In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations.

In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its applications are obtained and the integral manifolds of resonance oscillation systems are studied.

This book is intended for a wide circle of research workers, experts, and engineers interested in oscillation processes, as well as for students and post-graduate students specialized in ordinary differential equations.

Read about the dramatic life of an outstanding mathematical genius: Niels Henrik Abel (1802-1829). Arild Stubhaug, who is both a historian and a mathematician, has written the definitive biography of Niels Henrik Abel. The Norwegian original edition was a sensational success, and Arild Stubhaug was awarded the most prestigious Norwegian literary prize (Brageprisen) in the category non-fiction. Everyone with an interest in the history of mathematics and science will enjoy reading this book on one of the most famous mathematicians of the 19th century.

Understanding the causes and effects of explosions is important to experts in a broad range of disciplines, including the military, industrial and environmental research, aeronautic engineering, and applied mathematics. Offering an introductory review of historic research, Shock Waves and Explosions brings analytic and computational methods to a wide audience in a clear and thorough way. Beginning with an overview of the research on combustion and gas dynamics in the 1970s and 1980s, the author brings you up to date by covering modeling techniques and asymptotic and perturbative methods and ending with a chapter on computational methods. Most of the book deals with the mathematical analysis of explosions, but computational results are also included wherever they are available. Historical perspectives are provided on the advent of nonlinear science, as well as on the mathematical study of the blast wave phenomenon, both when visualized as a point explosion and when simulated as the expansion of a high-pressure gas. This volume clearly reveals the ingenuity of the human mind to conceptualize, model, and mathematically analyze highly complicated nonlinear phenomena such as nuclear explosions. It presents a solid foundation of knowledge that encourages further research and original ideas.

Pascal was a scientist and man of the world who came to be a passionately devout Christian. The fragments of his great defense of Christianity, left unfinished at his death in 1662, survive in the form of the Pensees. This series of brief, dramatic notes on his religious convictions are here translated into English. These thoughts expose Pascal's vision of the world and display powerful reasoning and a profound faith.

Mechanics 1 was written to provide thorough preparation for the revised 2004 specification. Based on the first editions, this series helps you to prepare for the new exams.

Ages: 7–11 Level: KS2 Subject: Maths  Power Maths is a leading primary maths mastery scheme, developed in partnership with White Rose Maths.   This edition is fully aligned with the new White Rose Maths schemes of learning (version 3.0) and has been updated in response to current mastery best practice and feedback from teachers.  The Power Maths Teacher Guides provide expert support for day-to-day teaching and continual professional development, including: How to implement a mastery approach using the Textbooks and Practice Books. Advice and commentary for each Textbook and Practice Book page, including ‘Strengthen’ and ‘Deepen’ ideas for children that need more support or stretch. A guide to the concepts introduced in each unit, including important structures and representations, key language, common misconceptions and intervention strategies. Support with key strategies such as modelling a growth mindset, assessing mastery, speedy same-day intervention, and using the Concrete-Pictorial-Abstract approach to embed deep understanding. Templates for teacher reflection, lesson study, and tracking pupil progress.

Described even today as "unsurpassed," this history of mathematical notation stretching back to the Babylonians and Egyptians is one of the most comprehensive written. In two impressive volumes-first published in 1928-9-distinguished mathematician Florian Cajori shows the origin, evolution, and dissemination of each symbol and the competition it faced in its rise to popularity or fall into obscurity. Illustrated with more than a hundred diagrams and figures, this "mirror of past and present conditions in mathematics" will give students and historians a whole new appreciation for "1 + 1 = 2." Swiss-American author, educator, and mathematician FLORIAN CAJORI (1859-1930) was one of the world's most distinguished mathematical historians. Appointed to a specially created chair in the history of mathematics at the University of California, Berkeley, he also wrote An Introduction to the Theory of Equations, A History of Elementary Mathematics, and The Chequered Career of Ferdinand Rudolph Hassler.

