This book develops the theoretical perspective on visuospatial reasoning in ecocultural contexts, granting insights on how the language, gestures, and representations of different cultures reflect visuospatial reasoning in context. For a number of years, two themes in the field of mathematics education have run parallel with each other with only a passing acquaintance. These two areas are the psychological perspective on visuospatial reasoning and ecocultural perspectives on mathematics education. This volume examines both areas of research and explores the intersection of these powerful ideas. In addition, there has been a growing interest in sociocultural aspects of education and in particular that of Indigenous education in the field of mathematics education. There has not, however, been a sound analysis of how environmental and cultural contexts impact visuospatial reasoning, although it was noted as far back as the 1980s when Alan Bishop developed his duality of visual processing and interpreting visual information. This book provides this analysis and in so doing not only articulates new and worthwhile lines of research, but also uncovers and makes real a variety of useful professional approaches in teaching school mathematics. With a renewed interest in visuospatial reasoning in the mathematics education community, this volume is extremely timely and adds significantly to current literature on the topic.

Covering network designs, discrete convex analysis, facility location and clustering problems, matching games, and parameterized complexity, this book discusses theoretical aspects of combinatorial optimization and graph algorithms. Contributions are by renowned researchers who attended NII Shonan meetings on this essential topic. The collection contained here provides readers with the outcome of the authors' research and productive meetings on this dynamic area, ranging from computer science and mathematics to operations research. Networks are ubiquitous in today's world: the Web, online social networks, and search-and-query click logs can lead to a graph that consists of vertices and edges. Such networks are growing so fast that it is essential to design algorithms to work for these large networks. Graph algorithms comprise an area in computer science that works to design efficient algorithms for networks. Here one can work on theoretical or practical problems where implementation of an algorithm for large networks is needed. In two of the chapters, recent results in graph matching games and fixed parameter tractability are surveyed. Combinatorial optimization is an intersection of operations research and mathematics, especially discrete mathematics, which deals with new questions and new problems, attempting to find an optimum object from a finite set of objects. Most problems in combinatorial optimization are not tractable (i.e., NP-hard). Therefore it is necessary to design an approximation algorithm for them. To tackle these problems requires the development and combination of ideas and techniques from diverse mathematical areas including complexity theory, algorithm theory, and matroids as well as graph theory, combinatorics, convex and nonlinear optimization, and discrete and convex geometry. Overall, the book presents recent progress in facility location, network design, and discrete convex analysis.

Dit stel ouers in staat om van vroeg af en te midde van 'n druk lewe alledaagse geleenthede om hulle te gebruik om hul kleingoed gemaklik in die wereld van wiskunde in te lei. En dit verg geen spesiale kennis of opleiding van ouers nie; net 'n positiewe instelling en 'n opskerping van hulle interaksie met hul kleingoed om hulle al spelenderwys vertroud te maak met wiskundebegrippe.

The extensive additions, and the inclusion of a new chapter, has made this classic work by Jeffrey, now joined by co-author Dr. H.H. Dai, an even more essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relationships between functions, and mathematical techniques that range from matrix theory and integrals of commonly occurring functions to vector calculus, ordinary and partial differential equations, special functions, Fourier series, orthogonal polynomials, and Laplace and Fourier transforms. During the preparation of this edition full advantage was taken of the recently updated seventh edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and other important reference works. Suggestions from users of the third edition of the Handbook have resulted in the expansion of many sections, and because of the relevance to boundary value problems for the Laplace equation in the plane, a new chapter on conformal mapping, has been added, complete with an atlas of useful mappings. A unique feature of the fourth edition is the provision of a CD-ROM that provides ready access to the most frequently used parts of the book, together with helpful notes for users of the Handbook.
- Comprehensive coverage in reference form of the branches of mathematics used in science and engineering
- Organized to make results involving integrals and functions easy to locate
- Results illustrated by worked examples
- Unique CD-ROMthat provides access to the most frequently used parts of the book
- CD-ROM contains helpful notes for users

Heinz Bauer (1928-2002) was one of the prominent figures in Convex Analysis and Potential Theory in the second half of the 20th century. The Bauer minimum principle and Bauer's work on Silov's boundary and the Dirichlet problem are milestones in convex analysis. Axiomatic potential theory owes him what is known by now as Bauer harmonic spaces. These Selecta collect more than twenty of Bauer's research papers including his seminal papers in Convex Analysis and Potential Theory. Above his research contributions Bauer is best known for his art of writing survey articles. Five of his surveys on different topics are reprinted in this volume. Among them is the well-known article Approximation and Abstract Boundary, for which he was awarded with the Chauvenet Price by the American Mathematical Association in 1980.

