helps readers understand differential equations, their meaning, and their analytical and computer solutions. It illustrates how and where differential equations develop, how they describe engineering systems, how to obtain the analytical solution, and how to use software to simulate the systems.

    

    

    There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras.           The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.

    Quantitative Methods: An Introduction for Business Management presents the application of quantitative mathematical modeling to decision making in a business management context and emphasizes not only the role of data in drawing conclusions, but also the pitfalls of undiscerning reliance of software packages that implement standard statistical procedures. With hands-on applications and explanations that are accessible to readers at various levels, the book successfully outlines the necessary tools to make smart and successful business decisions.Progressing from beginner to more advanced material at an easy-to-follow pace, the author utilizes motivating examples throughout to aid readers interested in decision making and also provides critical remarks, intuitive traps, and counterexamples when appropriate.The book begins with a discussion of motivations and foundations related to the topic, with introductory presentations of concepts from calculus to linear algebra. Next, the core ideas of quantitative methods are presented in chapters that explore introductory topics in probability, descriptive and inferential statistics, linear regression, and a discussion of time series that includes both classical topics and more challenging models. The author also discusses linear programming models and decision making under risk as well as less standard topics in the field such as game theory and Bayesian statistics. Finally, the book concludes with a focus on selected tools from multivariate statistics, including advanced regression models and data reduction methods such as principal component analysis, factor analysis, and cluster analysis.The book promotes the importance of an analytical approach, particularly when dealing with a complex system where multiple individuals are involved and have conflicting incentives. A related website features Microsoft Excel(R) workbooks and MATLAB(R) scripts to illustrate concepts as well as additional exercises with solutions.Quantitative Methods is an excellent book for courses on the topic at the graduate level. The book also serves as an authoritative reference and self-study guide for financial and business professionals, as well as readers looking to reinforce their analytical skills.

    The program covered in this series envisages the use of colored rods (Algebricks) and other books and printed materials that are available from: www.EducationalSolutions.com.

    Further, all main extensions of the classical Gaussian ensembles of Wigner and Dyson are introduced including sparse, heavy tailed, non-Hermitian or multi-matrix models. In the second and larger part, all major applications are covered, in disciplines ranging from physics and mathematics to biology and engineering. This includes standard fields such as number theory, quantum chaos or quantum chromodynamics, as well as recent developments such as partitions, growth models, knot theory, wireless communication or bio-polymer folding.The handbook is suitable both for introducing novices to this area of research and as a main source of reference for active researchers in mathematics, physics and engineering.

    This book is a continuation of Hungarian Problem Book III and takes the contest through 1963. Forty-eight problems in all are presented in this volume. Problems are classified under combinatorics, graph theory, number theory, divisibility, sums and differences, algebra, geometry, tangent lines and circles, geometric inequalities, combinatorial geometry, trigonometry and solid geometry. Multiple solutions to the problems are presented along with background material. There is a substantial section entitled 'Looking Back', which provides additional insights into the problems. Hungarian Problem Book IV is intended for beginners, although the experienced student will find much here. Beginners are encouraged to work the problems in each section and then to compare their results against the solutions presented in the book. They will find ample material in each section to help them improve their problem-solving techniques."

    Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers argues that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas-Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for 1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, it discusses applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. It also discusses general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations"

    Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts, at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.

    It explains how metric concepts may be best understood in projective terms and explores the beauty of the interplay of geometry, algebra and combinatorics."

    This volume aims to remedy these shortcomings. It provides state-of-the-art research in the area of philosophy of statistics by encouraging numerous experts to communicate with one another without feeling restricted by their disciplines or thinking piecemeal in their treatment of issues.A second goal of this book is to present work in the field without bias toward any particular statistical paradigm.Broadly speaking, the essays in this Handbook are concerned with problems of induction, statistics and probability. For centuries, foundational problems like induction have been among philosophers favorite topics; recently, however, non-philosophers have increasingly taken a keen interest in these issues. This volume accordingly contains papers by both philosophers and non-philosophers, including scholars from nine academic disciplines. Provides a bridge between philosophy and current scientific findingsCovers theory and applicationsEncourages multi-disciplinary dialogue"

    Includes full color illustrations and diagrams throughout.A resource for Steiner-Waldorf teachers for math for Class 7 (age 12-13) and Class 8 (age 13-14).This book is a combined edition of Mathematics Around Us (for Class 7) and Mathematics in Space and Time (for Class 8).

    It is a culmination of much of traditional calculus, making surprising connections with geometry and arithmetic. It is an extremely useful part of mathematics, knowledge of which is needed by specialists in many otherfields. It provides a model for a large number of more recent developments in areas including manifold topology, global analysis, algebraic geometry, Riemannian geometry, and diverse topics in mathematical physics.This graduate text on Riemann surface theory proves the fundamental analytical results on the existence of meromorphic functions and the Uniformisation Theorem. The approach taken emphasises PDE methods, applicable more generally in global analysis. The connection with geometric topology, and inparticular the role of the mapping class group, is also explained. To this end, some more sophisticated topics have been included, compared with traditional texts at this level. While the treatment is novel, the roots of the subject in traditional calculus and complex analysis are kept well in mind.Part I sets up the interplay between complex analysis and topology, with the latter treated informally. Part II works as a rapid first course in Riemann surface theory, including elliptic curves. The core of the book is contained in Part III, where the fundamental analytical results are proved.Following this section, the remainder of the text illustrates various facets of the more advanced theory.

