Quantum Potential

Quantum Potential

Recently the interest in Bohm realist interpretation of quantum mechanics has grown. The important advantage of this approach lies in the possibility to introduce non-locality ab initio, and not as an unexpected host. In this book the authors give a detailed analysis of quantum potential, the non-locality term and its role in quantum cosmology and information. The different approaches to the quantum potential are analysed, starting from the original attempt to introduce a realism of particles trajectories (influenced by de Broglie’s pilot wave) to the recent dynamic interpretation provided by Goldstein, Durr, Tumulka and Zangh, and the geometrodynamic picture, with suggestion about quantum gravity. Finally we focus on the algebraic reading of Hiley and Birbeck school, that analyse the meaning of the non-local structure of the world, bringing important consequences for the space, time and information concepts.

Quantum Potential

Digital Self-tuning Controllers

Digital Self-tuning Controllers

A complete course in self-tuning control, beginning with a survey of adaptive control and the formulation of adaptive control problems. Modelling and identification are dealt with before passing on to algebraic design methods. Finally, laboratory verification and experimentation will ground your theoretical knowledge in real plant control. Features: a strong emphasis on practical problem solving with control algorithms clearly laid out in easy-to-follow formats or as MATLAB functions suitable for use in project work; specially written MATLAB toolboxes for the presentation of typical control system and plant properties and ready for use in direct control of real or simulated plants; worked examples and tutorial exercises. This book shows graduate students and advanced undergraduates how to overcome the problems of putting the tools of adaptive control theory into practice. The text will also be of interest to engineers wishing to employ ideas of adaptive control in their designs and plant.

Digital Self-tuning Controllers

The Mathematics of Money

The Mathematics of Money

The Mathematics of Money: Math for Business and Personal Finance covers all the traditional topics of the business math course, but with a more algebraic focus than many of the texts currently on the market. The text develops a solid understanding of percent and interest early, then applies that foundation to other applications in business and personal finance. While it is appropriate for students of all levels, the book takes the approach that even if students are coming into the class with only high school math, neither they nor the instructor need to be afraid of algebra; it takes care to clearly present and reinforce the formulas given and to consistently return to them and apply the material to contexts that are relevant to the students.

The Mathematics of Money

Mathematica in Action - Third edition

Mathematica in Action - Third edition

With the third edition of his popular Mathematica in Action, award-winning author Stan Wagon guides readers through the important changes that have been made to Mathematica 6.0. To utilize the more sophisticated graphics capabilities of 6.0, Wagon has significantly expanded the chapters on surfaces and the parametric plotting of surfaces. The chapter on differential equations now includes material from VisualDSolve , built into Mathematica 6.0. Like previous editions, this is not only an introduction to Mathematica 6.0, but also a tour of modern mathematics by one of the fields most gifted expositors. Wagon explores some of the most important areas of modern mathematics with new chapters on optimization, including algebraic and numerical optimization, and linear and integer programming. Connections are also made to computer science with new material on graphs and networks. Wagon is the author of nine books on mathematics, including A Course in Computational Number Theory , named one of the ten best math books of 2000 by the American Library Association. He has written extensively on the educational applications of Mathematica, inlcuding the books VisualDSolve: Visualizing Differential Equations with Mathematica, and Animating Calculus: Mathematica Notebooks for the Laboratory. From Reviews of the Second Edition: ‘The bottom line is that is an outstanding book containing many examples of real uses of Mathematica for the novice, intermediate, and expert user.’ Mark McClure, Mathematica in Education and Research Journal ‘In a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional graphics and high-precision integer arithmetic can contribute to our understanding and enjoyment of mathematics.’ Richard Walker, The Mathematical Gazette

Mathematica in Action - Third edition

The Development of Arabic Mathematics

The Development of Arabic Mathematics

An understanding of developments in Arabic mathematics between the IXth and XVth century is vital to a full appreciation of the history of classical mathematics. This book draws together more than ten studies to highlight one of the major developments in Arabic mathematical thinking, provoked by the double fecondation between arithmetic and the algebra of al-Khwarizmi, which led to the foundation of diverse chapters of mathematics: polynomial algebra, combinatorial analysis, algebraic geometry, algebraic theory of numbers, diophantine analysis and numerical calculus. Thanks to epistemological analysis, and the discovery of hitherto unknown material, the author has brought these chapters into the light, proposes another periodization for classical mathematics, and questions current ideology in writing its history.

The Development of Arabic Mathematics

Algebra, Geometry and Software Systems

Algebra, Geometry and Software Systems

The book contains surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gr’obner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. Therefore the volumes other focus is on solutions towards the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

Algebra, Geometry and Software Systems

Generic and Indexed Programming

Generic and Indexed Programming

Generic programming is about making programs more widely applicable via exotic kinds of parametrization—not just along the dimensions of values or of types, but also of things such as the shape of data, algebraic structures, strategies, computational paradigms, and so on. Indexed programming is a lightweight form of dependently typed programming, constraining flexibility by allowing one to state and check relationships between parameters: that the shapes of two arguments agree, that an encoded value matches some type, that values transmitted along a channel conform to the stated protocol, and so on. The two forces of genericity and indexing balance each other nicely, simultaneously promoting and controlling generality. The 5 lectures included in this book stem from the Spring School on Generic and Indexed Programming, held in Oxford, UK, in March 2010 as a closing activity of the generic and indexed programming project at Oxford which took place in the years 2006-2010.

