With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.

Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.

In the first half of the book, the author quickly builds the operator algebra setting. He uses this as a unifying theme in the second half, in which he treats several active research topics, some for the first time in book form. These include the quantum plane and tori, operator spaces, Hilbert modules, Lipschitz algebras, and quantum groups.

For graduate students, Mathematical Quantization offers an ideal introduction to a research area of great current interest. For professionals in operator algebras and functional analysis, it provides a readable tour of the current state of the field.

For courses in Basic Mathematics. The Martin-Gay principle: Every student can succeed Elayn Martin-Gay's student-centric approach is woven seamlessly throughout her texts and MyLab (TM) courses, giving students the optimal amount of support through effective video resources, an accessible writing style, and study skills support built into the program. Elayn's legacy of innovations that support student success include Chapter Test Prep videos and a Video Organizer note-taking guide. Expanded resources in the latest revision bring even more updates to her program, all shaped by her focus on the student - a perspective that has made her course materials beloved by students and instructors alike. The Martin-Gay series offers market-leading content written by a preeminent author-educator, tightly integrated with the #1 choice in digital learning: MyLab Math. Also available with MyLab Math By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Bringing Elayn Martin-Gay's voice and approach into the MyLab course - though video resources, study skills support, and exercises refined with each edition - gives students the support to be successful in math. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0135307880 / 9780135307885 Basic College Mathematics with Early Integers Plus MyLab Math with Pearson eText - Access Card Package, 4e Package consists of: 013517693X / 9780135176931 Basic College Mathematics with Early Integers 0135190320 / 9780135190326 MyLab Math with Pearson eText - Standalone Access Card - for Basic College Mathematics with Early Integers

For courses in Basic Math & Beginning Algebra (combined). The Martin-Gay principle: Every student can succeed Elayn Martin-Gay's student-centric approach is woven seamlessly throughout her texts and MyLab (TM) courses, giving students the optimal amount of support through effective video resources, an accessible writing style, and study skills support built into the program. Elayn's legacy of innovations that support student success include Chapter Test Prep videos and a Video Organizer note-taking guide. Expanded resources in the latest revision bring even more updates to her program, all shaped by her focus on the student - a perspective that has made her course materials beloved by students and instructors alike. The Martin-Gay series offers market-leading content written by a preeminent author-educator, tightly integrated with the #1 choice in digital learning: MyLab Math. Also available with MyLab Math By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Bringing Elayn Martin-Gay's voice and approach into the MyLab course - though video resources, study skills support, and exercises refined with each edition - gives students the support to be successful in math. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0135307899 / 9780135307892 Developmental Mathematics Plus MyLab Math with Pearson eText - Access Card Package, 4e Package consists of: 0134896017 / 9780134896014 Developmental Mathematics 0135171482 / 9780135171486 MyLab Math with Pearson eText - Standalone Access Card - for Developmental Mathematics

For courses in Prealgebra. Trusted author content. Thoughtful innovation. In this revision of the Bittinger Paperback Worktext Series, the Bittinger author team brings their extensive experience to developmental math courses, paired with thoughtful integration of technology and content. The Bittinger Series enables students to get the most out of their MyLab (TM) Math course through an updated learning path, new review videos, and engaging new exercises that offer the support they need, when they need it. Bittinger offers superior content written by author-educators, tightly integrated with MyLab Math - the #1 choice in digital learning. Bringing the authors' voices and their approach into the MyLab course encourages student motivation and engagement, while reinforcing their understanding of the skills and concepts they need to master algebra. Also available with MyLab Math By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0135218284 / 9780135218280 Prealgebra Plus MyLab Math with Pearson eText - Access Card Package Package consists of: 0135182565 / 9780135182567 Prealgebra 0135184371 / 9780135184370 MyLab Math with Pearson eText - Standalone Access Card - for Prealgebra

The volume is a collection of 20 refereed articles written in connection with lectures presented at the 12th International Conference on Finite Fields and Their Applications ('Fq12') at Skidmore College in Saratoga Springs, NY in July 2015. Finite fields are central to modern cryptography and secure digital communication, and hence must evolve rapidly to keep pace with new technologies. Topics in this volume include cryptography, coding theory, structure of finite fields, algorithms, curves over finite fields, and further applications.Contributors will include: Antoine Joux (Fondation Partenariale de l'UPMC, France); Gary Mullen (Penn State University, USA); Gohar Kyureghyan (Otto-von-Guericke Universitat, Germany); Gary McGuire (University College Dublin, Ireland); Michel Lavrauw (Universita degli Studi di Padova, Italy); Kirsten Eisentraeger (Penn State University, USA); Renate Scheidler (University of Calgary, Canada); Michael Zieve (University of Michigan, USA).

Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics.

It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.

As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.

Model theory investigates mathematical structures by means of formal languages. These so-called first-order languages have proved particularly useful. The text introduces the reader to the model theory of first-order logic, avoiding syntactical issues that are not too relevant to model-theory. In this spirit, the compactness theorem is proved via the algebraically useful ultraproduct technique, rather than via the completeness theorem of first-order logic. This leads fairly quickly to algebraic applications, like Malcev's local theorems (of group theory) and, after a little more preparation, also to Hilbert's Nullstellensatz (of field theory). Steinitz' dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal sets. The final chapter is on the models of the first-order theory of the integers as an abelian group. This material appears here for the first time in a textbook of introductory level, and is used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory. The latter itself is not touched upon. The undergraduate or graduate, is assumed t

Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity-in a presentation that stresses insight, understanding, and applications. Among its most outstanding features is the integration of MATLAB throughout the text. Each chapter includes a MATLAB subsection that discusses the various commands used to do the computations in that section and offers code for the graphics and some algorithms used in the text.

All of the material is presented from a matrix point of view with enough rigor for students to learn to compose arguments and proofs and adjust the material to cover other problems. The treatment includes optional subsections covering applications, and the final chapters move beyond basic matrix theory to discuss more advanced topics, such as decompositions, positive definite matrices, graphics, and topology.

Filled with illustrations, examples, and exercises that reinforce understanding, Matrix Theory and Applications with MATLAB allows readers to experiment and visualize results in a way that no other text does. Its rigor, use of MATLAB, and focus on applications better prepares them to use the material in their future work and research, to extend the material, and perhaps obtain new results of their own.

This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brasov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.

A remarkable interplay exists between the fields of elliptic functions and orthogonal polynomials. In the first monograph to explore their connections, Elliptic Polynomials combines these two areas of study, leading to an interesting development of some basic aspects of each. It presents new material about various classes of polynomials and about the odd Jacobi elliptic functions and their inverses.

The term elliptic polynomials refers to the polynomials generated by odd elliptic integrals and elliptic functions. In studying these, the authors consider such things as orthogonality and the construction of weight functions and measures, finding structure constants and interesting inequalities, and deriving useful formulas and evaluations.

Although some of the material may be familiar, it establishes a new mathematical field that intersects with classical subjects at many points. Its wealth of information on important properties of polynomials and clear, accessible presentation make Elliptic Polynomials valuable to those in real and complex analysis, number theory, and combinatorics, and will undoubtedly generate further research.

This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.

Through three editions, Cryptography: Theory and Practice, has been embraced by instructors and students alike. It offers a comprehensive primer for the subject's fundamentals while presenting the most current advances in cryptography. The authors offer comprehensive, in-depth treatment of the methods and protocols that are vital to safeguarding the seemingly infinite and increasing amount of information circulating around the world. Key Features of the Fourth Edition: New chapter on the exciting, emerging new area of post-quantum cryptography (Chapter 9). New high-level, nontechnical overview of the goals and tools of cryptography (Chapter 1). New mathematical appendix that summarizes definitions and main results on number theory and algebra (Appendix A). An expanded treatment of stream ciphers, including common design techniques along with coverage of Trivium. Interesting attacks on cryptosystems, including: padding oracle attack correlation attacks and algebraic attacks on stream ciphers attack on the DUAL-EC random bit generator that makes use of a trapdoor. A treatment of the sponge construction for hash functions and its use in the new SHA-3 hash standard. Methods of key distribution in sensor networks. The basics of visual cryptography, allowing a secure method to split a secret visual message into pieces (shares) that can later be combined to reconstruct the secret. The fundamental techniques cryptocurrencies, as used in Bitcoin and blockchain. The basics of the new methods employed in messaging protocols such as Signal, including deniability and Diffie-Hellman key ratcheting.

This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac-Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.

This monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, this monograph is the first book on this theory. The volume is highly recommended to theoreticians in pure and applied mathematics.

Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP(2). Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book's second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert's sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert's sixteenth problem About the Author: Severine Fiedler-le Touze has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.

Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP(2). Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book's second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert's sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert's sixteenth problem About the Author: Severine Fiedler-le Touze has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.

Over the last thirty years, the subject of nonlinear integrable systems has grown into a full-fledged research topic. In the last decade, Lie algebraic methods have grown in importance to various fields of theoretical research and worked to establish close relations between apparently unrelated systems. The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool. The book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation. It then offers a detailed discussion of prolongation structure and its representation theory, the orbit approach-for both finite and infinite dimension Lie algebra. The author also presents the modern approach to symmetries of integrable systems, including important new ideas in symmetry analysis, such as gauge transformations, and the "soldering" approach. He then moves to Hamiltonian structure, where he presents the Drinfeld-Sokolov approach, the Lie algebraic approach, Kupershmidt's approach, Hamiltonian reductions and the Gelfand Dikii formula. He concludes his treatment of Lie algebraic methods with a discussion of the classical r-matrix, its use, and its relations to double Lie algebra and the KP equation.

