Download or read book Inverse Semigroups written by Mark V. Lawson and published by World Scientific. This book was released on 1998 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: "this volume represents an outstanding contribution to the field. The resolute graduate student or mature researcher, alike, can find a wealth of directions for future work".Mathematical Reviews

Download or read book Wagner s Theory of Generalised Heaps written by Christopher D. Hollings and published by Springer. This book was released on 2017-09-09 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theories of V. V. Wagner (1908-1981) on abstractions of systems of binary relations are presented here within their historical and mathematical contexts. This book contains the first translation from Russian into English of a selection of Wagner’s papers, the ideas of which are connected to present-day mathematical research. Along with a translation of Wagner’s main work in this area, his 1953 paper ‘Theory of generalised heaps and generalised groups,’ the book also includes translations of three short precursor articles that provide additional context for his major work. Researchers and students interested in both algebra (in particular, heaps, semiheaps, generalised heaps, semigroups, and groups) and differential geometry will benefit from the techniques offered by these translations, owing to the natural connections between generalised heaps and generalised groups, and the role played by these concepts in differential geometry. This book gives examples from present-day mathematics where ideas related to Wagner’s have found fruitful applications.

Download or read book Emergence of the Theory of Lie Groups written by Thomas Hawkins and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.

Download or read book A History of Abstract Algebra written by Jeremy Gray and published by Springer. This book was released on 2018-08-07 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.

Download or read book Differential Geometry written by I. M. James and published by Elsevier. This book was released on 2014-05-16 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry contains all of Whitehead's published work on differential geometry, along with some papers on algebras. Most of these were written in the period 1929-1937, but a few later articles are included. The book begins with a list of Whitehead's works, in chronological order of writing as well as a biographical note by M. H. A. Newman and Barbara Whitehead, and a mathematical appreciation by John Milnor. This is followed by separate chapters on topics such as linear connections; a method of obtaining normal representations for a projective connection; representation of projective spaces; convex regions in the geometry of paths; locally homogeneous spaces in differential geometry; and the decomposition of an infinitesimal group. Also included are chapters on locally homogeneous spaces in differential geometry; Maurer's equations; linear associative algebras; an expression of Hopf's invariant as an integral; and normalizators of transformation groups.

Download or read book Geometry and Discrete Mathematics written by Benjamin Fine and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-09-24 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion. The idea behind the two books is to provide substantials for assessing more modern developments in mathematics and to present impressions which indicate that mathematics is a fascinating subject with many ties between the diverse mathematical disciplines. The present volume examines many of the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history. Contents Geometry and geometric ideas Isometries in Euclidean vector spaces and their classification in Rn The conic sections in the Euclidean plane Special groups of planar isometries Graph theory and platonic solids Linear fractional transformation and planar hyperbolic geometry Combinatorics and combinatorial problems Finite probability theory and Bayesian analysis Boolean lattices, Boolean algebras and Stone’s theorem

Download or read book Linear Geometry with Computer Graphics written by John Loustau and published by CRC Press. This book was released on 1992-12-16 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stressing the interplay between theory and its practice, this text presents the construction of linear models that satisfy geometric postulate systems and develops geometric topics in computer graphics. It includes a computer graphics utility library of specialized subroutines on a 3.5 disk, designed for use with Turbo PASCAL 4.0 (or later version) - an effective means of computer-aided instruction for writing graphics problems.;Providing instructors with maximum flexibility that allows for the mathematics or computer graphics sections to be taught independently, this book: reviews linear algebra and notation, focusing on ideas of geometric significance that are often omitted in general purpose linear algebra courses; develops symmetric bilinear forms through classical results, including the inertia theorem, Witt's cancellation theorem and the unitary diagonalization of symmetric matrices; examines the Klein Erlanger programm, constructing models of geometries, and studying associated transformation groups; clarifies how to construct geometries from groups, encompassing topological notions; and introduces topics in computer graphics, including geometric modeling, surface rendering and transformation groups.

Download or read book Great Moments in Mathematics After 1650 written by Howard Eves and published by American Mathematical Soc.. This book was released on 2020-07-31 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: What a splendid addition this is to the Dolciani Mathematical Exposition series! This second set of lectures on great moments in mathematics (after 1650) is a fascinating collection of pivotal points in the historical development of mathematics...The four lectures devoted to the liberation of geometry and algebra are of particular interest. The lectures should be required reading for all teachers of mathematics. —Herbert Fremont, The Mathematics Teacher Eves is never less than tantalizing and usually inspiring...each 'great moment' has detailed exercises following it, as these have been carefully chosen to illustrate the depth of the ideas in question. —C. W. Kilmister, The London Times, Higher Education Supplement As is usual with Eves' work, the books are well written and entertaining. They give an historical background to many of the best known mathematical results, and, in addition, provide interesting pieces of information about the mathematicians involved. Eves includes relevant exercises at the end of each chapter. These are a good source of different, interesting problems, and when combined with the material in the chapter, could form the basis for a mathematical project...Eves' book provides an interesting, well-written, and enjoyable account. You won't be disappointed. —David Parrott, The Australian Mathematics Teacher

Download or read book Continuous Symmetry written by William H. Barker and published by American Mathematical Soc.. This book was released on 2007 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental idea of geometry is that of symmetry. With that principle as the starting point, Barker and Howe begin an insightful and rewarding study of Euclidean geometry. The primary focus of the book is on transformations of the plane. The transformational point of view provides both a path for deeper understanding of traditional synthetic geometry and tools for providing proofs that spring from a consistent point of view. As a result, proofs become more comprehensible, as techniques can be used and reused in similar settings. The approach to the material is very concrete, with complete explanations of all the important ideas, including foundational background. The discussions of the nine-point circle and wallpaper groups are particular examples of how the strength of the transformational point of view and the care of the authors' exposition combine to give a remarkable presentation of topics in geometry. This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises.