Generic and Indexed Programming

Educational Algebra

Educational Algebra

Given its abstract nature and the highly syntactical competence required by the use of symbolic algebra, research on its teaching and learning must rely on approaches that include semiotic concepts and analyses that recall the history of algebraic ideas, among others. Educational Algebra: A Theoretical and Empirical Approach deals with a theoretical perspective on the study of school algebra, in which both components (semiotics and history) occur. This perspective runs opposite to general theoretical models, since it submits components for the design of local frameworks for theoretical analysis. The Methodological design allows for the interpretation of specific phenomena and the inclusion, within such interpretative frameworks, of evidence not included in more general treatments. Such is the case of phenomena observed in subjects who are initiating the study of symbolic algebra, involving the production of personal sign systems at the intermediate level or the level previous to the mathematical sign system which is to be learned. Disciplines such as Linguistics, Logic, Psycholinguistics, Semiotics, general Cognitive Psychology, Mathematics Psychology, Mathematics Epistemology, History of Mathematics, and others have carried out research on the same topics approached by Mathematics Education and have redefined their results within the framework of their respective fields. Specifically, theorists in Linguistics, Information Processing and Didactics of Mathematics have done important work on the notion of code. Today, this notion is a key element to interpreting the idea of representation in the new explanatory models of cognitive problems placed by alternative teaching approaches, including those involving a technological environment. Additionally, Psycholinguistics and Artificial Intelligence in procedural models of human abilities have intended to explain how and why users of mathematical language naturally and commonly make mistakes in syntactical procedures. Educational Algebra: A Theoretical and Empirical Approach adds to previous developments with priority given to a pragmatic perspective on ‘meaning in use’ over ‘formal meaning’. The bulk of these approaches and others of similar nature have lead to a focus on competence rather than on a users activity with mathematical language. Such a shift in perspective has fundamental implications on the way mathematical language is studied. Essentially, Grammarthe abstract formal systemand Pragmaticsthe principles of the use of languageare complementary domains in this volume. Both are related to different teaching models, whether new or traditional, used in helping students to become competent users of Algebra. Because of this, Educational Algebra: A Theoretical and Empirical Approach will be of interest to researchers and practitioners within the mathematics education field.

Educational Algebra

Rational Algebraic Curves

Rational Algebraic Curves

The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.

Rational Algebraic Curves

Lectures on Algebra, Volume 1

Lectures on Algebra, Volume 1

This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author’s fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author’s lectures at Purdue University over the last few years.

Lectures on Algebra, Volume 1

A Course in Modern Analysis and Its Applications

A Course in Modern Analysis and Its Applications

Designed for one-semester courses at the senior undergraduate level, this book will appeal to mathematics majors, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance.Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for further developments. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.

A Course in Modern Analysis and Its Applications

From Quantum Cohomology to Integrable Systems

From Quantum Cohomology to Integrable Systems

Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry. Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework. Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.

From Quantum Cohomology to Integrable Systems

Basic Theory of Algebraic Groups and Lie Algebras

Basic Theory of Algebraic Groups and Lie Algebras

he theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and

Basic Theory of Algebraic Groups and Lie Algebras

Fractals and Universal Spaces in Dimension Theory

Fractals and Universal Spaces in Dimension Theory

Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods – the classical (separable metric) and the modern (not-necessarily separable metric). The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval. Unique features include: * The use of graphics to illustrate the fractal view of these spaces; * Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology; * A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings; * Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study – the interested reader will find many relevant open problems which will create further research into these topics.

Fractals and Universal Spaces in Dimension Theory

Algebraic Cobordism

Algebraic Cobordism

Following Quillen’s approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen’s theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications.

Algebraic Cobordism

Algebraic Cycles, Sheaves, Shtukas and Moduli

Algebraic Cycles, Sheaves, Shtukas and Moduli

The articles in this volume are devoted to: – moduli of coherent sheaves; – principal bundles and sheaves and their moduli; – new insights into Geometric Invariant Theory; – stacks of shtukas and their compactifications; – algebraic cycles vs. commutative algebra; – Thom polynomials of singularities; – zero schemes of sections of vector bundles. The main purpose is to give ‘friendly’ introductions to the above topics through a series of comprehensive texts starting from a very elementary level and ending with a discussion of current research. In these texts, the reader will find classical results and methods as well as new ones. The book is addressed to researchers and graduate students in algebraic geometry, algebraic topology and singularity theory. Most of the material presented in the volume has not appeared in books before. Contributors: Jean-Marc Drzet, Toms L. Gmez, Adrian Langer, Piotr Pragacz, Alexander H. W. Schmitt, Vasudevan Srinivas, Ngo Dac Tuan, Andrzej Weber

Algebraic Cycles, Sheaves, Shtukas and Moduli