The purpose of presenting this book to the scholarly world is twofold. In the first place, I wish to provide for the English reader a translation of the earliest extant Arabic work of Hindi arithmetic. It shows this system at its earliest stages and the first steps in its development, a subject not yet well known except for readers of some Arabic publications by the present writer. This book is therefore of particular importance for students of the history of mathematical techniques. The medieval author, AI-UqHdisI, was, it seems, not noticed by bibliographers; neither was his work, which lay hardly noticed by modern scholars until 1960 when I happened to see a microfilm copy of it in the Institute of Arabic Manu scripts in Cairo. A steady labour immediately followed to make a comparative study of the text together with over twenty other texts, some of them not yet known to scholars. This pursuit resulted in (i) a doctoral degree awarded to me in 1966 by the University of Khartoum, (ii) the publication of several texts in Arabic including the text here translated, and (iii) the publication of several articles in Arabic and English on the history of arithmetic in the Middle Ages. The second purpose of this book is to make the main results of my study available to the English reader."

PREFACE The Third International Mathematics and Science Study (TIMSS), sponsored by the International Association for the Evaluation of Educational Achievement (lEA) and the gov ernments of the participating countries, is a comparative study of education in mathematics and the sciences conducted in approximately 50 educational systems on five continents. The goal of TIMSS is to measure student achievement in mathematics and science in participating coun tries and to assess some of the curricular and classroom factors that influence student learning in these subjects. The study will provide educators and policy makers with an unparalleled and multidimensional perspective on mathematics and science curricula; their implementation; the nature of student performance in mathematics and science; and the social, economic, and edu cational context in which these occur. TIMSS focuses on student learning and achievement in mathematics and science at three different age levels, or populations. * Population 1 is defined as all students enrolled in the two adjacent grades that contain the largest proportion of 9-year-old students; * Population 2 is defined as all students enrolled in the two adjacent grades that contain the largest proportion of 13-year-old students; and * Population 3 is defined as all students in their final year of secondary education, includ ing students in vocational education programs. In addition, Population 3 has two "specialist" subpopulations: students taking advanced courses in mathematics (mathematics specialists), and students taking advanced courses in physics (science specialists).

Compared to other popular math books, there is more algebraic manipulation, and more applications of algebra in number theory and geometry

Presents an exciting variety of topics to motivate beginning students

May be used as an introductory course or as background reading

This book is a compilation of approximately nine hundred problems, which have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an increasing level of difficulty. This new edition contains approximately 120 new problems and 200 new solutions. It is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies.

Master the fundamentals of SPSS with this newly updated and instructive resource The newly and thoroughly revised Second Edition of SPSS Essentials delivers a comprehensive guide for students in the social sciences who wish to learn how to use the Statistical Package for the Social Sciences (SPSS) for the effective collection, management, and analysis of data. The accomplished researchers and authors provide readers with the practical nuts and bolts of SPSS usage and data entry, with a particular emphasis on managing and manipulating data. The book offers an introduction to SPSS, how to navigate it, and a discussion of how to understand the data the reader is working with. It also covers inferential statistics, including topics like hypothesis testing, one-sample Z-testing, T-testing, ANOVAs, correlations, and regression. Five unique appendices round out the text, providing readers with discussions of dealing with real-world data, troubleshooting, advanced data manipulations, and new workbook activities. SPSS Essentials offers a wide variety of features, including: A revised chapter order, designed to match the pacing and content of typical undergraduate statistics classes An explanation of when particular inferential statistics are appropriate for use, given the nature of the data being worked with Additional material on understanding your data sample, including discussions of SPSS output and how to find the most relevant information A companion website offering additional problem sets, complete with answers Perfect for undergraduate students of the social sciences who are just getting started with SPSS, SPSS Essentials also belongs on the bookshelves of advanced placement high school students and practitioners in social science who want to brush up on the fundamentals of this powerful and flexible software package.

Bifurcation theory has made a very fast upswing in the last fifteen years. Roughly speaking it generalises to dynamic systems the pos sibility of mUltiple solutions, a possibility already recognised in static systems - physical, chemical, social - when operating far from their equilibrium states. It so happened that quite a few staff members of the Erasmus University Rotterdam were thinking along those lines about certain aspects of their disciplines. To have a number of specialists and potential "fans" convene to discuss various aspects of bifurcation al thinking, seemed a natural development. The resulting papers were judged to be of interest to a larger public, and as such are logically regrouped in this volume, one in a series of studies resulting from the activities of the Steering Committee on Interdisciplinary Studies of the Erasmus University, Rotterdam. Although the volume is perhaps multidisciplinary rather than interdisciplinary - the interdisciplinary aspect being only "latent" -, as a "soft" interdisciplinary exercise (the application of formal structures of one discipline to another) it has a right to interdisciplinary existence This book could not have been published without a generous grant of the University Foundation of the Erasmus University Rotterdam, which allowed the conference to be held and the resulting papers to be published; that generosity is gratefully acknowledged."