The book compiles research on Condorcet's Paradox over some two centuries. It begins with a historical overview of the discovery of Condorcet's Paradox in the 18th Century, reviews numerous studies conducted to find actual occurrences of the paradox, and compiles research that has been done to develop mathematical representations for the probability that the paradox will be observed. Combines all approaches that have been used to study this very interesting phenomenon.

CALCULUS For the Practical Man by J. E. THOMPSON. Originally published in 1931. PREFACE: THIS book on simplified calculus is one of a series designed by the author and publisher for the reader with an interest in the meaning and simpler technique of mathematical science, and for those who wish to obtain a practical mastery of some of the more usual and directly useful branches of the science without the aid of a teacher. Like the other books in the series it is the outgrowth of the author's experience with students such as those mentioned and the demand experienced by the publisher for books which may be read as well as studied. One of the outstanding features of the book is the use of the method of rates instead of the method of limits. To the conven tional teacher of mathematics, whose students work for a college degree and look toward the modern theory of functions, the author hastens to say that for their purposes the limit method is the only method which can profitably be used. To the readers contem plated in the preparation of this book, however, the notion of a limit and any method of calculation based upon it always seem artificial and not hi any way connected with the familiar ideas of numbers, algebraic symbolism or natural phenomena. On the other hand, the method of rates seems a direct application of the principle which such a reader has often heard mentioned as the extension of arithmetic and algebra with which he must become acquainted before he can perform calculations which involve changing quantities. The familiarity of examples of changing quantities in every-day life also makes it a simple matter to in troduce the terminology of the calculus; teachers and readers willrecall the difficulty encountered in this connection in more formal treatments. The scope and range of the book are evident from the table of contents. The topics usually found in books on the calculus but not appearing here are omitted in conformity with the plan of the book as stated in the first paragraph above. An attempt has been made to approach the several parts of the subject as naturally and directly as possible, to show as clearly as possible the unity and continuity of the subject as a whole, to show what the calculus is all about and how it is used, and to present the material in as simple, straightforward and informal a style as it will permit. It is hoped thus that the book will be of the greatest interest and usefulness to the readers mentioned above. The first edition of this book was prepared before the other volumes of the series were written and the arrangement of the material in this volume was not the same as in the others. In this revised edition the arrangement has been changed somewhat so that it is now the same in all the volumes of the series.

This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik Ne etril. Leading experts have contributed survey and research papers in the areas of Algebraic Combinatorics, Combinatorial Number Theory, Game theory, Ramsey Theory, Graphs and Hypergraphs, Homomorphisms, Graph Colorings and Graph Embeddings.

The most useful tool for reviewing mathematical methods for business and economics classes-now with more content Schaum's Outline of Mathematical Methods for Business, Economics and Finance, Second Edition is the go-to study guide for students enrolled in business and economics courses that require a variety of mathematical skills. No mathematical proficiency beyond the high school level is assumed, enabling students to progress at their own rate and adapt the book to their own needs. With an outline format that facilitates quick and easy review, this guide helps you understand basic concepts and get the extra practice you need to excel in business and economics courses. Schaum's Outline of Mathematical Methods for Business, Economics and Finance, Second Edition supports the bestselling textbooks and is ideal study aid for classes such as Calculus for Business, Applied Calculus, Calculus for Social Sciences and Calculus for Economics. Chapters include Equations and Graphs, Functions, Systems of Equations, Linear (or Matrix) Algebra, Linear Programming, Differential Calculus, Exponential and Logarithmic Functions, Integral Calculus, Calculus of Multivariable Functions, and more. Features * NEW in this edition: Additional problems at the end of each chapter * NEW in this edition: An additional chapter on sequences and series * NEW in this edition: Three computer applications of Linear Programming in Excel * More than 1,000 fully solved problems * Outline format to provide a concise guide for study * Clear, concise explanations covers all course fundamentals * Supplements the major bestselling textbooks in economics courses * Appropriate for the following courses: Calculus for Business, Applied Calculus, Calculus for Social Sciences, Calculus for Economics

