This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831.
This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.
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.
Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.
This book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d’Alembert and Euler; Fourier’s solutions to the heat equation and the contribution of Kovalevskaya; the work of Euler, Gauss, Kummer, Riemann, and Poincaré on the hypergeometric equation; Green’s functions, the Dirichlet principle, and Schwarz’s solution of the Dirichlet problem; minimal surfaces; the telegraphists’ equation and Thomson’s successful design of the trans-Atlantic cable; Riemann’s paper on shock waves; the geometrical interpretation of mechanics; and aspects of the study of the calculus of variations from the problems of the catenary and the brachistochrone to attempts at a rigorous theory by Weierstrass, Kneser, and Hilbert. Three final chapters look at how the theory of partial differential equations stood around 1900, as they were treated by Picard and Hadamard. There are also extensive, new translations of original papers by Cauchy, Riemann, Schwarz, Darboux, and Picard. The first book to cover the history of differential equations and the calculus of variations in such breadth and detail, it will appeal to anyone with an interest in the field. Beyond secondary school mathematics and physics, a course in mathematical analysis is the only prerequisite to fully appreciate its contents. Based on a course for third-year university students, the book contains numerous historical and mathematical exercises, offers extensive advice to the student on how to write essays, and can easily be used in whole or in part as a course in the history of mathematics. Several appendices help make the book self-contained and suitable for self-study.
This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis.
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831.
Make quick and accurate diagnoses and treatment decisions at the point of care with this bestselling guide! The 5-Minute Clinical Consult 2017 is a practical and useful resource for primary care clinicians, as well as those in family medicine, emergency medicine, nursing, and pediatrics. Using a three-column, bulleted format, the print edition provides rapid access to diagnosis, treatment, medications, follow-up, and associated factors for more than 800 diseases and conditions, plus 225 diagnostic and therapeutic algorithms.
The 5-Minute Clinical Consult provides rapid-access information on the diagnosis, treatment, medications, follow-up, and associated conditions of more than 700 medical conditions. Organized alphabetically by diagnosis, this best-selling clinical reference continues to present brief, bulleted points on disease topics in a consistent templated format.
The 5-Minute Clinical Consult Premium 2015 helps physicians and healthcare professionals provide the best patient care by delivering quick answers you can trust where and when you need it most. The 5-Minute Clinical Consult Premium 2015 provides seamless access to www.5minuteconsult.com, where you,,ll find:2,000+ commonly encountered diseases and disorders Differential diagnosis support from an accessible, targeted search Treatment and diagnostic algorithms More than 1,250 customizable patient handouts from the AAFP ICD9, ICD10 and Snomed Codes Procedural and physical therapy videos Over 2,250 diagnostic images for over 840 topics ,Point-of-Care CME and CNE The 5-Minute Clinical Consult Premium 2015 provides the luxury of a traditional print product and delivers quick access the continually updated online content an ideal resource when you,,re treating patients. Written by esteemed internal medicine and family medicine practitioners and published by the leading publisher in medical content, The 5-Minute Clinical Consult Premium 2015: 1-Year Enhanced Online & Mobile Access + Print, 23e includes 1-Year access to 5minuteconsult.com. 5minuteconsult.com is the quickest, most affordable, evidence-based workflow tool at the point-of-care. What an incredible program for any health care provider involved in diagnosing and treating patients! Awesome set up, great resource. current subscriber to www.5minuteconsult.com.
The 5-Minute Clinical Consult Standard 2016, 24th Edition, provides rapid-access in a quick-reference print format. It delivers diagnosis, treatment, medications, follow-up, and associated factors for a broad range of diseases and conditions. Organized alphabetically by diagnosis, this best-selling clinical reference continues to present brief, bulleted information on disease topics in a consistent and reader-friendly three-column format. The 5-Minute Clinical Consult Standard 2016, 24th Edition provides: 650+ commonly encountered diseases and disorders 150+ Treatment and diagnostic algorithms ICD10 Codes Current evidence-based designations highlighted in each topic A revised and updated Health Maintenance section The Health Maintenance 1-page summaries, based on the US Preventive Services Task Force recommendations
Make the most effective diagnostic and therapeutic decisions in the least time! A best seller for over 25 years, The5-Minute Clinical Consult 2018 is a practical and useful resource for clinicians in primary care, family medicine, emergency medicine, nursing, and pediatrics. It provides rapid access to guidance on diagnosis, treatment, medications, follow-up, and associated factors for more than 540 diseases and conditions. The5-Minute Clinical Consult 2018 is designed to deliver maximum clinical confidence as efficiently as possible...allowing you to focus your valuable time on giving your patients the best possible care. Find the answers you need quickly thanks to an intuitive, at-a-glance format, with concise, bulleted text; hundreds of diagnostic and therapeutic algorithms; ICD-10 codes, DSM-5 criteria; and much more. Make confident decisions aided by current evidence-based designations in each topic. Written by esteemed internal medicine and family medicine practitioners and published by the leading publisher in medical content, The 5-Minute Clinical Consult 2018, 26th Edition includes a Free Trial to 5MinuteConsult.com.
From the difficult to diagnose to the difficult to treat, Manson’s Tropical Diseases prepares you to effectively handle whatever your patients may have contracted. Featuring an internationally recognized editorial team, global contributors, and expert authors, this revised and updated medical reference book provides you with the latest coverage on parasitic and infectious diseases from around the world. Consult this title on your favorite e-reader, conduct rapid searches, and adjust font sizes for optimal readability. Incorporate the latest therapies into your practice, such as recently approved drugs and new treatment options. Find what you need easily and apply it quickly with highlighted key information, convenient boxes and tables, extensive cross-referencing, and clinical management diagrams. Make the most accurate Tropical Disease diagnoses through a completely redesigned and modernized format, which includes full-color images throughout. Apply the latest treatment strategies for HIV/AIDS, tropical neurology, malaria, and much more. Put the latest international expertise to work for you and your patients with new chapters covering Global Health; Global Health Governance and Tropical Diseases; Non-communicable Diseases; Obesity in the Tropics; and Emergency and Intensive Care Medicine in Resource-poor Settings. See which diseases are most prevalent in specific areas of the tropics through a new index of diseases by country, as well as online-only maps that provide additional detail. Better understand the variations in treatment approaches across the globe.
This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
This is an undergraduate textbook that reveals the intricacies of geometry. The approach used is that a geometry is a space together with a set of transformations of that space (as argued by Klein in his Erlangen programme). The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case the key results are explained carefully, and the relationships between the geometries are discussed. This richly illustrated and clearly written text includes full solutions to over 200 problems, and is suitable both for undergraduate courses on geometry and as a resource for self study.
David Hilbert was arguably the leading mathematician of his generation. He was among the few mathematicians who could reshape mathematics, and was able to because he brought together an impressive technical power and mastery of detail with a vision of where the subject was going and how it should get there. This was the unique combination which he brought to the setting of his famous 23 Problems. Few problems in mathematics have the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving individual ones such as Fermat's last theorem, and several remain unsolved including the Riemann hypotheses, which has eluded all the great minds of this century. A hundred years on, it is timely to take a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this fascinating new book, Jeremy Gray and David Rowe consider what has made this the pre-eminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics. The book is written in a clear and lively manner and will appeal both to the general reader with an interest in mathematics and to mathematicians themselves.
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