The Art Of Proof

The Art Of Proof Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of The Art Of Proof book. This book definitely worth reading, it is an incredibly well-written.

The Art of Proof

Matthias Beck,Ross Geoghegan
The Art of Proof Book PDF

Author : Matthias Beck,Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 182 pages
File Size : 49,7 Mb
Release : 2010-08-17
Category : Mathematics
ISBN : 9781441970237

Get Book

The Art of Proof by Matthias Beck,Ross Geoghegan Pdf

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.

Proof and the Art of Mathematics

Joel David Hamkins
Proof and the Art of Mathematics Book PDF

Author : Joel David Hamkins
Publisher : MIT Press
Page : 132 pages
File Size : 49,6 Mb
Release : 2021-02-23
Category : Mathematics
ISBN : 9780262362566

Get Book

Proof and the Art of Mathematics by Joel David Hamkins Pdf

How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.

Book of Proof

Richard H. Hammack
Book of Proof Book PDF

Author : Richard H. Hammack
Publisher : Unknown
Page : 314 pages
File Size : 54,5 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 0989472116

Get Book

Book of Proof by Richard H. Hammack Pdf

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.

Proofs that Really Count

Arthur T. Benjamin,Jennifer J. Quinn
Proofs that Really Count Book PDF

Author : Arthur T. Benjamin,Jennifer J. Quinn
Publisher : American Mathematical Society
Page : 210 pages
File Size : 54,9 Mb
Release : 2022-09-21
Category : Mathematics
ISBN : 9781470472597

Get Book

Proofs that Really Count by Arthur T. Benjamin,Jennifer J. Quinn Pdf

Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.

Proofs from THE BOOK

Martin Aigner,Günter M. Ziegler
Proofs from THE BOOK Book PDF

Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 40,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437

Get Book

Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf

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.

Gödel's Theorems and Zermelo's Axioms

Lorenz Halbeisen,Regula Krapf
G del s Theorems and Zermelo s Axioms Book PDF

Author : Lorenz Halbeisen,Regula Krapf
Publisher : Springer Nature
Page : 236 pages
File Size : 51,7 Mb
Release : 2020-10-16
Category : Mathematics
ISBN : 9783030522797

Get Book

Gödel's Theorems and Zermelo's Axioms by Lorenz Halbeisen,Regula Krapf Pdf

This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.

How to Prove It

Daniel J. Velleman
How to Prove It Book PDF

Author : Daniel J. Velleman
Publisher : Cambridge University Press
Page : 401 pages
File Size : 55,6 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780521861243

Get Book

How to Prove It by Daniel J. Velleman Pdf

This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.

The Meaning of Proofs

Gabriele Lolli
The Meaning of Proofs Book PDF

Author : Gabriele Lolli
Publisher : MIT Press
Page : 177 pages
File Size : 47,7 Mb
Release : 2022-09-27
Category : Mathematics
ISBN : 9780262371049

Get Book

The Meaning of Proofs by Gabriele Lolli Pdf

Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.

99 Variations on a Proof

Philip Ording
99 Variations on a Proof Book PDF

Author : Philip Ording
Publisher : Princeton University Press
Page : 272 pages
File Size : 55,6 Mb
Release : 2021-10-19
Category : Mathematics
ISBN : 9780691218977

Get Book

99 Variations on a Proof by Philip Ording Pdf

An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

Principia Mathematica

Alfred North Whitehead,Bertrand Russell
Principia Mathematica Book PDF

Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 50,5 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X

Get Book

Principia Mathematica by Alfred North Whitehead,Bertrand Russell Pdf

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

The Art of Proving Binomial Identities

Michael Z. Spivey
The Art of Proving Binomial Identities Book PDF

Author : Michael Z. Spivey
Publisher : CRC Press
Page : 231 pages
File Size : 47,5 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9781351215800

Get Book

The Art of Proving Binomial Identities by Michael Z. Spivey Pdf

The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton’s binomial series), differentiation (Leibniz’s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.

Interactive Theorem Proving and Program Development

Yves Bertot,Pierre Castéran
Interactive Theorem Proving and Program Development Book PDF

Author : Yves Bertot,Pierre Castéran
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 51,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662079645

Get Book

Interactive Theorem Proving and Program Development by Yves Bertot,Pierre Castéran Pdf

A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.

Computing the Continuous Discretely

Matthias Beck,Sinai Robins
Computing the Continuous Discretely Book PDF

Author : Matthias Beck,Sinai Robins
Publisher : Springer
Page : 285 pages
File Size : 42,9 Mb
Release : 2015-11-14
Category : Mathematics
ISBN : 9781493929696

Get Book

Computing the Continuous Discretely by Matthias Beck,Sinai Robins Pdf

This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE

The Art and Craft of Problem Solving

Paul Zeitz
The Art and Craft of Problem Solving Book PDF

Author : Paul Zeitz
Publisher : John Wiley & Sons
Page : 389 pages
File Size : 40,5 Mb
Release : 2017
Category : Problem solving
ISBN : 9781119239901

Get Book

The Art and Craft of Problem Solving by Paul Zeitz Pdf

This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.

Q.E.D.

Anonim
Q E D Book PDF

Author : Anonim
Publisher : Bloomsbury Publishing USA
Page : 65 pages
File Size : 47,7 Mb
Release : 2004-05-01
Category : Mathematics
ISBN : 9780802714312

Get Book

Q.E.D. by Anonim Pdf

Q.E.D. presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and find out how slicing cones helped save a city and put a man on the moon.