FINANCIAL MATHEMATICS BY CLARENCE H. RICHARDSON, PH. D. Professor of Mathematics, Bucknell University AND ISAIAH LESLIE MILLER Late Professor of Mathematics, South Dakota State College of Agriculture and Mechanic Arts NEW YORK D. VAN NOSTRAND COMPANY, INC. 250 FOURTH AVENUE 1946 COPY RIGHT, 1946 BY D. VAN NOSTHAND COMPANY, INC. All Rights Reserved Thin book, or any parts thereof, may not be reproduced in any form without written per mission from the authors and the publishers. Based on Business fathematics, I. L. Miller, copyright 1935 second edition copyright 1939 and Commercial Algebra and Mathematics of Finance, I. L. Miller and C. H. Richardson, copyright 1939 by D. Van Nostrand Company, Inc. PRINTED IN THE UNITED STATES OF AMERICA PREFACE This text is designed for a three-hour, one-year course for students who desire a knowledge of the mathematics of modern business and finance. While the vocational aspects of the subject should be especially attractive to students of commerce and business administration, yet an understanding of the topics that are considered interest, discount, an nuities, bond valuation, depreciation, insurance may well be desirable information for the educated layman. To live intelligently in this complex age requires more than a super ficial knowledge of the topics to which we have just alluded, and it is pal pably absurd to contend that the knowledge of interest, discount, bonds, and insurance that one acquires in school arithmetic is sufficient to under stand modern finance. Try as one may, one cannot escape questions of finance. The real issue is shall we deal with them with understanding and effectiveness or with superficiality and ineffectiveness Whilethis text presupposes a knowledge of elementary algebra, we have listed for the students convenience, page x, a page of important formulas from Miller and Richardson, Algebra Commercial Statistical that should be adequate for the well-prepared student. Although we make frequent reference to this Algebra in this text on Financial Mathematics, the necessary formulas are found in this reference list. In the writing of this text the general student and not the pure mathe matician has been kept constantly in mind. The text includes those tech niques and artifices that many years of experience in teaching the subject have proved to be pedagogically fruitful. Some general features may be enumerated here 1 The illustrative examples are numerous and are worked out in detail, many of them having been solved by more than one method in order that the student may compare the respective methods of attack. 2 Line diagrams, valuable in the analysis and presentation of problem material, have been given emphasis. 3 Summaries of important formulas occur at strategic points. 4 The exercises and problems are nu frierous, and they are purposely selected to show the applications of the theory to the many fields of activity. These exercises and problems are abundant, and no class will hope to do more than half of them. 5 Sets iv Preface of review problems are found at the ends of the chapters and the end of the book. A few special features have also been included 1 Interest and dis count have been treated with unusual care, the similarities and differences having been pointed out with detail. 2 The treatment of annuities is pedagogical and logical. This treatment has been made purposely flexible so that, if itis desired, the applications may be made to depend upon two general formulas. No new formulas are developed for the solution of problems involving annuities due and deferred annuities, and these special annuities are analyzed in terms of ordinary annuities. 3 The discussion of probability and its application to insurance is more extended than that found in many texts. In this edition we are including Answers to the exercises and problems...

Plasticity and Geotechnics is the first attempt to summarize and present, in one volume, the major developments achieved to date in the field of plasticity theory for geotechnical materials and its applications to geotechnical analysis and design. The author believes that there is an urgent need for the geotechnical and solid mechanics community to have a unified presentation of plasticity theory and its application to geotechnical engineering. In its thorough, comprehensive treatment of the subject, the book covers classical, recent, and modern developments of appropriate constitutive theories of stress-strain relations for geomaterials and a wide range of analytical and computational techniques that are available for solving geotechnical design problems. The emphasis is on key concepts behind the most useful theoretical developments, the inter-relation of these concepts, and their implementation in numerical procedures for solving practical problems in geotechnical engineering.

Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its value in the mathematical community. The writing is expository, not technical, and should be accessible and informative to a diverse audience. The primary readership includes all those in departments of mathematical sciences in two or four year colleges and universities, and their administrators, as well as graduate students. Researchers in education may also find topics of interest. Other potential readers include those doing work in mathematics education in schools of education, and teachers of secondary or middle school mathematics as well as those involved in their professional development.

