Download or read book Limits Limits Everywhere written by David Applebaum and published by OUP Oxford. This book was released on 2012-03-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books of this type. It includes proofs of the irrationality of e and π, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject. A lot of material found in a standard university course on "real analysis" is covered and most of the mathematics is written in standard theorem-proof style. However, more details are given than is usually the case to help readers who find this style daunting. Both set theory and proof by induction are avoided in the interests of making the book accessible to a wider readership, but both of these topics are the subjects of appendices for those who are interested in them. And unlike most university texts at this level, topics that have featured in popular science books, such as the Riemann hypothesis, are introduced here. As a result, this book occupies a unique position between a popular mathematics book and a first year college or university text, and offers a relaxed introduction to a fascinating and important branch of mathematics.
Download or read book Limits Limits Everywhere written by David Applebaum and published by Oxford University Press. This book was released on 2012-03 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account of elementary real analysis positioned between a popular mathematics book and a first year college or university text. This book doesn't assume knowledge of calculus and, instead, the emphasis is on the application of analysis to number theory.
Download or read book Advanced Calculus Revised Edition written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Download or read book The Off Limits Rule written by Sarah Adams and published by . This book was released on 2020-12-13 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: I have found rock bottom. It's here, moving in with my older brother because I'm too broke to afford to live on my own. It's okay though, because we've always been close and I think I'm going to have fun living with him again.That is until I meet Cooper...Turns out, my brother has very strong opinions on the idea of me dating his best friend and is dead set against it. According to him, Cooper is everything I should stay away from: flirtatious, adventurous, non-committal, and freaking hot. (I added that last part because I feel like you need the whole picture.) My brother is right-I should stay away from Cooper James and his pretty blue eyes. He's the opposite of what I need right now.Nah-who am I kidding? I'm going for it.The Off Limits Rule is a closed door romance, perfect for readers who love lots of sizzle but no explicit content.
Download or read book Pushing Limits written by Ted Hill and published by American Mathematical Soc.. This book was released on 2017-04-03 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pushing Limits: From West Point to Berkeley and Beyond challenges the myth that mathematicians lead dull and ascetic lives. It recounts the unique odyssey of a noted mathematician who overcame military hurdles at West Point, Army Ranger School and the Vietnam War, and survived many civilian escapades—hitchhiking in third-world hotspots, fending off sharks in Bahamian reefs, and camping deep behind the forbidding Iron Curtain. From ultra-conservative West Point in the ’60s to ultra-radical Berkeley in the ’70s, and ultimately to genteel Georgia Tech in the ’80s, this is the tale of an academic career as noteworthy for its offbeat adventures as for its teaching and research accomplishments. It brings to life the struggles and risks underlying mathematical research, the unparalleled thrill of making scientific breakthroughs, and the joy of sharing those discoveries around the world. Hill's book is packed with energy, humor, and suspense, both physical and intellectual. Anyone who is curious about how one maverick mathematician thinks, who wants to relive the zanier side of the ’60s and ’70s, who wants an armchair journey into the third world, or who seeks an unconventional view of several of society's iconic institutions, will be drawn to this book.
Download or read book Calculus Reordered written by David M. Bressoud and published by Princeton University Press. This book was released on 2021-05-04 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends instead that the historical order--which follows first integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
Download or read book Counterexamples in Analysis written by Bernard R. Gelbaum and published by Courier Corporation. This book was released on 2012-07-12 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Download or read book The Gift of Beauty written by Stephen David Ross and published by State University of New York Press. This book was released on 1996-07-03 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ross explores the developments in Western thought, from Plato and Aristotle through Kant and Hegel, when art was separated from science and philosophy. At the heart of the project is a reexamination of the good, found in Plato as that which makes being possible, which gives authority to knowledge and beckons to art, preserved in Levinas as infinite responsibility. The idea of the good is interpreted as nature's abundance, giving beauty and truth as gifts, calling us to respond. It gives rise to an ethics of inclusion, expressed in art.
Download or read book The Lacan Tradition written by Lionel Bailly and published by Routledge. This book was released on 2018-04-09 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lacanian Tradition is unique among psychoanalytic schools in its influence upon academic fields such as literature, philosophy, cultural and critical studies. This book aims to make Lacan's ideas accessible and relevant also to mainstream psychoanalysts, and to showcase developments in Lacanian thinking since his death in 1981. The volume highlights the clinical usefulness of such concepts as the paternal metaphor, the formula of fantasy, psychic structure, the central role of desire and the interlinking of the individual subject in the matrix of the Other. While these themes are woven through all the papers, each is a highly individual reflection upon some aspect of Lacanian theory, practice or history.
Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Download or read book Life Within Limits written by Michael Jackson and published by Duke University Press. This book was released on 2011-02-16 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of life satisfaction, happiness, and wellbeing in the first world and third world.
Download or read book A Sequential Introduction To Real Analysis written by J Martin Speight and published by World Scientific Publishing Company. This book was released on 2015-10-29 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time.This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course.
