This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.

    This guide answers some of the questions of this complex but endlessly fascinating saga.

    It is more concise and easier to read than some, yet it covers the breadth of emergency medicine practice more comprehensively than others. The bottom line is that I like this book. Just as previous editions did, the seventh presents all of the most pertinent and up-to-date information in a well-organized format that is comprehensive yet easy to read. That and many of the attractive new features in this current edition will ensure its place on my bookshelf for years to come."--JAMAWith 418 contributors representing over 120 medical centers around the world, Tintinalli’s Emergency Medicine is the most practical and clinically rigorous reference of its kind. It covers everything from prehospital care, disaster preparedness, and basic resuscitative techniques, to all the major diseases requiring emergency treatment, such as pulmonary emergencies, renal and GU disorders, and hemophilia. This authoritative, in-depth coverage makes this classic text indispensible not only in emergency departments, but also for residents and practitioners when studying or preparing for any exam they may face.While continuing to provide the most current information for acute conditions, the Seventh Edition of Tintinalli’s Emergency Medicine has been substantially revised and updated to cover all of the conditions for which patients seek emergency department care in a concise and easy-to-read-manner.NEW Features• Full-color design with more figures and tables than ever• Reader-friendly chapter presentation makes it easy to find important material.• Updated tables covering drugs and important clinical information• Patient safety considerations and injury prevention are integrated into chapters, as appropriate• Total revision of the dermatology section enables diagnosis by lesion description and body area affected, and provides current treatment• Organ systems sections reorganized to reflect considerations for actual clinical practice.• New chapters: New adult chapters include Natural Disasters, Aneurysms of the Aorta and Major Arteries; Hip and Knee Pain, Aortic Dissection; Acute Urinary Retention; Subarachnoid Hemorrhage and Intracranial Bleeding; Clotting Disorders; Community –acquired Pneumonia and Noninfectious Pulmonary Infiltrates; Type I Diabetes; Type II Diabetes; Anemia; Tests of Hemostasis; Clotting Disorders; Head Injury in Adults and Children; the Transplant Patient; Grief, Death and Dying; and Legal Issues in Emergency Medicine. Twelve new pediatric chapters including The Diabetic Child, Hematologic-Oncologic Emergencies, Ear and Mastoids, Eye Problems in Infants and Children, Neck Masses, GI Bleeding, Nose and Sinuses, Urologic and Gynecologic Procedures in children, Renal emergencies in children, Behavioral and Psychiatric Disorders in children, Pediatric Procedures, Pediatric ECG Interpretation• Greater coverage of procedures throughout for the most common conditions seen in the emergency department.• Companion DVD features an additional 17 chapters, such as Hyperbaric Oxygen Therapy, Principles of Imaging, Prison Medicine, Military Medicine, The Violent Patient, Forensics, Wound Ballistics, and Drug Interactions.• Companion DVD also features videos and animations for teaching and learning performance of important procedures, especially Ultrasound-Guided Procedures

    Pure mathematics, the area of Bourbaki's work, seems on the surface to be an abstract field of human study with no direct connection with the real world. In reality, however, it is closely intertwined with the general culture that surrounds it. Major developments in mathematics have often followed important trends in popular culture; developments in mathematics have acted as harbingers of change in the surrounding human culture. The seeds of change, the beginnings of the revolution that swept the Western world in the early decades of the twentieth century — both in mathematics and in other areas — were sown late in the previous century. This is the story both of Bourbaki and the world that created him in that time. It is the story of an elaborate intellectual joke — because Bourbaki, one of the foremost mathematicians of his day — never existed.

    Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.

    Since then, Sylvia Nasar's celebrated biography A Beautiful Mind, the basis of a new major motion picture, has revealed the man. The Essential John Nash reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics--from Riemannian geometry and partial differential equations--in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949.From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness.In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography.The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from.

    This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

    Whether it is a visualization of the Catalan numbers or an explanation of how the Fibonacci numbers occur in nature, there is something in here to delight everyone. The diagrams and pictures, many of which are in color, make this book particularly appealing and fun. A few of the discussions may be confusing to those who are not adept mathematicians; those who are may be irked that certain facts are mentioned without an accompanying proof. Nonetheless, The Book of Numbers will succeed in infecting any reader with an enthusiasm for numbers.

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    He is regarded by many as the greatest manager ever, building three brilliant sides with players such as Charlton, Edwards, Law & Best. Originally written just two years before Busby's death, this book is now available with a new introduction.

    He has now abandoned his past. Through interviews with Barrett's family and friends, this book provides an account of the man and his illness.

    From Beethoven's connection to plumbing to why rotten eggs smell like sulfur, the technical explanations included in this scientific primer tackle 99 chemistry-related questions and provide answers designed to inform and entertain.

    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

    While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world inwhich we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics andengineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

    Reveals mathematics' great power as an alternative language for understanding things and explores such concepts as logic as a computing tool, digital versus analog processes and communication as information transmission.