The title 'Integral equations' covers many things which have very little connection with each other. However, they are united by the following important feature. In most cases, the equations involve an unknown function operated on by a bounded and often compact operator defined on some Banach space. The aim of the book is to list the main results concerning integral equations. The classical Fredholm theory and Hilbert-Schmidt theory are presented in Chapters II and III. The preceding Chapter I contains a description of the most important types of integral equations which can be solved in 'closed' form. Chapter IV is an important addition to Chapters II and III, as it contains the theory of integral equations with non-negative kernels. The development of this theory is mainly due to M. G. Krein. The content of the first four chapters is fairly elementary. It is well known that the Fredholm theory has been generalized for equations with compact operators. Chapter V is devoted tothis generalization. In Chapter VI one-dimensional (i.e. with one dependent variable) singular integral equations are considered. The last type of equations differ from that considered in the preceding chapters in that singular integral operators are not compact but only bounded in the usual functional spaces.

A title that sounds like poetry, and a subtitle that seems to contradict the title! But the subtitle is right, and originally it was just the title. A strange subtitle, isn't it? Preface to a Science of Mathematical Education. All sciences - in their prenatal stage - have known this kind of literature: only the term used was not 'Preface', but, for instance, 'Prolegomena', which * means the same though it sounds less provisional. In fact such works were thicker than the present one, by up to ten times. There is much more that can be said about a science before it comes into being than after; with the first results comes modesty. This is the preface to a book that will never be written: not by me, nor by anybody else. Once a science of mathematical education exists, it will get the preface it deserves. Nevertheless this preface - or what for honesty's sake I have labelled so - must fulfil a function: the function of accelerating the birth of a science of mathematical education, which is seriously impeded by the unfounded view that such already exists. Against this view I have to argue: it rests on a wrong estimation - both over and under estimation at the same time - of what is to be considered as science.

A unique and detailed account of all important relations in the analytic theory of determinants, from the classical work of Laplace, Cauchy and Jacobi to the latest 20th century developments. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. The solutions are verified by applying theorems established in earlier chapters, and the book ends with an extensive bibliography and index. Several contributions have never been published before. Indispensable for mathematicians, physicists and engineers wishing to become acquainted with this topic.

Developed from the author's course on advanced mechanics of composite materials, Finite Element Analysis of Composite Materials with Abaqus (R) shows how powerful finite element tools tackle practical problems in the structural analysis of composites. This Second Edition includes two new chapters on "Fatigue" and "Abaqus Programmable Features" as well as a major update of chapter 10 "Delaminations" and significant updates throughout the remaining chapters. Furthermore, it updates all examples, sample code, and problems to Abaqus 2020. Unlike other texts, this one takes theory to a hands-on level by actually solving problems. It explains the concepts involved in the detailed analysis of composites, the mechanics needed to translate those concepts into a mathematical representation of the physical reality, and the solution of the resulting boundary value problems using Abaqus. The reader can follow a process to recreate every example using Abaqus graphical user interface (CAE) by following step-by-step directions in the form of pseudo-code or watching the solutions on YouTube. The first seven chapters provide material ideal for a one-semester course. Along with offering an introduction to finite element analysis for readers without prior knowledge of the finite element method (FEM), these chapters cover the elasticity and strength of laminates, buckling analysis, free edge stresses, computational micromechanics, and viscoelastic models for composites. Emphasizing hereditary phenomena, the book goes on to discuss continuum and discrete damage mechanics as well as delaminations and fatigue. The text also shows readers how to extend the capabilities of Abaqus via "user subroutines" and Python scripting. Aimed at advanced students and professional engineers, this textbook features 62 fully developed examples interspersed with the theory, 82 end-of-chapter exercises, and 50+ separate pieces of Abaqus pseudo-code that illustrate the solution of example problems. The author's website offers the relevant Abaqus and MATLAB model files available for download, enabling readers to easily reproduce the examples and complete the exercises. Video recording of solutions to examples are available on YouTube with multilingual captions.

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Imagine algebra class meets The Hitchhiker 's Guide to the Galaxy

Meet JJ, an unusual character with a unique vantage position from which he can measure and monitor humanity 's progress. Armed with a device that compels all around it to tell the truth, JJ offers a satirical evaluation of our attitudes to numeracy and logic, touching upon several aspects of life on Earth along the way, from the criminal justice system and people 's use of language to highway driving and modern art.

A collection of mathematically-flavored stories and jokes, interlaced with puzzles, paradoxes and problems, fuse together in an entertaining, free-flowing narrative that will engage and amuse anyone with an interest in the issues confronting society today. JJ demonstrates how a lack of elementary mathematical knowledge can taint our work and general thinking and reflects upon the importance of what is arguably our most valuable weapon against ignorance: a sound mathematical education.