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1967 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The World Process Or The Origin and Evolution of Life Mind Thought and Language Out of the One Element of Existence written by Mabel P. Malter and published by . This book was released on 1914 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Analysis written by Corey M. Dunn and published by CRC Press. This book was released on 2017-06-26 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Analysis is an ideal text for a one semester course on analysis. The book covers standard material on the real numbers, sequences, continuity, differentiation, and series, and includes an introduction to proof. The author has endeavored to write this book entirely from the student’s perspective: there is enough rigor to challenge even the best students in the class, but also enough explanation and detail to meet the needs of a struggling student. From the Author to the student: "I vividly recall sitting in an Analysis class and asking myself, ‘What is all of this for?’ or ‘I don’t have any idea what’s going on.’ This book is designed to help the student who finds themselves asking the same sorts of questions, but will also challenge the brightest students." Chapter 1 is a basic introduction to logic and proofs. Informal summaries of the idea of proof provided before each result, and before a solution to a practice problem. Every chapter begins with a short summary, followed by a brief abstract of each section. Each section ends with a concise and referenced summary of the material which is designed to give the student a "big picture" idea of each section. There is a brief and non-technical summary of the goals of a proof or solution for each of the results and practice problems in this book, which are clearly marked as "Idea of proof," or as "Methodology", followed by a clearly marked formal proof or solution. Many references to previous definitions and results. A "Troubleshooting Guide" appears at the end of each chapter that answers common questions.
Download or read book Feversong written by Karen Marie Moning and published by Dell. This book was released on 2017-10-17 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: NEW YORK TIMES BESTSELLER • MacKayla Lane and Jericho Barrons return in the epic conclusion to the pulse-pounding Fever series, where a world thrown into chaos grows more treacherous at every turn. As Mac, Barrons, Ryodan, and Jada struggle to restore control, enemies become allies, right and wrong cease to exist, and the lines between life and death, lust and love, disappear completely. Black holes loom menacingly over Dublin, threatening to destroy the earth, yet the greatest danger is the one MacKayla Lane has unleashed from within: The Sinsar Dubh—a sentient book of unthinkable evil—has possessed her body and will stop at nothing in its insatiable quest for power. The fate of Man and Fae rests on destroying the book and recovering the long-lost Song of Making, the sole magic that can repair the fragile fabric of the earth. But to achieve these aims, sidhe-seers, the Nine, Seelie, and Unseelie must form unlikely alliances and make heart-wrenching choices. For Barrons and Jada, this means finding the Seelie queen, who alone can wield the mysterious song, negotiating with a lethal Unseelie prince hell-bent on ruling the Fae courts, and figuring out how to destroy the Sinsar Dubh while keeping Mac alive. This time, there’s no gain without sacrifice, no pursuit without risk, no victory without irrevocable loss. In the battle for Mac’s soul, every decision exacts a tremendous price. Look for all of Karen Marie Moning’s sensational Fever novels: DARKFEVER | BLOODFEVER | FAEFEVER | DREAMFEVER | SHADOWFEVER | ICED | BURNED | FEVERBORN | FEVERSONG Praise for Feversong “Bold and brilliantly layered, deeply emotive and all-consuming, the story curves full circle as Mac and Dani try to save the world. . . . Fans of the series . . . will love every moment, every page. As one now expects from the incredibly talented [Karen Marie] Moning, gasp-inducing surprises await.”—USA Today “Heart-pounding.”—Entertainment Weekly “Epic.”—New Orleans Gambit “Moning is one of the best. . . . [Feversong is] an exciting, pulse-pounding action-filled adventure that at times is dark and terrifying, and other times gloriously happy and romantic. . . . Another fantastic story.”—The Reading Cafe “[Feversong is an] epic ending to an epic series. . . . It’s all feels.”—The Review Loft
Download or read book Undergraduate Analysis written by Aisling McCluskey and published by Oxford University Press. This book was released on 2018 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis underpins calculus, much as calculus underpins virtually all mathematical sciences. A sound understanding of analysis' results and techniques is therefore valuable for a wide range of disciplines both within mathematics itself and beyond its traditional boundaries. This text seeks to develop such an understanding for undergraduate students on mathematics and mathematically related programmes. Keenly aware of contemporary students' diversity of motivation, background knowledge and time pressures, it consistently strives to blend beneficial aspects of the workbook, the formal teaching text, and the informal and intuitive tutorial discussion. The authors devote ample space and time for development of confidence in handling the fundamental ideas of the topic. They also focus on learning through doing, presenting a comprehensive range of examples and exercises, some worked through in full detail, some supported by sketch solutions and hints, some left open to the reader's initiative. Without undervaluing the absolute necessity of secure logical argument, they legitimise the use of informal, heuristic, even imprecise initial explorations of problems aimed at deciding how to tackle them. In this respect they authors create an atmosphere like that of an apprenticeship, in which the trainee analyst can look over the shoulder of the experienced practitioner.
