Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists of invited expository and research articles on new developments arising from Manin's outstanding contributions to mathematics.

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.

A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Triangle and paper folding; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics.

This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.

Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces

Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.

This timely volume raises issues concerning the nature of school mathematics and mathematics at work, and the challenges of teaching valuable mathematics in school and providing appropriate training for a variety of careers. It offers lively commentaries on important hot' topics: transferring knowledge and skill across contexts; 'authentic mathematics'; comparability of different types of assessment; and analyses of research methods.

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Digital Functions and Data Reconstruction: Digital-Discrete Methods provides a solid foundation to the theory of digital functions and its applications to image data analysis, digital object deformation, and data reconstruction. This new method has a unique feature in that it is mainly built on discrete mathematics with connections to classical methods in mathematics and computer sciences. Digitally continuous functions and gradually varied functions were developed in the late 1980s. A. Rosenfeld (1986) proposed digitally continuous functions for digital image analysis, especially to describe the "continuous" component in a digital image, which usually indicates an object. L. Chen (1989) invented gradually varied functions to interpolate a digital surface when the boundary appears to be continuous. In theory, digitally continuous functions are very similar to gradually varied functions. Gradually varied functions are more general in terms of being functions of real numbers; digitally continuous functions are easily extended to the mapping from one digital space to another. This will be the first book about digital functions, which is an important modern research area for digital images and digitalized data processing, and provides an introduction and comprehensive coverage of digital function methods. Digital Functions and Data Reconstruction: Digital-Discrete Methods offers scientists and engineers who deal with digital data a highly accessible, practical, and mathematically sound introduction to the powerful theories of digital topology and functional analysis, while avoiding the more abstruse aspects of these topics.

This volume contains all twenty-three of the principal survey papers presented at the Symposium on Ordered Sets held at Banff, Canada from August 28 to September 12, 1981. The Symposium was supported by grants from the NATO Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada, the Canadian Mathematical Society Summer Research Institute programme, and the University of Calgary. tve are very grateful to these Organizations for their considerable interest and support. Over forty years ago on April 15, 1938 the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. in conjunction with a meeting of the American Mathematical Society. The principal addresses on that occasion were Lattices and their applications by G. Birkhoff, On the application of structure theory to groups by O. Ore, and The representation of Boolean algebras by M. H. Stone. The texts of these addresses and three others by R. Baer, H. M. MacNeille, and K. Menger appear in the Bulletin of the American Mathematical Society, Volume 44, 1938. In those days the theory of ordered sets, and especially lattice theory was described as a "vigorous and promising younger brother of group theory." Some early workers hoped that lattice theoretic methods would lead to solutions of important problems in group theory."

Multiple Perspectives on Mathematics Teaching and Learning offers a collection of chapters that take a new look at mathematics education. Leading authors, such as Deborah Ball, Paul Cobb, Jim Greeno, Stephen Lerman, and Michael Apple, draw from a range of perspectives in their analyses of mathematics teaching and learning. They address such practical problems as: the design of teaching and research that acknowledges the social nature of learning, maximizing the impact of teacher education programs, increasing the learning opportunities of students working in groups, and ameliorating the impact of male domination in mixed classrooms. These practical insights are combined with important advances in theory. Several of the authors address the nature of learning and teaching, including the ways in which theories and practices of mathematics education recognize learning as simultaneously social and individual. The issues addressed include teaching practices, equity, language, assessment, group work and the broader political context of mathematics reform. The contributors variously employ sociological, anthropological, psychological, sociocultural, political, and mathematical perspectives to produce powerful analyses of mathematics teaching and learning.

New research in mathematics education deals with the complexity of the mathematicsa (TM) classroom. The classroom teaching situation constitutes a pertinent unit of analysis for research into the ternary didactic relationship which binds teachers, students and mathematical knowledge. The classroom is considered as a complex didactic system, which offers the researcher an opportunity to gauge the boundaries of the freedom that is left with regard to choices about the knowledge to be taught and the ways of organizing the studentsa (TM) learning, while giveing rise to the study of interrelations between three main elements of the teaching process the: mathematical content to be taught and learned, management of the various time dimensions, and activity of the teacher who prepares and manages the class, to the benefit of the students' knowledge and the teachers' own experience.

