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Author: Matthias Beck Publisher: Springer Science & Business Media ISBN: 1441970231 Category : Mathematics Languages : en Pages : 185
Book Description
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.
Author: Matthias Beck Publisher: Springer Science & Business Media ISBN: 1441970231 Category : Mathematics Languages : en Pages : 185
Book Description
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.
Author: Joel David Hamkins Publisher: MIT Press ISBN: 0262362562 Category : Mathematics Languages : en Pages : 132
Book Description
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.
Author: Arthur T. Benjamin Publisher: American Mathematical Society ISBN: 1470472597 Category : Mathematics Languages : en Pages : 210
Book Description
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.
Author: Rhea Myers Publisher: MIT Press ISBN: 1915103045 Category : Art Languages : en Pages : 322
Book Description
A beautifully produced anthology of crypto-artist, writer, and hacker Rhea Myers's pioneering blockchain art, along with a selection of her essays, reviews, and fictions. DAO? BTC? NFT? ETH? ART? WTF? HODL as OG crypto-artist, writer, and hacker Rhea Myers searches for faces in cryptographic hashes, follows a day in the life of a young shibe in the year 2032, and patiently explains why all art should be destructively uploaded to the blockchain. Now an acknowledged pioneer whose work has graced the auction room at Sotheby’s, Myers embarked on her first art projects focusing on blockchain tech in 2011, making her one of the first artists to engage in creative, speculative, and conceptual engagements with "the new internet." Proof of Work brings together annotated presentations of Myers’s blockchain artworks along with her essays, reviews, and fictions—a sustained critical encounter between the cultures and histories of the artworld and crypto-utopianism, technically accomplished but always generously demystifying and often mischievous. Her deep understanding of the technical history and debates around blockchain technology is complemented by a broader sense of the crypto movement and the artistic and political sensibilities that accompanied its ascendancy. Remodeling the tropes of conceptual art and net.art to explore what blockchain technology reveals about our concepts of value, culture, and currency, Myers’s work has become required viewing for anyone interested in the future of art, consensus, law, and collectivity.
Author: Lorenz Halbeisen Publisher: Springer Nature ISBN: 3030522792 Category : Mathematics Languages : en Pages : 236
Book Description
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.
Author: Joseph E. Aoun Publisher: MIT Press ISBN: 0262549859 Category : Education Languages : en Pages : 221
Book Description
A fresh look at a “robot-proof” education in the new age of generative AI. In 2017, Robot-Proof, the first edition, foresaw the advent of the AI economy and called for a new model of higher education designed to help human beings flourish alongside smart machines. That economy has arrived. Creative tasks that, seven years ago, seemed resistant to automation can now be performed with a simple prompt. As a result, we must now learn not only to be conversant with these technologies, but also to comprehend and deploy their outputs. In this revised and updated edition, Joseph Aoun rethinks the university’s mission for a world transformed by AI, advocating for the lifelong endeavor of a “robot-proof” education. Aoun puts forth a framework for a new curriculum, humanics, which integrates technological, data, and human literacies in an experiential setting, and he renews the call for universities to embrace lifelong learning through a social compact with government, employers, and learners themselves. Drawing on the latest developments and debates around generative AI, Robot-Proof is a blueprint for the university as a force for human reinvention in an era of technological change—an era in which we must constantly renegotiate the shifting boundaries between artificial intelligence and the capacities that remain uniquely human.
Author: Martin Aigner Publisher: Springer Science & Business Media ISBN: 3662223430 Category : Mathematics Languages : en Pages : 194
Book Description
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.
Author: Richard H. Hammack Publisher: ISBN: 9780989472111 Category : Mathematics Languages : en Pages : 314
Book Description
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.
Author: Yves Bertot Publisher: Springer Science & Business Media ISBN: 366207964X Category : Mathematics Languages : en Pages : 492
Book Description
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.
Author: Matthias Beck
Author: Matthias Beck
Author: Adele Yunck
Author: Joel David Hamkins
Author: Arthur T. Benjamin
Author: Rhea Myers
Author: Lorenz Halbeisen
Author: Joseph E. Aoun
Author: Martin Aigner
Author: Richard H. Hammack
Author: Yves Bertot