Download or read book Introduction to Differential Geometry and Riemannian Geometry written by Erwin Kreyszig and published by University of Toronto Press. This book was released on 1968-12-15 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space and to n-dimensional Riemannian geometry. Based on Kreyszig's earlier book Differential Geometry, it is presented in a simple and understandable manner with many examples illustrating the ideas, methods, and results. Among the topics covered are vector and tensor algebra, the theory of surfaces, the formulae of Weingarten and Gauss, geodesics, mappings of surfaces and their applications, and global problems. A thorough investigation of Reimannian manifolds is made, including the theory of hypersurfaces. Interesting problems are provided and complete solutions are given at the end of the book together with a list of the more important formulae. Elementary calculus is the sole prerequisite for the understanding of this detailed and complete study in mathematics.

Download or read book The Legacy of Tatjana Afanassjewa written by Jos Uffink and published by Springer Nature. This book was released on 2020-11-28 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of essays that explore the life and works of Tatjana Afanassjewa (1876–1964), a Russian–Dutch physicist–mathematician. Readers will discover a scientist whose work on the foundations of thermodynamics significantly influenced the field itself as well as the philosophy of physics. This book highlights the philosophical consequences of her work in physics and mathematics and discusses historical aspects of her writings on the foundations of physics. In addition, it features English translations and critical reviews of key selections from her texts. First and foremost, the book highlights the numerous contributions that Afanassjewa made to the field. In particular, the authors examine her work on the foundations of thermodynamics and statistical physics, starting in the 1920s and extending to 1956, well after the untimely death of her husband in 1933. They also explore her almost entirely forgotten work on the didactics of mathematics. In addition, they discuss her influential collaboration with her husband, the Austrian physicist Paul Ehrenfest (1880–1933). The portrait that emerges is that of a highly original physicist and mathematician, whose legacy continues to influence scientists and philosophers today and whose lesser-known works deserve more attention than they have received. Readers will find a rich body of work that continues to this day to yield insights into the foundations of physics and mathematics.

Download or read book The Emergence of the American Mathematical Research Community 1876 1900 written by Karen Hunger Parshall and published by American Mathematical Soc.. This book was released on 1994 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cover -- Title page -- Contents -- Preface -- Acknowledgments -- Photograph and Figure Credits -- Chapter 1. An overview of American mathematics: 1776-1876 -- Chapter 2. A new departmental prototype: J.J. Sylvester and the Johns Hopkins University -- Chapter 3. Mathematics at Sylvester's Hopkins -- Chapter 4. German mathematics and the early mathematical career of Felix Klein -- Chapter 5. America's wanderlust generation -- Chapter 6. Changes on the horizon -- Chapter 7. The World's Columbian exposition of 1893 and the Chicago mathematical congress -- Chapter 8. Surveying mathematical landscapes: The Evanston colloquium lectures -- Chapter 9. Meeting the challenge: The University of Chicago and the American mathematical research community -- Chapter 10. Epilogue: Beyond the threshold: The American mathematical research community, 1900-1933 -- Bibliography -- Subject Index -- Back Cover

Download or read book Collected Mathematical Papers written by A. Ostrowski and published by Springer Science & Business Media. This book was released on 1984-01-01 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication was made possible through a bequest from my beloved late wife. by the author which United together in this present collection are those works have not previously appeared in book form. The following are excepted: Vorlesungen fiber Differential und Integralrechnung (Lectures on Differential and Integral Calculus) Vols 1-3, Birkhauser Verlag, Basel (1965-1968); Aufgabensammlung zur Infinitesimalrechnung (Exercises in Infinitesimal Calculus) Vols 1, 2a, 2b, and 3, Birkhauser Verlag, Basel (1967-1977); two issues from Memorial des Sciences on Conformal Mapping (written together with C. Gattegno), Gauthier-Villars, Paris (1949); Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York (1973); and Stu dien fiber den Schottkyschen Satz (Studies on Schottky's Theorem), Wepf & Co., Basel (1931). Where corrections have had to be implemented in the text of certain papers, references to these are made at the conclusion of each paper. In the few instances where this system does not, for technical reasons, seem appropriate, an asterisk in the page margin indicates wherever a correction is necessary and this is then given at the end of the paper. (There is one exception: the correc tions to the paper on page 561 are presented on page 722. The works are published in 6 volumes and are arranged under 16 topic headings. Within each heading, the papers are ordered chronologically according to the date of original publication."

Download or read book The Prehistory of Mathematical Structuralism written by Erich H. Reck and published by Oxford University Press. This book was released on 2020 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.

Download or read book Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences written by Ivor Grattan-Guiness and published by Routledge. This book was released on 2004-11-11 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

Download or read book From a Geometrical Point of View written by Jean-Pierre Marquis and published by Springer Science & Business Media. This book was released on 2008-11-20 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

Download or read book Structure and Geometry of Lie Groups written by Joachim Hilgert and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.