Proofs From The Book

Autore: Martin Aigner
Editore: Springer Science & Business Media
ISBN: 3662054124
Grandezza: 59,67 MB
Formato: PDF, ePub, Mobi
Vista: 500
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The mathematical heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background.

Proofs From The Book

Autore: Martin Aigner
Editore: Springer
ISBN: 3642010377
Grandezza: 59,26 MB
Formato: PDF, ePub, Docs
Vista: 6018
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Proofs From The Book

Autore: Martin Aigner
Editore: Springer Science & Business Media
ISBN: 3662223430
Grandezza: 17,55 MB
Formato: PDF, Kindle
Vista: 1051
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According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Discrete Mathematics

Autore: Martin Aigner
Editore: American Mathematical Soc.
ISBN: 9780821886151
Grandezza: 10,60 MB
Formato: PDF, ePub, Docs
Vista: 1599
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The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints andsolutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition ... This book is a well-written introduction to discrete mathematics and is highly recommended to every student ofmathematics and computer science as well as to teachers of these topics. --Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of theMAA for expository writing, and his book Proofs from the BOOK with Gunter M. Ziegler has been an international success with translations into 12 languages.

Reverse Mathematics

Autore: John Stillwell
Editore: Princeton University Press
ISBN: 1400889030
Grandezza: 70,47 MB
Formato: PDF
Vista: 889
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This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis—finding the “right axioms” to prove fundamental theorems—and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the “right axiom” to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.

Briefwechsel

Autore: Sigmund Freud
Editore:
ISBN: 9783205984566
Grandezza: 41,91 MB
Formato: PDF, ePub, Docs
Vista: 3120
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Introduction To Mathematical Proofs

Autore: Charles Roberts
Editore: CRC Press
ISBN: 9781420069563
Grandezza: 14,10 MB
Formato: PDF, Mobi
Vista: 7929
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Shows How to Read & Write Mathematical Proofs Ideal Foundation for More Advanced Mathematics Courses Introduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills necessary to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It will prepare them to succeed in more advanced mathematics courses, such as abstract algebra and geometry.

Ritualism Exposed A Protestant Catechism For The Times With Proofs From The Prayer Book Etc

Autore: RITUALISM.
Editore:
ISBN:
Grandezza: 20,98 MB
Formato: PDF, ePub, Docs
Vista: 8912
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Proofs Without Words

Autore: Roger B. Nelsen
Editore: MAA
ISBN: 9780883857007
Grandezza: 17,27 MB
Formato: PDF, Mobi
Vista: 7926
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Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

Proof Patterns

Autore: Mark Joshi
Editore: Springer
ISBN: 3319162500
Grandezza: 25,47 MB
Formato: PDF, ePub, Docs
Vista: 9902
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This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

Charming Proofs

Autore: Claudi Alsina
Editore: MAA
ISBN: 0883853485
Grandezza: 10,33 MB
Formato: PDF
Vista: 7420
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A collection of remarkable proofs that are exceptionally elegant, and thus invite the reader to enjoy the beauty of mathematics.

Fifty Plain Proofs From The Scriptures That Christ Will Personally Appear Again To Receive His Church And Reign With Her On Or Over The Earth Signed J D

Autore: J. D.
Editore:
ISBN:
Grandezza: 62,56 MB
Formato: PDF, Kindle
Vista: 8500
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A Course In Enumeration

Autore: Martin Aigner
Editore: Springer Science & Business Media
ISBN: 3540390359
Grandezza: 65,58 MB
Formato: PDF
Vista: 2721
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Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

The Shorter Catechism With Proofs From The Scriptures With Additional Scripture References

Autore: Assembly of Divines (England)
Editore:
ISBN:
Grandezza: 38,50 MB
Formato: PDF, ePub
Vista: 9209
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Woe To The Legislative Anarchs Or Proofs From The Laws Of The Land That The Radical Sweeping Reform Denounced By Mr Brougham Is The Only Reform With Which The Starving People Of England Ought To Be Satisfied

Autore: Carpenter (Political Writer)
Editore:
ISBN:
Grandezza: 52,50 MB
Formato: PDF, ePub, Mobi
Vista: 912
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Proofs Of The Prophets

Autore: Peter Terry
Editore: Lulu.com
ISBN: 143571346X
Grandezza: 53,36 MB
Formato: PDF, Kindle
Vista: 8618
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A description of forty proofs of prophethood derived from a close study of the Babi and Baha'i Writings, as well as the Sacred Texts of several other religious traditions.

