-Offers an innovative introduction to the psychology of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. - In clear, engaging writing, award-winning mathematician and educator Norton Anderson explores the psychological basis for mathematics at every level, relevant for pre-service and in-service secondary and elementary math teachers, math teacher educators, and anyone interested in the nature of mathematics. -Reflections and exercises are included in each chapter, as well as footnotes for those interested in building off their understanding with related research.

-Offers an innovative introduction to the psychology of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. - In clear, engaging writing, award-winning mathematician and educator Norton Anderson explores the psychological basis for mathematics at every level, relevant for pre-service and in-service secondary and elementary math teachers, math teacher educators, and anyone interested in the nature of mathematics. -Reflections and exercises are included in each chapter, as well as footnotes for those interested in building off their understanding with related research.

Exam Board: AQA Level: AS/A-level Subject: Mathematics First Teaching: September 2017 First Exam: June 2018 AQA Approved Give students the confidence to identify connections between topics and apply their reasoning to mathematical problems, so as to develop a deeper understanding of mathematical concepts and their applications, with resources developed with subject specialists and MEI (Mathematics in Education and Industry). - Prepare students for assessment with plenty of practice questions, worked examples and skill-focused exercises. - Help build connections between topics with points of interest and things to notice such as links to real world examples and noticing patterns in the mathematics. - Enhance understanding of problem-solving, proof and modelling with dedicated sections on these key areas. - Address the new statistics requirements with five dedicated statistics chapters and questions around the use of large data sets. - Supports the use of technology with activities based around the use of spreadsheets, graphing software and graphing calculators. - Provide clear paths of progression that combine pure and applied maths into a coherent whole. - Reinforce Year 1 content with short review chapters.

This book is of interest to mathematics educators, researchers in mathematics education, gender, social justice, equity and democracy in education; and practitioners/teachers interested in the use of project work in mathematics teaching and learning. The book builds theoretical ideas from a careful substantial description of practice, in the attempt to improve both theory and practice in mathematics education. It thus interrogates and develops theoretical research tools for mathematics education and provides ideas for practice in mathematics classrooms.

From Euclidian to Hilbert Spaces analyzes the transition from finite dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, a notion that can sometimes be difficult for non-specialists to grasp. The focus is on the parallels and differences between the properties of the finite and infinite dimensions, noting the fundamental importance of coherence between the algebraic and topological structure, which makes Hilbert spaces the infinite-dimensional objects most closely related to Euclidian spaces. The common thread of this book is the Fourier transform, which is examined starting from the discrete Fourier transform (DFT), along with its applications in signal and image processing, passing through the Fourier series and finishing with the use of the Fourier transform to solve differential equations. The geometric structure of Hilbert spaces and the most significant properties of bounded linear operators in these spaces are also covered extensively. The theorems are presented with detailed proofs as well as meticulously explained exercises and solutions, with the aim of illustrating the variety of applications of the theoretical results.

In this easily readable volume, the author explains some of the reasons for our preference toward the number seven. He reviews its occurrences in our cultural, biological, chemical, physical, algebraic and geometrical world in an attempt to find the reasons behind them.

Attention to design patterns is unquestionably growing in software engineering because there is a strong belief that using made to measure solutions for solving frequently occurring problems encountered throughout the design phase greatly reduces the total cost and the time of developing software products. Stable Design Patterns for Software and Systems presents a new and fresh approach for creating stable, reusable, and widely applicable design patterns. It deals with the concept of stable design patterns based on software stability as a contemporary approach for building stable and highly reusable and widely applicable design patterns. This book shows that a formation approach to discovering and creating stable design patterns accords with Alexander’s current understanding of architectural patterns. Stable design patterns are a type of knowledge pattern that underline human problem solving methods and appeal to the pattern community. This book examines software design patterns with respect to four central themes: How do we develop a solution for the problem through software stability concepts? This book offers a direct application of using software stability concepts for modeling solutions. How do we achieve software stability over time and design patterns that are effective to use? What are the unique roles of stable design patterns in modeling the accurate solution of the problem at hand and in providing stable and undisputed design for such problems? This book enumerates a complete and domain-less list of stable patterns that are useful for designing and modeling solutions for frequently recurring problems. What is the most efficient way to document the stable design patters to ensure efficient reusability? This book is an extension to the contemporary templates that are used in documenting design patterns. This book gives a pragmatic and a novel approach toward understanding the problem domain and in proposing stable solutions for engineering stable software systems, components, and frameworks.