The twentieth century has been one of great international conflict, but also one of increasing globalization and cooperation among nations. The history of international mathematical cooperation over the last hundred years--from the first international congress in 1897 to plans for the World Mathematical Year 2000--as told by Professor Olli Lehto, is a surprisingly compelling story. For reflected in the history of the International Mathematical Union (IMU) is all the strife among world powers, as well as aspirations for cooperation among nations in an increasingly interdependent world. The IMU, founded in the aftermath of World War I, for fifteen years excluded Germany and the other defeated Central Powers. But in the 1920s the IMU embraced principles of political neutrality, inviting every national mathematical organization to join the IMU, and this principle of nondiscrimination, while sometimes sorely tried, has held the IMU in good stead. Then came the Second World War, and again international cooperation was threatened. After World War II, a number of issues--the Cold War, the conflict between the People's Republic of China and Taiwan, a divided Germany, problems in the emerging nations of Africa--at times led to attempts to influence the IMU Executive Committee in its decisions regarding membership, location of international congresses, committee assignments, handling of protests, and awarding the coveted Fields Medals. Throughout the tumultuous past half century the IMU has sponsored International Congresses throughout the world, and Mathematics Without Borders will fill you in on all the mathematical and organizational details. But what keeps you turning pages is the very humanstory of individuals, among them many of the great mathematicians of our

Projective geometry, and the Cayley-Klein geometries embedded into it, were originated in the 19th century. It is one of the foundations of algebraic geometry and has many applications to differential geometry.

The book presents a systematic introduction to projective geometry as based on the notion of vector space, which is the central topic of the first chapter. The second chapter covers the most important classical geometries which are systematically developed following the principle founded by Cayley and Klein, which rely on distinguishing an absolute and then studying the resulting invariants of geometric objects.

An appendix collects brief accounts of some fundamental notions from algebra and topology with corresponding references to the literature.

This self-contained introduction is a must for students, lecturers and researchers interested in projective geometry.

This book details a unique training evaluation approach developed by David J. Basarab, Sr. currently the Manager of Evaluation at Motorola University. This approach was developed in part based on information from his graduate coursework with Dr. Darrell K. Root, professor of program evaluation and educational administration at the University of Dayton. It enabled Motorola to evaluate their corporate training programs to determine whether money spent on training was an investment or an expense. This evaluation approach is also significant in determining either the effectiveness of or the opportunities to improve corporate training programs. In this text, The Training Evaluation Process, David Basarab and Darrell Root provide commercial industry training with a step-by-step approach to use when evaluating training progrruns, thus allowing training to be viewed as an investment rather than an expense. This text focuses on assessing training programs, so that they may be improved. This approach provides a successful procedure to use when evaluating training programs. Included in the text is a comprehensive explanation of the evaluation model developed by D. L. Kirkpatrick (Kirkpatrick, D. L., November 1959) in which he described four levels of evaluating training progrruns: Level 1 -Reaction: Evaluate to learn participants' perception to the training program. Level 2 -Learning: Evaluate to determine whether participants have learned the course subject matter. Level 3 -Behavior: Evaluate participants' use of newly acquired job skills on the job. Level 4 -Results: Evaluate the organizational impact of training on company's workforce.

Codes, Designs, and Geometry brings together in one place important contributions and up-to-date research results in this important area. Codes, Designs, and Geometry serves as an excellent reference, providing insight into some of the most important research issues in the field.

This volume features substantive biographical essays on 59 women from around the world who have made significant contributions to mathematics from antiquity to the present. Designed for secondary school students and the general public, each profile describes major life events, obstacles faced and overcome, educational and career milestones--including a discussion of mathematical research in non-technical terms--and interests outside of 2 promotics. Although the collection includes historical women, the emphasis is on contemporary mathematicians, many of whom have not been profiled in any previous work. The work also celebrates the contributions of minority women, including 10 African-American, Latina, and Asian mathematicians. Written by practicing mathematicians, teachers and researchers, these profiles give voice to the variety of pathways into mathematics that women have followed and the diversity of areas in which mathematics can work. Many profiles draw on interviews with the subject, and each includes a short list of suggested reading by and about the mathematician. Most mathematicians profiled stress the value, importance, and enjoyment of collaborative research, contradicting the prevailing notion that doing good mathematics requires isolation. This collection provides not only a substantial number of role models for girls interested in a career in mathematics, but also a unique depiction of a field that can offer a lifetime of challenge and enjoyment.