Matrices are used in many areas such as staustics, econometrics, mathematics, natural sciences and engineering. This handbook provides a collection of numerous results for easy reference in one source, together with a comprehensive dictionary of matrices and related terms. The book is structured and cross-referenced so that specific results and information are easy to locate References for proofs and computational algorithms are provided. Researchers, professionals and students using matrix techniques will find this book to be an invaluable resource for their work. Contents

• Definitions, Notation, Terminology
• Rules for Matrix Operations
• Matrix Valued Functions of a Matrix
• Trace, Determinant and Rank of a Matrix
• Eigenvalues and Singular Values
• Matrix Decompositions and Canonical Forms
• Vectorization Operators
• Vector and Matrix Norms
• Properties of Special Matrices
• Vector and Matrix Derivatives
• Polynomials, Power Series and Matrices

Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological algebraic structures, and provides more than 600 current references and 570 display equations for further exploration of the topic. It provides stimulating discussions from world-renowned names including Laszlo Fuchs, Robert Gilmer, Saharon Shelah, Daniel Simson, and Richard Swan to celebrate 40 years of study on cumulative rings. Describing emerging theories

Quaternionic and Clifford analysis have in recent years become increasingly important tools in the analysis of partial differential equations and their application in mathematical physics and engineering. This book reflects the main ideas in the field and covers quaternions and multivectors, Clifford valued functions and forms, Clifford operator calculus, boundary value problems, numerical Clifford analysis. Further results and research problems are also included The authors’ intention is to equip the reader with the understanding necessary to adapt these methods to their own work. It is assumed that the reader is familiar with the basics of complex function theory in one variable, functional analysis and algebra. With an ever increasing literature on quaternionic and Clifford analysis the need for an accessible and applicable book on the subject has never been greater. This volume meets this need and will be invaluable for students and researchers in mathematics, physics and engineering who wish to apply quaternionic and Clifford analysis in their work.

The feedback control of nonlinear differential and algebraic equation systems (DAEs) is a relatively new subject. Developing steadily over the last few years, it has generated growing interest inspired by its engineering applications and by advances in the feedback control of nonlinear ordinary differential equations (ODEs). This book-the first of its kind-introduces the reader to the inherent characteristics of nonlinear DAE systems and the methods used to address their control, then discusses the significance of DAE systems to the modeling and control of chemical processes. Within a unified framework, Control of Nonlinear Differential Algebraic Equation Systems presents recent results on the stabilization, output tracking, and disturbance elimination for a large class of nonlinear DAE systems.

Written at a basic mathematical level-assuming some familiarity with analysis and control of nonlinear ODEs-the authors focus on continuous-time systems of differential and algebraic equations in semi-explicit form. Beginning with background material about DAE systems and their differences from ODE systems, the book discusses generic classes of chemical processes, feedback control of regular and non-regular DAE systems, control of systems with disturbance inputs, the connection of the DAE systems considered with singularly perturbed systems, and finally offers examples that illustrate the application of control methods and the advantages of using high-index DAE models as the basis for controller design.
Mathematicians and engineers will find that this book provides unique, timely results that also clearly documents the relevance of DAE systems to chemical processes.

"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."

A thorough understanding of statistical mechanics depends strongly on the insights and manipulative skills that are acquired through the solving of problems. Problems on Statistical Mechanics provides over 120 problems with model solutions, illustrating both basic principles and applications that range from solid-state physics to cosmology. An introductory chapter provides a summary of the basic concepts and results that are needed to tackle the problems, and also serves to establish the notation that is used throughout the book. The problems themselves occupy five chapters, progressing from the simpler aspects of thermodynamics and equilibrium statistical ensembles to the more challenging ideas associated with strongly interacting systems and nonequilibrium processes. Comprehensive solutions to all of the problems are designed to illustrate efficient and elegant problem-solving techniques. Where appropriate, the authors incorporate extended discussions of the points of principle that arise in the course of the solutions. The appendix provides useful mathematical formulae.

This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons. There is also new work on multizeta values and logalgebraicity. The author has included numerous worked-out examples. Many open problems, which can serve as good thesis problems, are discussed.

On its original publication, this book provided the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it, before moving on to a discussion of Deligne-Lusztig induction and Lusztig's Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.