This volume, reprinted from Educational Studies in Mathematics, Volume 59, focuses on classroom situations as a unit of analysis, the work of the teacher, and is strongly anchored in original theoretical frameworks. The contributions are formulated from the perspective of one or more theoretical frameworks but they are tackled by means of empirical investigations.

MATHEMATICAL THEORY OF ROCKET FLIGHT BY J. BARKLEY ROSSER, PH. D. Professor of Mathematics at Cornell University Formerly, Chief, Theoretical Ballistics Section Alleyany Ballistics Laboratory ROBERT R. NEWTON, PH. D. Member of Technical Staff, Bell Telephone Laboratories, Inc., Murray Hill, N. J. Formerly, Research Associate Allegany Ballistics Laboratory GEORGE L. GROSS, PH. D. Research Engineer in Applied Mathematics, Grumman Aircraft Engineering Corporation Beth page, N. Y. Formerly, Research Associate A lleyany Ballistics Laboratory Office of Scientific Research and Development National Defense Research Committee NKW YORK AND LONDON MCGRAW-HILL BOOK COMPANY, INC. 1947 MATHEMATICAL THEORY OF ROCKET FLIGHT PRINTED IN THE UNITED STATES OF AMERICA PREFACE This is the official final report to the Office of Scientific Research and Development concerning the work done on the exterior ballistics of fin-stabilized rocket projectiles under the supervision of Section H of Division 3 of the National Defense Research Committee at the Allegany Ballistics Laboratory during 1944 and 1945, when the laboratory was operated by The George Washington University under contract OEMsr-273 with the Office of Scientific Research and Devel opment. As such, its official title is Final Report No. B2.2 of the Allegany Ballistics Laboratory, OSRD 5878. After the removal of secrecy restrictions on this report, a consider able amount of expository material was added. It is our hope that thereby the report has been made readable for anyone interested in the flight of rockets. Two slightly different types of readers are antici pated. One is the trained scientist who has had no previous experience with rockets. Theother is the person with little scientific training who is interested in what makes a rocket go. The first type of reader should be able to comprehend the report in its entirety. For the benefit of the second type of reader, who will wish to skip the more mathematical portions, wo have attempted to supply simple explana tions at the beginnings of most sections telling what is to be accom plished in those sections. It is our hope that a reader can, if so minded, skip most of the mathematics and still be able to form a general idea of rocket flight. Although this is a report of the work done at Allegany Ballistics Laboratory, it must not be supposed that all the material in the report originated there. We have been most fortunate in receiving the whole hearted cooperation and assistance of scientists in other laboratories. Many of them, notably the English scientists, were well advanced in the theory before we even began. Without the fine start given us by these other workers, this report could certainly not have been written. However, we were fortunate enough to discover two means of avoiding certain difficulties of the theory. The first is that of using some dynamical laws especially suited to rockets in deriving the equations of motion, and the second is that of using some mathematical functions especially suited to rockets in solving the equations of motion. The explanation and illustration of these simplifying devices take up a considerable portion of the report, although for completeness we have included material not involving them. vi PREFACE In attempting to acknowledge the contributions of other workers, we are in a difficult position. Approximately a hundred reports by otherworkers were useful in one way or another in the preparatf on of this report. However, most of them are still bound by military secrecy, so that only the few cited in our meager list of bibliographical references can be mentioned here. Many figures are copied from these unmentioiied reports. Sizable portions of our report, such as Chap. II and Appendix 1, lean very heavily on certain of these unmentioned reports, but no specific credit is given...

This book confronts the issue of how young people can find a way into the world of algebra. It represents multiple perspectives which include an analysis of situations in which algebra is an efficient problem-solving tool, the use of computer-based technologies, and a consideration of the historical evolution of algebra. The book emphasizes the situated nature of algebraic activity as opposed to being concerned with identifying students' conceptions in isolation from problem-solving activity.

