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Zeta Functions, Topology and Quantum Physics
This volume focuses on various aspects of zeta functions: multiple zeta values, Ohno’s relations, the Riemann hypothesis, L-functions, polylogarithms, and their interplay with other disciplines. Eleven articles on recent advances are written by outstanding experts in the above-mentioned fields. Each article starts with an introductory survey leading to the exciting new research developments accomplished by the contributors.
Zeta Functions of Groups and Rings
This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations.
Walks on Ordinals and Their Characteristics
The analysis of the characteristics of walks on ordinals is a powerful new technique for building mathematical structures, developed by the author over the last twenty years. This is the first book-length exposition of this method. Particular emphasis is placed on applications which are presented in a unified and comprehensive manner and which stretch across several areas of mathematics such as set theory, combinatorics, general topology, functional analysis, and general algebra. The intended audience for this book are graduate students and researchers working in these areas interested in mastering and applying these methods.
Visualization, Explanation and Reasoning Styles in Mathematics
Contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy of mathematics that pays more attention to mathematical practice. Questions concerning concept-formation, understanding, heuristics, changes in style of reasoning, the role of analogies and diagrams etc.
Vector Semantics
Links the formal theory of word vectors to the cognitive theory of linguistics. The computational linguists and deep learning researchers who developed word vectors have relied primarily on the ever-increasing availability of large corpora and of computers with highly parallel GPU and TPU compute engines, and their focus is with endowing computers with natural language capabilities for practical applications such as machine translation or question answering. Cognitive linguists investigate natural language from the perspective of human cognition, the relation between language and thought, and questions about conceptual universals, relying primarily on in-depth investigation of language in use.
Vector Analysis for Computer Graphics
Vector Analysis for Computer Graphics provides a complete introduction to vector analysis, especially within the context of computer graphics. The author shows why vectors are useful and how it is possible to develop analytical skills in manipulating the vector algebra. Each topic covered is placed in the context of a practical application within computer graphics. The book is divided into eleven chapters covering the mathematical foundations of vector algebra and its application to lines, planes, intersections, rotating vectors, vector differentiation, projections, rendering and motion.
Vector Analysis for Computer Graphics
Divided into eleven chapters covering the history of vector analysis, linear equations, vector algebra, vector products, differentiating vector-valued functions, vector differential operators, tangent and normal vectors, straight lines, planes, intersections and rotating vectors.
Variations on Constants : Flow Analysis of Sequential and Parallel Programs
This monograph, a revised version of the author's habilitation thesis, focusses on optimal flow analysis of sequential and parallel programs. It studies algorithmic properties of various versions of the well-known constant-propagation problem. In order to come to grips with the variants considered, it combines techniques from different areas such as linear algebra, computable ring theory, abstract interpretation, program verification, complexity theory, etc. Combination of techniques is the key to further progress in automatic analysis and constant-propagation allows us to illustrate this point in a theoretical study.
Valued Fields
In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge acquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.
Using the Borsuk-Ulam Theorem : Lectures on Topological Methods in Combinatorics and Geometry
Matousek's lively little textbook now shows that Lovász' insight as well as beautiful work of many others (such as Vrecica and Zivaljevic, and Sarkaria) have opened up an exciting area of mathematics that connects combinatorics, graph theory, algebraic topology and discrete geometry.
Using Algebraic Geometry
In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gröbner bases and resultants.
Universal Algebra
Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science.
Unitals in Projective Planes
This clearly written text is the first book on unitals embedded in finite projective planes. Unitals are key structures in square order projective planes, and have connections with other structures in algebra. They provide a link between groups and geometries. There is a considerable number of research articles concerning unitals, and there also exist many open problems. This book is a thorough survey of the research literature on embedded unitals which collects this material in book form for the first time.
Understanding and Using Linear Programming
An introductory textbook of linear programming, written mainly for students of computer science and mathematics. Our guiding phrase is, "what every theoretical computer scientist should know about linear programming". The book is relatively concise, in order to allow the reader to focus on the basic ideas. For a number of topics commonly appearing in thicker books on the subject, we were seriously tempted to add them to the main text, but we decided to present them only very brie?y in a separate glossary. At the same time, we aim at covering the main results with complete proofs and in su?cient detail, in a way ready for presentation in class. One of the main focuses is applications of linear programming, both in practice and in theory.
Undergraduate Algebra
Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text.
Unconstrained Face Recognition
This volume provides a comprehensive view of unconstrained face recognition, especially face recognition from multiple still images and/or video sequences, assembling a collection of novel approaches able to recognize human faces under various unconstrained situations. The underlying basis of these approaches is that, unlike conventional face recognition algorithms, they exploit the inherent characteristics of the unconstrained situation and thus improve the recognition performance when compared with conventional algorithms. Unconstrained Face Recognition is accessible to a wide audience with an elementary level of linear algebra, probability and statistics, and signal processing.
Un invito allAlgebra = An Invitation to Algebra
The book offers a basic course in algebra for university students, structured according to the new regulations. Themes such as groups, rings and fields are first introduced through simple examples (as well as numbers, polynomials and permutations) and are subsequently discussed in depth in the second part of the book. It also deals with topics such as applications to cryptography, codes, computer science, also providing historical hints. The volume aims to offer an introduction to algebra in a schematic and easily understandable way.
Types for Proofs and Programs ; International Conference, TYPES 2007, Cividale des Friuli, Italy, May 2-5, 2007 Revised Selected Papers
The topic of this book was formal reasoning and computer programming based on type theory. Great importance was attached to languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certified software, formalization of mathematics and mathematics
Two Cultures : Essays in Honour of David Speiser
Editor Kim Williams has assembled a group of notes where scholars contribute essays inspired by their contact with Prof David Speiser. In honour of his eightieth birthday. Topics range from history of sciences to history of art, from architecture theory to music theory, from particle physics to the proliferation of nuclear weapons, to an essay on the very nature of interdisciplinary studies.
Two Algebraic Byways from Differential Equations : Gröbner Bases and Quivers
Presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types.Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line.