Kvasz's book is a contribution to the history and philosophy of mat- matics, or, as one might say, the historical approach to the philosophy of mathematics. This approach is for mathematics what the history and philosophy of science is for science. Yet the historical approach to the philosophy of science appeared much earlier than the historical approach to the philosophy of mathematics. The ?rst signi?cant work in the history and philosophy of science is perhaps William Whewell's Philosophy of the Inductive Sciences, founded upon their History. This was originally published in 1840, a second, enlarged edition appeared in 1847, and the third edition appeared as three separate works p- lished between 1858 and 1860. Ernst Mach's The Science of Mech- ics: A Critical and Historical Account of Its Development is certainly a work of history and philosophy of science. It ?rst appeared in 1883, and had six further editions in Mach's lifetime (1888, 1897, 1901, 1904, 1908, and 1912). Duhem's Aim and Structure of Physical Theory appeared in 1906 and had a second enlarged edition in 1914. So we can say that history and philosophy of science was a well-established ?eld th th by the end of the 19 and the beginning of the 20 century. By contrast the ?rst signi?cant work in the history and philosophy of mathematics is Lakatos's Proofs and Refutations, which was p- lished as a series of papers in the years 1963 and 1964.

This is a translation of Landau's famous Elementare Zahlentheorie with added exercises by Paul T. Bateman and Eugene E. Kohlbecker. This three-volume classic work is reprinted here as a single volume.

A comprehensive and hands-on guide to crucial math concepts and terminology In the newly revised third edition of All the Math You'll Ever Need: A Self-Teaching Guide, veteran math and computer technology teacher Carolyn Wheater and veteran mathematics author Steve Slavin deliver a practical and accessible guide to math you can use every day and apply to a wide variety of life tasks. From calculating monthly mortgage payments to the time you'll need to pay off a credit card, this book walks you through the steps to understanding basic math concepts. This latest edition is updated to reflect recent changes in interest rates, prices, and wages, and incorporates information on the intelligent and efficient use of calculators and mental math techniques. It also offers: A brand-new chapter on hands-on statistics to help readers understand common graphs An easy-to-use-format that provides an interactive method with frequent questions, problems, and self-tests Complete explanations of necessary mathematical concepts that explore not just how math works, but also why it works Perfect for anyone seeking to make practical use of essential math concepts and strategies in their day-to-day life, All the Math You'll Ever Need is an invaluable addition to the libraries of students who want a bit of extra help applying math in the real world.

This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.

This volume is dedicated to the career of Jill Adler and the role she has played in growing mathematics education research in South Africa, Africa and beyond. Her work epitomises what is referred to as the 'engaged scholar': i.e. doing rigorous and theoretically rich research at the cutting edge of international work in the field which at the same time contributes to critical areas of local and regional need in education. Jill is one of the world's leading experts in mathematics education research and her exemplary career is a continuous source of inspiration for generations of researchers and students. The chapters in this volume are authored by Jill's former PhD students, a few select colleagues from different parts of the world that she collaborated with as well as leading scholars who she worked with in PME, ICMI and in her many international assignments. In essence, this volume celebrates Jill's contribution not only to mathematics education but also to our contributions as her friends and colleagues. Topics covered include language and mathematics, teacher education, and the dilemma of an activist researcher engaging in issues that matter hugely to the participants in the research, students and teachers in post-apartheid schooling, whilst also setting up the separation that is needed for good research.

This volume collects the contributions of a Conference held in June 2005 at the laboratoire Paul Painleve (UMR CNRS 8524) in Lille, France. The meeting was intended to review hot topics and future trends in fluid dynamics, with the objective to foster exchanges of various viewpoints (e.g. theoretical, and numerical) on the addressed questions. It comprises a collection of research articles on recent advances in the analysis and simulation of fluid dynamics.

Whether you are returning to school, studying for an adult numeracy test, helping your kids with homework, or seeking the confidence that a firm maths foundation provides in everyday encounters, "Basic Maths For Dummies, " UK Edition, provides the content you need to improve your basic maths skills.

Based upon the Adult Numeracy Core Curriculum, this title covers such topics as: Getting started with the building blocks of maths and setting yourself up for success Dealing with decimals, percentages and tackling fractions without fear Sizing Up weights, measures, and shapes How to handle statistics and gauge probability Filled with real-world examples and written by a PhD-level mathematician who specialises in tutoring adults and students, "Basic Maths For Dummies "also provides practical advice on overcoming maths anxiety and a host of tips, tricks, and memory aids that make learning maths (almost) painless - and even fun.

This book provides an interdisciplinary presentation of the current knowledge of pattern formation in complex system, with sufficiently many details, tools, and concrete examples to be useful for the graduate student or scientist entering this area of research.