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 new series, International Mathematical Series founded by Kluwer / Plenum Publishers and the Russian publisher, Tamara Rozhkovskaya is published simultaneously in English and in Russian and starts with two volumes dedicated to the famous Russian mathematician Professor Olga Aleksandrovna Ladyzhenskaya, on the occasion of her 80th birthday.

O.A. Ladyzhenskaya graduated from the Moscow State University. But throughout her career she has been closely connected with St. Petersburg where she works at the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences.

Many generations of mathematicians have become familiar with the nonlinear theory of partial differential equations reading the books on quasilinear elliptic and parabolic equations written by O.A. Ladyzhenskaya with V.A. Solonnikov and N.N. Uraltseva.

Her results and methods on the Navier-Stokes equations, and other mathematical problems in the theory of viscous fluids, nonlinear partial differential equations and systems, the regularity theory, some directions of computational analysis are well known. So it is no surprise that these two volumes attracted leading specialists in partial differential equations and mathematical physics from more than 15 countries, who present their new results in the various fields of mathematics in which the results, methods, and ideas of O.A. Ladyzhenskaya played a fundamental role.

Nonlinear Problems in Mathematical Physics and Related Topics I presents new results from distinguished specialists in the theory of partial differential equations and analysis. A large part of the material is devoted to the Navier-Stokes equations, which play an important role in the theory of viscous fluids. In particular, the existence of a local strong solution (in the sense of Ladyzhenskaya) to the problem describing some special motion in a Navier-Stokes fluid is established. Ladyzhenskaya's results on axially symmetric solutions to the Navier-Stokes fluid are generalized and solutions with fast decay of nonstationary Navier-Stokes equations in the half-space are stated. Application of the Fourier-analysis to the study of the Stokes wave problem and some interesting properties of the Stokes problem are presented. The nonstationary Stokes problem is also investigated in nonconvex domains and some Lp-estimates for the first-order derivatives of solutions are obtained. New results in the theory of fully nonlinear equations are presented. Some asymptotics are derived for elliptic operators with strongly degenerated symbols. New results are also presented for variational problems connected with phase transitions of means in controllable dynamical systems, nonlocal problems for quasilinear parabolic equations, elliptic variational problems with nonstandard growth, and some sufficient conditions for the regularity of lateral boundary.

Additionally, new results are presented on area formulas, estimates for eigenvalues in the case of the weighted Laplacian on Metric graph, application of the direct Lyapunov method in continuum mechanics, singular perturbation property of capillary surfaces, partially free boundary problem for parametric double integrals.

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.

Fuzzy modeling has become one of the most productive and successful results of fuzzy logic. Among others, it has been applied to knowledge discovery, automatic classification, long-term prediction, or medical and engineering analysis. The research developed in the topic during the last two decades has been mainly focused on exploiting the fuzzy model flexibility to obtain the highest accuracy. This approach usually sets aside the interpretability of the obtained models. However, we should remember the initial philosophy of fuzzy sets theory directed to serve the bridge between the human understanding and the machine processing. In this challenge, the ability of fuzzy models to express the behavior of the real system in a comprehensible manner acquires a great importance. This book collects the works of a group of experts in the field that advocate the interpretability improvements as a mechanism to obtain well balanced fuzzy models.

The gratifying response to Counterexamples in analysis (CEA) was followed, when the book went out of print, by expressions of dismay from those who were unable to acquire it. The connection of the present volume with CEA is clear, although the sights here are set higher. In the quarter-century since the appearance of CEA, mathematical education has taken some large steps reflected in both the undergraduate and graduate curricula. What was once taken as very new, remote, or arcane is now a well-established part of mathematical study and discourse. Consequently the approach here is designed to match the observed progress. The contents are intended to provide graduate and ad vanced undergraduate students as well as the general mathematical public with a modern treatment of some theorems and examples that constitute a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. The items included are presented in the spirit of a conversation among mathematicians who know the language but are interested in some of the ramifications of the subjects with which they routinely deal. Although such an approach might be construed as demanding, there is an extensive GLOSSARY jlNDEX where all but the most familiar notions are clearly defined and explained. The object ofthe body of the text is more to enhance what the reader already knows than to review definitions and notations that have become part of every mathematician's working context."

This first book in the series will describe the Net Generation as visual learners who thrive when surrounded with new technologies and whose needs can be met with the technological innovations. These new learners seek novel ways of studying, such as collaborating with peers, multitasking, as well as use of multimedia, the Internet, and other Information and Communication Technologies. Here we present mathematics as a contemporary subject that is engaging, exciting and enlightening in new ways. For example, in the distributed environment of cyber space, mathematics learners play games, watch presentations on YouTube, create Java applets of mathematics simulations and exchange thoughts over the Instant Messaging tool. How should mathematics education resonate with these learners and technological novelties that excite them?

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.

Ages: 5–7  Level: KS1 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.

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.

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.

This book presents the latest knowledge of the newly discovered Earth-like exoplanets and reviews improvements in both radio and optical SETI. A key aim is to stimulate fresh discussion on algorithms that will be of high value in this extremely complicated search. Exoplanets resembling Earth could well be able to sustain life and support the evolution of technological civilizations, but to date, all searches for such life forms have proved fruitless. The failings of SETI observations are well recognized, and a new search approach is necessary. In this book, different detection algorithms that exploit state-of-the-art, low-cost, and extremely fast multiprocessors are examined and compared. Novel methods such as the agnostic entropy and high-sensitivity blind signal extraction algorithms should represent a quantum leap forward in SETI. The book is of interest to all researchers in the field and hopefully stimulates significant progress in the search for extraterrestrial intelligence.

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.

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.

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.

Do your students believe that division "doesn't make sense" if the divisor is greater than the dividend? Explore rich, researched-based strategies and tasks that show how students are reasoning about and making sense of mulitplication and division. This book focuses on the specialised pedagogical content knowledge that you need to teach multiplication and division effectively in grades 3-5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these computations - not only in their current work, but also in higher-level maths and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of multiplication and division. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning. About the Series: You have essential understanding. It's time to put it into practise in your teaching. The Putting Essential Understanding into Practice Series moves NCTM's Essential Understanding Series into the classroom. The new series details and explores best practises for teaching the essential ideas that students must grasp about fundamental topics in mathematics - topics that are challenging to learn and teach but are critical to the development of mathematical understanding. Classroom vignettes and samples of student work bring each topic to life and questions for reader reflection open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, understanding into practise, instructional strategies and assessment that pedagogical content knowledge entails. Maximise the potential of student-centred learning and teaching by putting essential understanding into practise.

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

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).

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.

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."