For courses in mathematical statistics. Comprehensive coverage of mathematical statistics - with a proven approach Introduction to Mathematical Statistics by Hogg, McKean, and Craig enhances student comprehension and retention with numerous, illustrative examples and exercises. Classical statistical inference procedures in estimation and testing are explored extensively, and the text's flexible organisation makes it ideal for a range of mathematical statistics courses. Substantial changes to the 8th Edition - many based on user feedback - help students appreciate the connection between statistical theory and statistical practice, while other changes enhance the development and discussion of the statistical theory presented.

The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].

GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS A stand-alone introduction to specific integration problems in the probabilistic theory of stochastic calculus Picking up where his previous book, A Modern Theory of Random Variation, left off, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics introduces readers to particular problems of integration in the probability-like theory of quantum mechanics. Written as a motivational explanation of the key points of the underlying mathematical theory, and including ample illustrations of the calculus, this book relies heavily on the mathematical theory set out in the author's previous work. That said, this work stands alone and does not require a reading of A Modern Theory of Random Variation in order to be understandable. Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics takes a gradual, relaxed, and discursive approach to the subject in a successful attempt to engage the reader by exploring a narrower range of themes and problems. Organized around examples with accompanying introductions and explanations, the book covers topics such as: Stochastic calculus, including discussions of random variation, integration and probability, and stochastic processes Field theory, including discussions of gauges for product spaces and quantum electrodynamics Robust and thorough appendices, examples, illustrations, and introductions for each of the concepts discussed within An introduction to basic gauge integral theory (for those unfamiliar with the author's previous book) The methods employed in this book show, for instance, that it is no longer necessary to resort to unreliable "Black Box" theory in financial calculus; that full mathematical rigor can now be combined with clarity and simplicity. Perfect for students and academics with even a passing interest in the application of the gauge integral technique pioneered by R. Henstock and J. Kurzweil, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics is an illuminating and insightful exploration of the complex mathematical topics contained within.

The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.

Published for the Eidgenossische Technische Hochschule Zurich

From the reviews of the First Edition:

"This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zurich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews)

This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text."

Examines flawed usage of math in public affairs through actual cases of how mathematical data and conclusions can be distorted and misrepresented to influence public opinion. Highlights how slippery numbers and questionable mathematical conlusions emerge and what can be done to safeguard against them. This pragmatic book examines flawed usage of math in public affairs through actual cases of how mathematical data and conclusions can be distorted and misrepresented to influence public opinion-highlighting how slippery numbers and questionable mathematical conclusions emerge and what can be done to safeguard against them. Gives specific examples of governmental and private sector math manipulation. Slippery Math in Public Affairs analyzes the cost of "slippery math" in terms of squandered resources identifies common misperceptions about the role of math in public affairs discusses how math education can be reformed to sharpen public awareness of "slippery math" offers exemplary self-study programs to improve perspective on the use of math depicts the development of math models and their use and misuse considers proper and improper polling methods With nearly 200 references cited, this book will benefit math teachers; educators; mathematicians; applied statisticians; multivariate analysts; biomathematicians and medical personnel; public administrators; political scientists; business administrators; operations managers; urban and public affairs officials; economists; demographers; sociologists; anthropologists; public-policy makers; public affairs analysts and commentators; journalists; and the general reader who seeks to avoid being manipulated by math; and is essential reading for undergraduate and graduate students in the aforementioned disciplines.

The fourteenth volume of the Second Edition covers central topics in philosophical logic that have been studied for thousands of years, since Aristotle: Inconsistency, Causality, Conditionals, and Quantifiers. These topics are central in many applications of logic in central disciplines and this book is indispensable to any advanced student or researcher using logic in these areas. The chapters are comprehensive and written by major figures in the field.

This chronological survey explores Pascal's (162362) achievement as mathematician, physicist and religious thinker; it also has a chapter on his life. His work on conic sections, the probability calculus, number theory, cycloid curves and hydrostatics is considered in detail. Analyses of the Provincial Letters and the Thoughts bring out the many distinctive features, thematicnn and technical, of each text. Pascal's lesser known works are also studied. There is a chapter on the Wager argument. A wide-ranging bibliography completes the book.