Longman Advanced Mathematics is a series of comprehensive texts, with books for the current OCR core for AS and core for A2. The series develops mathematical skills through clear and thorough explanations, and comes packed with worked examples and progressive exercises. It also includes focused exam question practise and sample module papers. A CD-ROM included with every book, contains full worked solutions to exam-style papers using Live Authoring, plus additional questions and support for lower and higher attaining students. Covers all the A2 Core Modules C3 and C4 in one affordable, coherent book. Teacher and student-friendly explanations. Thousands of questions and clear worked examples support a variety of teaching styles and ability ranges. Lots of support and questions focused on students working for the top grades. Aids revision with practise papers, model answers and 'live-authored' solutions on the student CD-ROM. Additional support for teachers available on the teacher CD-ROM.

This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.

The papers presented in this volume are all very welcome because they challenge accepted wisdoms about both the nature of mathematics and of education. They bring to bear on this intersection a postmodern sensibility which engages with the grand narratives of mathematics education. It is a groundbreaking volume in which each of the chapters develops for mathematics education the importance of insights from mainly French intellectuals of the past: Foucault, Lacan, Lyotard, Deleuze. The chapters address issues relevant to mathematics education, not from the discipline's familiar viewpoints, but towards theory development for mathematics education in contemporary society. What is particularly important is the way in which their analyses of the discursive practices that make up mathematics education allow us to think differently about researching and teaching mathematics.

Presents recent breakthroughs in the theory, methods, and applications of safety and risk analysis for safety engineers, risk analysts, and policy makers Safety principles are paramount to addressing structured handling of safety concerns in all technological systems. This handbook captures and discusses the multitude of safety principles in a practical and applicable manner and is organized by five overarching categories of safety principles: Safety Reserves; Information and Control; Demonstrability; Optimization; and Organizational Principles and Practices. With a focus on the structured treatment of a large number of safety principles relevant to all related fields, each chapter defines the principle in question and discusses its application as well as how it relates to other principles and terms. This treatment includes the history, the underlying theory, and the limitations and criticism of the principle. Several chapters also problematize and critically discuss the very concept of a safety principle. In addition, the book treats issues such as: What are safety principles and what roles do they have? What kinds of safety principles are there? When, if ever, should rules and principles be disobeyed? How do safety principles relate to the law; what is the status of principles in different domains? The book also features: * Insight from leading international experts on safety and reliability * Real-world applications and case studies including systems usability, verification and validation, human reliability, and safety barriers * Different taxonomies for how safety principles are categorized * Breakthroughs in safety and risk science that can significantly change, improve, and inform important practical decisions * A structured treatment of safety principles relevant to numerous disciplines and application areas in industry and other sectors of society * Comprehensive and practical coverage of the multitude of safety principles including maintenance optimization, substitution, safety automation, risk communication, precautionary approaches, non-quantitative safety analysis, safety culture, and safety management The Handbook of Safety Principles is an ideal reference and resource for professionals engaged in risk and safety analysis and research. This book is also appropriate as a graduate and PhD-level textbook for courses in risk and safety analysis, reliability, safety engineering, and risk management offered within mathematics, operations research, and engineering departments.

Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: A Mathematical Sketchbook provides a brief but rigorous introduction to the abstract theory of computation, sometimes also referred to as recursion theory. It develops major themes in computability theory, such as Rice's theorem and the recursion theorem, and provides a systematic account of Blum's complexity theory as well as an introduction to the theory of computable real numbers and functions. The book is intended as a university text, but it may also be used for self-study; appropriate exercises and solutions are included.

These proceedings of the 18th International Conference on Difference Equations and Applications cover a number of different aspects of difference equations and discrete dynamical systems, as well as the interplay between difference equations and dynamical systems. The conference was organized by the Department of Mathematics at the Universitat Autonoma de Barcelona (UAB) under the auspices of the International Society of Difference Equations (ISDE) and held in Barcelona (Catalonia, Spain) in July 2012. Its purpose was to bring together experts and novices in these fields to discuss the latest developments. The book gathers contributions in the field of combinatorial and topological dynamics, complex dynamics, applications of difference equations to biology, chaotic linear dynamics, economic dynamics and control and asymptotic behavior, and periodicity of difference equations. As such it is of interest to researchers and scientists engaged in the theory and applications of difference equations and discrete dynamical systems.