Proofs And Fundamentals

Autore: Ethan D. Bloch
Editore: Springer Science & Business Media
ISBN: 9781441971272
Grandezza: 10,61 MB
Formato: PDF, ePub
Vista: 9713
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“Proofs and Fundamentals: A First Course in Abstract Mathematics” 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra and real analysis. This 3-part work carefully balances Proofs, Fundamentals, and Extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. New to the second edition: 1) A new section about the foundations of set theory has been added at the end of the chapter about sets. This section includes a very informal discussion of the Zermelo– Fraenkel Axioms for set theory. We do not make use of these axioms subsequently in the text, but it is valuable for any mathematician to be aware that an axiomatic basis for set theory exists. Also included in this new section is a slightly expanded discussion of the Axiom of Choice, and new discussion of Zorn's Lemma, which is used later in the text. 2) The chapter about the cardinality of sets has been rearranged and expanded. There is a new section at the start of the chapter that summarizes various properties of the set of natural numbers; these properties play important roles subsequently in the chapter. The sections on induction and recursion have been slightly expanded, and have been relocated to an earlier place in the chapter (following the new section), both because they are more concrete than the material found in the other sections of the chapter, and because ideas from the sections on induction and recursion are used in the other sections. Next comes the section on the cardinality of sets (which was originally the first section of the chapter); this section gained proofs of the Schroeder–Bernstein theorem and the Trichotomy Law for Sets, and lost most of the material about finite and countable sets, which has now been moved to a new section devoted to those two types of sets. The chapter concludes with the section on the cardinality of the number systems. 3) The chapter on the construction of the natural numbers, integers and rational numbers from the Peano Postulates was removed entirely. That material was originally included to provide the needed background about the number systems, particularly for the discussion of the cardinality of sets, but it was always somewhat out of place given the level and scope of this text. The background material about the natural numbers needed for the cardinality of sets has now been summarized in a new section at the start of that chapter, making the chapter both self-contained and more accessible than it previously was. 4) The section on families of sets has been thoroughly revised, with the focus being on families of sets in general, not necessarily thought of as indexed. 5) A new section about the convergence of sequences has been added to the chapter on selected topics. This new section, which treats a topic from real analysis, adds some diversity to the chapter, which had hitherto contained selected topics of only an algebraic or combinatorial nature. 6) A new section called ``You Are the Professor'' has been added to the end of the last chapter. This new section, which includes a number of attempted proofs taken from actual homework exercises submitted by students, offers the reader the opportunity to solidify her facility for writing proofs by critiquing these submissions as if she were the instructor for the course. 7) All known errors have been corrected. 8) Many minor adjustments of wording have been made throughout the text, with the hope of improving the exposition.

The Art Of Proof

Autore: Matthias Beck
Editore: Springer Science & Business Media
ISBN: 9781441970237
Grandezza: 53,42 MB
Formato: PDF, ePub, Docs
Vista: 5786
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The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.

The Nuts And Bolts Of Proofs

Autore: Antonella Cupillari
Editore: Academic Press
ISBN: 9780121994518
Grandezza: 60,88 MB
Formato: PDF, ePub
Vista: 5941
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This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments. * Successfully class-tested over a number of years * Index for easy reference * Extensive list of definitions and concepts * Updated biblography

Journey Into Mathematics

Autore: Joseph J. Rotman
Editore:
ISBN:
Grandezza: 72,74 MB
Formato: PDF, ePub, Docs
Vista: 4481
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Rotman, Joseph, Journey into Mathematics: The World of Proof Prompting readers to do mathematics, not merely read about it, this proactive book has users reading and writing proofs at the outset. Complete proofs are given from the start, and coverage begins with elementary mathematics to allow focus on the writing and reading of proofs without the distraction of absorbing new ideas simultaneously.KEY TOPICS:Contains material that is familiar to calculus readers (i.e., induction, binomial theorem, polygonal, using the Diophantine parametrization of the circle by rational functions to solve trigonometric identities, etc.), and engages readers throughout with interesting expositions using history, etymology, and humorous asides. Material is presented as a 'single story' to aid in the subjects progressive growth and development.For mathematicians.