The importance of mathematics competitions has been widely recognized for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded.
Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in thefinal toolchest.
An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement.
As a bonus the aspiring "mathlete" may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum.

This textbook introduces students of economics to the fundamental notions and instruments in linear algebra. Linearity is used as a first approximation to many problems that are studied in different branches of science, including economics and other social sciences. Linear algebra is also the most suitable to teach students what proofs are and how to prove a statement. The proofs that are given in the text are relatively easy to understand and also endow the student with different ways of thinking in making proofs. Theorems for which no proofs are given in the book are illustrated via figures and examples. All notions are illustrated appealing to geometric intuition. The book provides a variety of economic examples using linear algebraic tools. It mainly addresses students in economics who need to build up skills in understanding mathematical reasoning. Students in mathematics and informatics may also be interested in learning about the use of mathematics in economics.

Palmprint Authentication is the first book to provide a comprehensive introduction to palmprint technologies. It reveals automatic biometric techniques for personal identification using palmprint, from the approach based on offline palmprint images, to the current state-of-the-art algorithm using online palmprint images.

Palmprint Authentication provides the reader with a basic concept of Palmprint Authentication. It also includes an in-depth discussion of Palmprint Authentication technologies, a detailed description of Palmprint Authentication systems, and an up-to-date coverage of how these issues are developed. This book is suitable for different levels of readers: those who want to learn more about palmprint technology, and those who wish to understand, participate, and/or develop a palmprint authentication system.

Palmprint Authentication is effectively a handbook for biometric research and development. Graduate students and researchers in computer science, electrical engineering, systems science, and information technology will all find it uniquely useful, not only as a reference book, but also as a text book. Researchers and practitioners in industry, and R&D laboratories working in the fields of security system design, biometrics, immigration, law enforcement, control, and pattern recognition will also benefit from this volume.

This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book's origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to f- ?ll the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university's Master's in Teaching p- gram for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of ma- ematical interest.

This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative algebras and includes an introduction to derived categories. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.

Details the basic theory of polynomial and fractional representation methods for algebraic analysis and synthesis of linear multivariable control systems. It also serves as a self-contained treatise of the mathematical theory so that results and techniques of the state space approaches'' for regular and singular systems appear as special cases of a general theory covering the wider class of PMDs of linear systems. Among the topics covered are: real rational vector spaces and rational matrices, pole and zero structure of rational matrices at infinity, proper and omega stable rational fuctions and matrices.

This volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d'enfant.Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d'Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010.This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures.iv>

This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting "Homological and Computational Methods in Commutative Algebra" held in Cortona (Italy) from May 30 to June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns' research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.

This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 22-28. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung.

The eighteenth International Workshop on Operator Theory and Applications (IWOTA) was hosted by the Unit for Business Mathematics and Informatics of the North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference was dedicated to Professor Joseph A. Ball on the occasion of his 60th birthday and to Professor Marinus M. Kaashoek on the occasion of his 70th birthday, and we wish to similarly honour them by dedicating this volume of the proceedings to them. TheaimoftheIWOTAmeetingsistobringtogethermathematiciansworking in operator theory and its applications to related ?elds. Each conference therefore has a unique character, depending on the related ?elds chosen by the local or- nizers. In the present case Functional Analysis and Von Neumann algebras were decided on, due to the number of people actively working in those ?elds in South Africa. The meetings are intended to be truly international (the seventeen pre- ous ones were held in 11 di?erent countries) and this conference was no exception, with participants drawn from 17 countries. IWOTA is directed by an international steering committee of 25 members under the guidance of the president I. Gohberg (Tel Aviv), assisted by the Vice PresidentsJ.W.Helton(LaJolla)andM.A.Kaashoek(Amsterdam).TheProce- ings of the IWOTA workshops regularly appear in the Birkhauser .. series: Operator Theory: Advances and Applications, and we thank them for their willingness to continue this cooperation by publishing this volume.

A group of Gerry Schwarz's colleagues and collaborators gathered at the Fields Institute in Toronto for a mathematical festschrift in honor of his 60th birthday. This volume is an outgrowth of that event, covering the wide range of mathematics to which Gerry Schwarz has either made fundamental contributions or stimulated others to pursue. The articles are a sampling of modern day algebraic geometry with associated group actions from its leading experts, with a particular focus on characteristic 0 and modular invariant theory.

Contributors:

M. Brion

A. Broer

D. Daigle

J. Elmer

P. Fleischmann

G. Freudenberg

D. Greb

P. Heinzner

A. Helminck

B. Kostant

H. Kraft

R. J. Shank

W. Traves

N. R. Wallach

D. Wehlau

This volume is the result of two international workshops; "Infinite Analysis 11 Frontier of Integrability" held at University of Tokyo, Japan in July 25th to 29th, 2011, and "Symmetries, Integrable Systems and Representations" held at Universite Claude Bernard Lyon 1, France in December 13th to 16th, 2011.

Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions.

Through these topics, the readerwill find some recent developments in the field of mathematical physics and their interactions with several other domains.
"

Only book on Hopf algebras aimed at advanced undergraduates

This book is aimed at graduate students in physics who are studying group theory and its application to physics. It contains a short explanation of the fundamental knowledge and method, and the fundamental exercises for the method, as well as some important conclusions in group theory. The book has been designed as a supplement to the author's textbook Group Theory for Physicists, also published by World Scientific. Together these two books can be used in a course on group theory for first-year graduate students in physics, especially theoretical physics. They are also suitable for some graduate students in theoretical chemistry.

This book is aimed at graduate students in physics who are studying group theory and its application to physics. It contains a short explanation of the fundamental knowledge and method, and the fundamental exercises for the method, as well as some important conclusions in group theory. The book has been designed as a supplement to the author's textbook Group Theory for Physicists, also published by World Scientific. Together these two books can be used in a course on group theory for first-year graduate students in physics, especially theoretical physics. They are also suitable for some graduate students in theoretical chemistry.

This present volume is the Proceedings of the 18th International C- ference on Nearrings and Near?elds held in Hamburg at the Universit] at derBundeswehrHamburgfromJuly27toAugust03,2003. ThisConf- ence was organized by Momme Johs Thomsen and Gerhard Saad from the Universit] at der Bundeswehr Hamburg and by Alexander Kreuzer, Hubert Kiechle and Wen-Ling Huang from the Universit] a ]t Hamburg. It was already the second Conference on Nearrings and Near?elds in Hamburg after the Conference on Nearrings and Near?elds at the same venue from July 30 to August 06, 1995. TheConferencewasattendedby57mathematiciansandmanyacc- panying persons who represented 16 countries from all ?ve continents. The ?rst of these conferences took place 35 years earlier in 1968 at the Mathematische Forschungsinstitut Oberwolfach in the Black Forest inGermany. Thiswasalsothesiteofthesecond, third, ?fthandeleventh conference in 1972, 1976, 1980 and 1989. The other twelve conferences held before the second Hamburg Conference took place in nine di?erent countries. For details about this and, moreover, for a general histo- cal overview of the development of the subject we refer to the article "On the beginnings and developments of near-ring theory" by Gerhard Betsch 3] in the proceedings of the 13th Conference in Fredericton, New Brunswick, Canada. Duringthelast?ftyyearsthetheoryofnearringsandrelatedalgebraic structures like near?elds, nearmodules, nearalgebras and seminearrings has developed into an extensive branch of algebra with its own features."

This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 "International Conference on Automorphic Forms and Number Theory," held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of: Borcherds products Congruences and Codes Jacobi forms Siegel and Hermitian modular forms Special values of L-series Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and Japan. The conference was hosted by the Sultan Qaboos University and the German University of Technology in Oman.

The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.

The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some advanced topics are included like derivatives of stochastic processes. It is an essential reference for researchers in mathematics, physics, and engineering.

The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics.
As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones.
Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.
- Considers both the algebraic and logical perspective within a common framework.
- Written by experts in the area.
- Easily accessible to graduate students and researchers from other fields.
- Results summarized in tables and diagrams to provide an overview of the area.
- Useful as a textbook for a course in algebraic logic, with exercises and suggested research directions.
- Provides a concise introduction to the subject and leads directly to research topics.
- The ideas from algebra and logic are developed hand-in-hand and the connections are shown in every level.

This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail.

This book deals with the dynamics of general systems such as foliations, groups and pseudogroups, systems which are closely related via the notion of holonomy. It concentrates on notions and results related to different ways of measuring complexity of systems under consideration. More precisely, it deals with different types of growth, entropies and dimensions of limiting objects. Problems related to the topics covered are provided throughout the book.

The field of generalized inverses has grown much since the appearance of the first edition in 1974, and is still growing. This book accounts for these developments while maintaining the informal and leisurely style of the first edition. New material has been added, including a chapter on applications, an appendix on the work of E.H. Moore, new exercises and applications.

This book is an introduction to the theory of complex manifolds. The authors¿ intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involving sheaves, coherence, and higher-dimensional cohomology have been completely avoided. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Nevertheless, deep results can be proved. The book can be used as a first introduction to several complex variables as well as a reference for the expert.

Clifford, or geometric algebra, provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. This book introduces the concepts and framework of Clifford algebra and provides a rich source of examples of how to work with this formalism.