The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia. He wondered what a complex polynomial function would look like, such as the ones named after him (in the form of z2 + c, where c is a complex constant with real and imaginary parts). The idea behind this formula is that one takes the x and y coordinates of a point z, and plug them into z in the form of x + i*y, where i is the square root of -1, square this number, and then add c, a constant. Then plug the resulting pair of real and imaginary numbers back into z, run the operation again, and keep doing that until the result is greater than some number. The number of times you have to run the equations to get out of an 'orbit' not specified here can be assigned a colour and then the pixel (x,y) gets turned that colour, unless those coordinates can't get out of their orbit, in which case they are made black. Later it was Benoit Mandelbrot who used computers to produce fractals. A basic property of fractals is that they contain a large degree of self similarity, i.e., they usually contain little copies within the original, and these copies also have infinite detail. That means the more you zoom in on a fractal, the more detail you get, and this keeps going on forever and ever. The well-written book 'Getting acquainted with fractals' by Gilbert Helmberg provides a mathematically oriented introduction to fractals, with a focus upon three types of fractals: fractals of curves, attractors for iterative function systems in the plane, and Julia sets. The presentation is on an undergraduate level, with an ample presentation of the corresponding mathematical background, e.g., linear algebra, calculus, algebra, geometry, topology, measure theory and complex analysis. The book contains over 170 color illustrations.

Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra, complex analysis, discrete mathematics, dynamical systems, number theory and topology. Several papers on computational and applied mathematics such as wavelet analysis, quantum mechanics, piecewise linear modeling, cosmological models of super symmetry, fluid dynamics, interpolation theory, optimization, ergodic theory and games theory are also presented.

This book presents important works by the Scottish mathematician Colin MacLaurin (1698-1746), translated in English for the first time. It includes three of the mathematician 's less known and often hard to obtain works. A general introduction puts the works in context and gives an outline of MacLaurin's career. Each translation is also accompanied by an introduction and analyzed both in modern terms and from a historical point of view.

This contributed volume is an exciting product of the 22nd MAVI conference, which presents cutting-edge research on affective issues in teaching and learning math. The teaching and learning of mathematics is highly dependent on students' and teachers' values, attitudes, feelings, beliefs and motivations towards mathematics and mathematics education. These peer-reviewed contributions provide critical insights through their theoretically and methodologically diverse analyses of relevant issues related to affective factors in teaching and learning math and offer new tools and strategies by which to evaluate affective factors in students' and teachers' mathematical activities in the classroom. Among the topics discussed: The relationship between proxies for learning and mathematically related beliefs. Teaching for entrepreneurial and mathematical competences. Prospective teachers' conceptions of the concepts mean, median, and mode. Prospective teachers' approach to reasoning and proof The impact of assessment on students' experiences of mathematics. Through its thematic connections to teacher education, professional development, assessment, entrepreneurial competences, and reasoning and proof, Students' and Teachers' Values, Attitudes, Feelings and Beliefs in Mathematics Classrooms proves to be a valuable resource for educators, practitioners, and students for applications at primary, secondary, and university levels.

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject.

As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with the finite ones gave a new impetus and led to spectacular success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometrically-oriented world of function fields have led to new insights in the more arithmetically-oriented world of number fields, or vice versa.

These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives.

This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections.

Contributors: G. BAckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. KAhler; U. KA1/4hn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner.

This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible for displacements of the natural sloshing modes. Algorithms for computing the hydrodynamic coefficients in the approximate mathematical models are proposed. Numerical values of these coefficients are listed for some tank shapes and liquid fillings. The mathematical models are also derived for the contained liquid characterized by the Newton-type dissipation. Formulas for hydrodynamic force and moment are derived in terms of the solid body quasi-velocities and the sloshing-related generalized coordinates. For prescribed harmonic excitations of upright circular (annular) cylindrical and/or conical tanks, the steady-state sloshing regimes are theoretically classified; the results are compared with known experimental data. The book can be useful for both experienced and early-stage mechanicians, applied mathematicians and engineers interested in (semi-)analytical approaches to the "fluid-structure" interaction problems, their fundamental mathematical background as well as in modeling the dynamics of complex mechanical systems containing a rigid tank partly filled by a liquid.