    Within the last 10 years, his work on realism and quantifier variance has been front-and-center in the mindsof many metaphysicians. Metametaphysics, which looks at foundational questions about the very practice of metaphysics and the questions it raises, is now a popular area of discussion. There is a lot of anxiety about what ontology is, and Hirsch's diagnosis of how revisionary ontologists go wrongis one of the main views being discussed. This volume collects HIrsch's essays from the last decade (with the exception of one article from 1978) on ontology and metametaphysics which are very much tied to these debates. His essays develop a distinctive language-based argument against variousanti-commonsensical views that have recently dominated ontology. All these views go astray, Hirsch says, by failing to interpret ordinary assertions about existence in a plausibly charitable way, so their philosophizing leads them to misuse language about ontology -- our ordinary concept of 'whatexists' -- in favor of a position othat is quite different. Hirsch will supply a new introduction. The volume will interest philosophers of metaphysics currently engaged in these debates.

    Both rigorous and friendly, the book contains:Introductory chapters examining each new concept or assumption Just-in-time mathematics - the presentation of ideas just before they are applied Summary and exercises at the end of each chapter Discussion of maximization of expected utility The basics of Markov Chain Monte Carlo computing techniques Problems involving more than one decision-makerWritten in an appealing, inviting style, and packed with interesting examples, Principles of Uncertainty introduces the most compelling parts of mathematics, computing, and philosophy as they bear on statistics. Although many books present the computation of a variety of statistics and algorithms while barely skimming the philosophical ramifications of subjective probability, this book takes a different tack. By addressing how to think about uncertainty, this book gives readers the intuition and understanding required to choose a particular method for a particular purpose.

    With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

    Multiply your chances of success on the ACT Math TestThe ACT Mathematics Test is a 60-question, 60-minute subtest designed to measure the mathematical skills students have typically acquired in courses taken by the end of 11th grade, and is generally considered to be the most challenging section of the ACT."ACT Math For Dummies" is an approachable, easy-to-follow study guide specific to the Math section, complete with practice problems and strategies to help you prepare for exam day.Review chapters for algebra, geometry, and trigonometryThree practice tests modeled from questions off the most recent ACT testsPacked with tips, useful information, and strategies"ACT Math For Dummies" is your one-stop guide to learn, review, and practice for the test

    Introduction.-Number Sets and Algebra.-Complex Numbers.-The Complex Plane.-Quaternion Algebra.-3D Rotation Transforms.-Quaternions in Space.-Conclusion.

    Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Pade approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA."

    The program covered in this series envisages the use of colored rods (Algebricks) and other books and printed materials that are available from: www.EducationalSolutions.com.

    This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections.A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods' great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.

    If you think that math is difficult, confusing, dull or just plain scary, then "The Math Handbook" is your ideal companion." " Covering all the basics including fractions, equations, primes, squares and square roots, geometry and fractals, Dr. Richard Elwes will lead you gently towards a greater understanding of this fascinating subject. Even apparently daunting concepts will be explained simply, with the assistance of useful diagrams, and with a refreshing lack of jargon. So whether you're an adult or a student, whether you're the sort of person who does Sudoku puzzles, crosswords, or has always been daunted by numbers at work, school or in everyday life, you won't find a better way of overcoming your nervousness about math and learning to enjoy this most amazing of human discoveries.

    So what you won't find in Easy Pre-calculus Step-by-Step is a lot of endless drills. Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused exercises that are linked to core skills--enabling learners to grasp when and how to apply those techniques.This book features:Large step-by-step charts breaking down each step within a process and showing clear connections between topics and annotations to clarify difficultiesStay-in-step panels show how to cope with variations to the core stepsStep-it-up exercises link practice to the core steps already presentedMissteps and stumbles highlight common errors to avoidYou can master pre-calculus as long as you take it Step-by-Step!

    It concentrates on developing basic concepts and studying their fundamental properties.

    Sold at auction in 1998, it has since been the subject of a privately funded project to conserve, image and transcribe its texts. In this volume the scientists, conservators, classicists and historians involved in the project discuss in full their techniques and their discoveries. These include new speeches by the classical Athenian orator Hyperides, a lost commentary on Aristotle's Categories from the second or third century AD and substantial re-readings and reinterpretations of the works by Archimedes. The book discusses the pioneering imaging and post-processing techniques used to reveal the texts and includes detailed codicological descriptions of all eight manuscripts comprising the Palimpsest. It will be of interest to manuscript scholars, classicists and historians of science.

    The Dummies Essentials Way:The key concepts you need to learn the subjectEasy-to-follow and conciseFocuses on the skills needed to succeed