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The Italian mathematician Mario Pieri (1860¿1913) played a major role in the development of algebraic geometry and foundations of mathematics around the turn of the twentieth century. This volume is the second in a series intended to make Pieri¿s research in diverse fields¿mathematical logic and philosophy of mathematics, foundations of projective, inversive, and elementary geometry, algebraic and differential geometry, and vector analysis¿accessible to today¿s scholars and to assess its importance (yet little recognized) in historical and modern contexts. The Legacy of Mario Pieri in Foundations and Philosophy of Mathematics examines Pieri¿s underlying philosophy of mathematics and his research goals, highlighting one of his most influential achievements, his axiomatizations of projective and elementary geometry. Its chapters include three of Pieri¿s pioneering works, translated by the authors and appearing in English for the first time, as well as an analysis of the role of this research in its larger context. Together, these translations and the accompanying interpretation accurately capture Pieri¿s expository style, philosophical perspective, and his foundational research, which has influenced generations.With an excellent index, exhaustive references, and engaging discussions that reveal Pieri¿s work in its historical context, this volume will appeal to scholars and advanced students interested in the history and philosophy of mathematics and logic, as well as readers with a general knowledge of geometry at the intermediate level.A list of errata can be found on the author Smith¿s personal webpage.

Concisely written, gentle introduction to graph theory suitable as a textbook or for self-studyGraph-theoretic applications from diverse fields (computer science, engineering, chemistry, management science)2nd ed.

Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato's unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone's representation of unitary semigroups.

Various general techniques have been developed for control and systems problems, many of which involve indirect methods. Because these indirect methods are not always effective, alternative approaches using direct methods are of particular interest and relevance given the advances of computing in recent years.The focus of this book, unique in the literature, is on direct methods, which are concerned with finding actual solutions to problems in control and systems, often algorithmic in nature. Throughout the work, deterministic and stochastic problems are examined from a unified perspective and with considerable rigor. Emphasis is placed on the theoretical basis of the methods and their potential utility in a broad range of control and systems problems.The book is an excellent reference for graduate students, researchers, applied mathematicians, and control engineers and may be used as a textbook for a graduate course or seminar on direct methods in control.  

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration.

Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.

This monograph presents a groundbreaking scholarly treatment of the German mathematician Jost Bürgi's original work on logarithms, Arithmetische und Geometrische Progreß Tabulen. It provides the first-ever English translation of Bürgi's text and illuminates his role in the development of the conception of logarithms, for which John Napier is traditionally given priority. High-resolution scans of each page of the his handwritten text are reproduced for the reader and as a means of preserving an important work for which there are very few surviving copies.The book begins with a brief biography of Bürgi to familiarize readers with his life and work, as well as to offer an historical context in which to explore his contributions. The second chapter then describes the extant copies of the Arithmetische und Geometrische Progreß Tabulen, with a detailed description of the copy that is the focus of this book, the 1620 "Graz manuscript". A complete facsimile of the text is included in the next chapter, along with a corresponding transcription and an English translation; a transcription of a second version of the manuscript (the "Gdansk manuscript") is included alongside that of the Graz edition so that readers can easily and closely examine the differences between the two. The final chapter considers two important questions about Bürgi's work, such as who was the copyist of the Graz manuscript and what the relationship is between the Graz and Gdansk versions. Appendices are also included that contain a timeline of Bürgi's life, the underlying concept of Napier's construction of logarithms, and scans of all 58 sheets of the tables from Bürgi's text.Anyone with an appreciation for the history of mathematics will find this book to be an insightful and interesting look at an important and often overlooked work. It will also be a valuable resource for undergraduates taking courses in the history of mathematics, researchers of the history of mathematics, and professors of mathematics education who wish to incorporate historical context into their teaching.

The sixth edition of the Atlas of Hypertension builds on the tremendous success of earlier editions, but significant revision has been done since the last editionΓÇöa third of the chapters are new, and more than half of the chapters are written by new authors. Expanded topics include home blood pressure; secondary hypertension; information on newer agents such as nebivolol, aliskiren, and new vasopeptidase inhibitors; the possible role and pharmacology of renin inhibition; and American and European guidelines for antihypertensive treatment and their influence on physician practice. The striking, four-color format combined with the breadth of information it contains make this Atlas an invaluable resource for physicians, cardiologists, and all professionals involved in the study and treatment of hypertension.

In a broad sense Design Science is the fail to perceive the system of organiza grammar of a language of images rather tion determining the form of such than of words.

Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance and engineering.

Includes problem-solving tactics and practical test-taking techniques that provide enrichment and preparation for various math competitions. This title provides comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry.

A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra.

It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions.

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations.

The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups.

This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions.

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory.

Covers such topics as: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities.

The Collected Papers of Raoul Bott are contained in five volumes, with each volume covering a different subject and each representing approximately a decade of Bott's work.

Examines a nonlinear system of parabolic partial differential equations (PDE) arising in mathematical biology and statistical mechanics. This book describes the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, and quantized blowup mechanism based on several PDE techniques.

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas. This title contains articles which explore various aspects of the parallel worlds of function fields and number fields, ranging from Arakelov geometry to Drinfeld modules, and t-motives.

The theory of the top, originally made public as a lecture by Felix Klein at the University of Goettingen in 1895, was improved by Klein's collaboration with Arnold Sommerfeld. This volume provides a thorough and insightful account and includes recent advances.

The theory and applications of finite tight frames has developed rapidly in recent years. This text offers an overview of the field and discusses future research directions. It includes exercises, MATLAB examples for classroom use, and numerous illustrations.

This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group.The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions.The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. Thereare four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology. This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time.¿

Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. No knowledge of measure theory is presumed.

* Uses a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn* Self-contained and standalone text that may be used in the classroom, for an online course, for self-study, as a reference* Using MAPLE allows the reader to easily and quickly change the models and parameters

This book presents the principles of functional analysis. It includes recent simple proofs of the isoperimetric and the Faber-Krahn inequality, an elementary introduction to capacity theory, and a new perspective on the history of functional analysis.