The Logic of Infinity PDF Download
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Author: Barnaby Sheppard
Publisher: Cambridge University Press
ISBN: 1107058317
Category : Mathematics
Languages : en
Pages : 498
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Book Description
This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.
Author: Barnaby Sheppard
Publisher: Cambridge University Press
ISBN: 1107058317
Category : Mathematics
Languages : en
Pages : 498
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Book Description
This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.
Author: Shaughan Lavine
Publisher: Harvard University Press
ISBN: 0674265335
Category : Mathematics
Languages : en
Pages : 262
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Book Description
An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical commentary on, the modern notion of infinity as formalized in axiomatic set theory . . . An amazingly readable [book] given the difficult subject matter. Most of all, it is an eminently sensible book. Anyone who wants to explore the deep issues surrounding the concept of infinity . . . will get a great deal of pleasure from it.” —Ian Stewart, New Scientist “How, in a finite world, does one obtain any knowledge about the infinite? Lavine argues that intuitions about the infinite derive from facts about the finite mathematics of indefinitely large size . . . The issues are delicate, but the writing is crisp and exciting, the arguments original. This book should interest readers whether philosophically, historically, or mathematically inclined, and large parts are within the grasp of the general reader. Highly recommended.” —D. V. Feldman, Choice
Author: Fedor Bogomolov
Publisher: Springer Science & Business Media
ISBN: 146146482X
Category : Mathematics
Languages : en
Pages : 324
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Book Description
This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.
Author: David Foster Wallace
Publisher: W. W. Norton & Company
ISBN: 0393339289
Category : Mathematics
Languages : en
Pages : 352
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Book Description
The period from the 5th to the 7th century AD was characterised by far-reaching structural changes that affected the entire west of the Roman Empire. This process used to be regarded by scholars aspart of the dissolution of Roman order, but in current discussions it is nowexamined more critically. The contributions to this volume of conference papers combine approaches from history and literature studies in order to review the changing forms and fields of the establishment of collective identities, and to analyse them in their mutual relationships.
Author: S. C. Malik
Publisher: New Age International
ISBN: 8122422772
Category : Functions of real variables
Languages : en
Pages : 24
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Book Description
Author: Charles Chapman Pugh
Publisher: Springer
ISBN: 3319177710
Category : Mathematics
Languages : en
Pages : 486
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Book Description
Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis. New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the undergraph approach of Burkill. Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini's theorem from Cavalieri’s Principle, and, in many cases, the ability to see an integral result from measure theory. The presentation includes Vitali’s Covering Lemma, density points — which are rarely treated in books at this level — and the almost everywhere differentiability of monotone functions. Several new exercises now join a collection of over 500 exercises that pose interesting challenges and introduce special topics to the student keen on mastering this beautiful subject.
Author: Jayant Burde
Publisher: Motilal Banarsidass
ISBN: 8120841689
Category : Mathematics
Languages : en
Pages : 208
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Book Description
This book explores the bizarre but fascinating world of infinity in different disciplines of knowledge; mathematics, science, philosophy and religion. It projects the views of eastern as well as western scholars. This world is not only mysterious but also treacherous and conceals many conundrums such as a multitude of infinities, the mystic's experience of the infinite, conception of God as absolute infinity. The author also discusses many paradoxes relating to space and time. It is interesting to discover that some eastern philosophies try to reconcile two opposite concepts of sunya (zero) and Ananta (the infinite). The author also ventures to address a difficult question: Does infinity exist as a physical reality?
Author: S. C. Malik
Publisher: New Age International
ISBN: 9788122403237
Category : Mathematics
Languages : en
Pages : 920
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Book Description
The Book Is Intended To Serve As A Text In Analysis By The Honours And Post-Graduate Students Of The Various Universities. Professional Or Those Preparing For Competitive Examinations Will Also Find This Book Useful.The Book Discusses The Theory From Its Very Beginning. The Foundations Have Been Laid Very Carefully And The Treatment Is Rigorous And On Modem Lines. It Opens With A Brief Outline Of The Essential Properties Of Rational Numbers And Using Dedekinds Cut, The Properties Of Real Numbers Are Established. This Foundation Supports The Subsequent Chapters: Topological Frame Work Real Sequences And Series, Continuity Differentiation, Functions Of Several Variables, Elementary And Implicit Functions, Riemann And Riemann-Stieltjes Integrals, Lebesgue Integrals, Surface, Double And Triple Integrals Are Discussed In Detail. Uniform Convergence, Power Series, Fourier Series, Improper Integrals Have Been Presented In As Simple And Lucid Manner As Possible And Fairly Large Number Solved Examples To Illustrate Various Types Have Been Introduced.As Per Need, In The Present Set Up, A Chapter On Metric Spaces Discussing Completeness, Compactness And Connectedness Of The Spaces Has Been Added. Finally Two Appendices Discussing Beta-Gamma Functions, And Cantors Theory Of Real Numbers Add Glory To The Contents Of The Book.
Author: H. M. Hubey
Publisher: World Scientific
ISBN: 9789810230814
Category : Mathematics
Languages : en
Pages : 550
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Book Description
CD-ROM consists of four directories: parametric plots, fractals, etc; nonlinear differential equations; fuzzy logics; and graphics files.
Author: Educart
Publisher: Educart
ISBN: 9360541141
Category :
Languages : en
Pages : 348
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Book Description
What You Get: Time Management ChartsSelf-evaluation ChartCompetency-based Q’sMarking Scheme Charts Educart ‘Maths’ Class 9 Strictly based on the latest CBSE Curriculum released on March 31st, 2023Simplified NCERT theory with diagram, flowcharts, bullet points and tablesCaution and Important Points to really work on common mistakes made during the examIncludes all New Pattern Q’s (objective+subjective), along with case-based examples in every chapterExtra practice questions from various CBSE sources such as DIKSHA platform and NCERT exemplars Why choose this book? You can find the simplified complete with diagrams, flowcharts, bullet points, and tablesBased on the revised CBSE pattern for competency-based questionsEvaluate your performance with the self-evaluation charts