The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep -seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers' patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students' learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov's Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.

These book consists of two parts:(i) A detailed introduction by the editor to provide a full exposition on the developments of the study of Goldbach conjecture, including a complete reference.(ii) A collection of original papers on Goldbach Conjecture and is intended for graduate students and researchers in analytic number theory who have an understanding of basic elementary number theory and the theory of the distribution of prime numbers. The basic methods for treating Goldbach Conjecture are the circle method of Hardy and Littlewood and the sieve method of Brun. This book contains papers with originalities and important progresses on these two methods and all the papers in Chinese, French, German and Russian have been translated into English.

The International Mathematical Olympiad (IMO) is a very important competition for high school students. China has taken part in the IMO 31 times since 1985 and has won the top ranking for countries 19 times, with a multitude of gold medals for individual students. The six students China has sent every year were selected from 60 students among approximately 300 students who took part in the annual China Mathematical Competition during the winter months.This book includes the problems and solutions of the most important mathematical competitions from 2010 to 2014 in China, such as China Mathematical Competition, China Mathematical Olympiad, China Girls' Mathematical Olympiad. These problems are almost exclusively created by the experts who are engaged in mathematical competition teaching and researching. Some of the solutions are from national training team and national team members, their wonderful solutions being the feature of this book. This book is useful to mathematics fans, middle school students engaged in mathematical competition, coaches in mathematics teaching and teachers setting up math elective courses.

The new and revised version of this comprehensive pocket reference guide is ideal for anyone who deals with physics, chemistry, mathematics, finance, and computer systems and needs to review or quickly refresh their memory of what they studied in school. It covers the fundamentals of arithmetic, algebra, geometry, trigonometry, and analytical geometry, and statistics, and presents the application of differential equations and integral calculus. It reveals the comparative advantages of binomial distribution, standard distribution, Poisson distribution, and normal distribution, and includes most used definitions and formulas of kinematics, dynamics, statics, mechanics of fluids, thermal variable of state, thermodynamics, electricity and magnetism, light, and atomic and nuclear physics. It also presents applications and solutions to problems concerning simple interest, compound interest, effective rate, annuity, amortization of loans, and sinking fund payments. Features A quick reference for engineers, technicians, toolmakers, machinists, students, and teachers. Includes more than 1,300 formulas, definitions, and figures used in mathematics and physics, plus complete coverage of S.I., metric, and U.S. customary units. New to this revised edition are sections on arithmetic, mathematical fundamentals of computer science, units of measure in precious metals, and more. Key topics have been clarified, and more than 150 line illustrations have been improved. The index has been expanded to help guide readers through this information-packed reference. Vukota Boljanovic, Ph.D., has more than 40 year of experience in applied engineering in the aircraft and automotive industries as well as in education. He received his B.S., M.S., and Ph.D. in Mechanical Engineering and worked in Europe for many years in both academia and industry, including as a Professor of Aerospace Engineering and later as Vice President for Research and Development for a major aircraft company. He has performed extensive research in development and manufacturing engineering, including the impact of design modification on tools, dies, and processes selection, aircraft assembly, and inspection. He also spent five years working in the American automotive industry. The author of multiple books and numerous technical papers, Boljanovic has been widely recognized by both academia and industry for his contributions to manufacturing processes. Preface; List of Greek Letters;Part I, Units: International System of Units, Metric Units of Measurement, U.S. Units of Measurement, Tables of Equivalents; Part II, Mathematics: Arithmetic, Algebra, Geometry, Trigonometry, Analytical Geometry, Mathematics of Finance, Calculus, Statistics, Mathematical Fundamentals of Computer Science; Part III, Physics: Mechanics, Mechanics of Fluid, Temperature and Heat, Electricity and Magnetism, Light, Wave Motion and Sound; Appendix: Fundamental Physics Constants; Index.

A database management system (DBMS) is a collection of programs that enable users to create and maintain a database; it also consists of a collection of interrelated data and a set of programs to access that data. Hence, a DBMS is a general-purpose software system that facilitates the processes of defining, constructing, and manipulating databases for various applications. The primary goal of a DBMS is to provide an environment that is both convenient and efficient to use in retrieving and storing database information. It is an interface between the user of application programs, on the one hand, and the database, on the other. The objective of Database Management System: An Evolutionary Approach, is to enable the learner to grasp a basic understanding of a DBMS, its need, and its terminologies discern the difference between the traditional file-based systems and a DBMS code while learning to grasp theory in a practical way study provided examples and case studies for better comprehension This book is intended to give under- and postgraduate students a fundamental background in DBMSs. The book follows an evolutionary learning approach that emphasizes the basic concepts and builds a strong foundation to learn more advanced topics including normalizations, normal forms, PL/SQL, transactions, concurrency control, etc. This book also gives detailed knowledge with a focus on entity-relationship (ER) diagrams and their reductions into tables, with sufficient SQL codes for a more practical understanding.

Covers unit A2 1: Pure Mathematics for the CCEA specification The book has been completely re-designed to follow the same layout as the Further Maths book. Answers are included at the rear of the book. Contents: Algebra and Graphs Functions Radian Measur Coordinate Geometry Sequences and Series Binomial Expansion Trigonometric Function Trigonometric Identities and Equations Differentiation Further Differentiation Integration Differential Equations Numerical Methods Problem Solving

Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.

This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing the minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax or guaranteed estimates. It is established that these estimates are expressed explicitly via solutions to some uniquely solvable linear systems of ordinary differential equations of the special type. The authors apply these results for obtaining the optimal estimates of solutions from indirect noisy observations. Similar estimation problems for solutions of boundary value problems for linear differential equations of order n with general boundary conditions are considered. The authors also elaborate guaranteed estimation methods under incomplete data of unknown right-hand sides of equations and boundary data and obtain representations for the corresponding guaranteed estimates. In all the cases estimation errors are determined.

This unique book allows instructors both within mathematics courses and course taught in other departments to motivate students to use mathematics to better conceptualize how it is used in a cross-disciplinary manner. The book is aimed at mathematics educators to satisfy the need for innovative and interesting ways to engage students in mathematics. There no similar books. The authors approach to employing math to the history of the United States, its geography, art, and practical topics such as shopping for food and entertainment.

This unique book allows instructors both within mathematics courses and course taught in other departments to motivate students to use mathematics to better conceptualize how it is used in a cross-disciplinary manner. The book is aimed at mathematics educators to satisfy the need for innovative and interesting ways to engage students in mathematics. There no similar books. The authors approach to employing math to the history of the United States, its geography, art, and practical topics such as shopping for food and entertainment.

Introduces flexible statistical models that have yet to systematically introduced in course materials. Discusses applications of the proposed modelling framework in several important statistical problems, ranging from biased sampling designs and missing data, graphical models, survival analysis, Gibbs sampler and model compatibility, and density estimations Includes real data examples to demonstrate the use of the proposed models, and estimation and inference tools.

What does mathematics have to do with poetry? Seemingly, nothing. Mathematics deals with abstractions while poetry with emotions. And yet, the two share something essential: Beauty. "Euclid alone has looked on beauty bare," says the title of a poem by Edna St. Vincent Millay.A winner of the CHOICE Outstanding Academic Title 2015, "Mathematics, Poetry and Beauty" tries to solve the secret of the similarity between the two domains. It tries to explain how a mathematical argument and a poem can move us in the same way. Mathematical and poetic techniques are compared, with the aim of showing how they evoke the same sense of beauty.The reader may find that, as Bertrand Russell said, "Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty hold and austere, like that of sculpture ... sublimely pure, and capable of a stern perfection such as only the greatest art can show."

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more.

Unparalleled in its depth of coverage, "The Princeton Companion to Mathematics" surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.Features nearly 200 entries, organized thematically and written by an international team of distinguished contributorsPresents major ideas and branches of pure mathematics in a clear, accessible styleDefines and explains important mathematical concepts, methods, theorems, and open problemsIntroduces the language of mathematics and the goals of mathematical researchCovers number theory, algebra, analysis, geometry, logic, probability, and moreTraces the history and development of modern mathematicsProfiles more than ninety-five mathematicians who influenced those working todayExplores the influence of mathematics on other disciplinesIncludes bibliographies, cross-references, and a comprehensive index

Contributors incude:

Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Bela Bollobas, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, Jose Ferreiros, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvea, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolo Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, Janos Kollar, T. W. Korner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-Francois Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lutzen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rudiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger"