Автор: Petr Hajek Название: Metamathematics of First-Order Arithmetic ISBN: 1107168414 ISBN-13(EAN): 9781107168411 Издательство: Cambridge Academ Рейтинг: Цена: 16743.00 р. 23918.00-30% Наличие на складе: Есть (1 шт.) Описание: This much-needed monograph on the metamathematics of first-order arithmetic pays particular attention to subsystems (fragments) of Peano arithmetic and gives the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness.
Автор: John Stillwell Название: Mathematics and Its History ISBN: 1461426324 ISBN-13(EAN): 9781461426325 Издательство: Springer Рейтинг: Цена: 7680.00 р. Наличие на складе: Поставка под заказ.
Описание: From a review of the second edition:"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations.
Автор: Friedman, Michael. Название: A history of folding in mathematics : ISBN: 331972486X ISBN-13(EAN): 9783319724867 Издательство: Springer Рейтинг: Цена: 30745.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised?Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete.In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.
Автор: Van Brummelen Glen Название: Heavenly Mathematics ISBN: 0691148929 ISBN-13(EAN): 9780691148922 Издательство: Wiley Рейтинг: Цена: 4744.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. "Heavenly Mathematics" traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions.
"Heavenly Mathematics" is illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.
Автор: Stillwell John Название: Reverse Mathematics: Proofs from the Inside Out ISBN: 0691177171 ISBN-13(EAN): 9780691177175 Издательство: Wiley Рейтинг: Цена: 3485.00 р. Наличие на складе: Поставка под заказ.
Описание:
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.
Автор: Stillwell John Название: Concise History of Mathematics for Philosophers . ISBN: 1108456235 ISBN-13(EAN): 9781108456234 Издательство: Cambridge Academ Рейтинг: Цена: 2851.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Presents an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. Ranges from ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous.
Автор: Hassan Tahiri Название: The Philosophers and Mathematics ISBN: 3030067122 ISBN-13(EAN): 9783030067120 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Поставка под заказ.
Описание: This book explores the unique relationship between two different approaches to understand the nature of knowledge, reality, and existence. It collects essays that examine the distinctive historical relationship between mathematics and philosophy. Readers learn what key philosophers throughout the ages thought about mathematics. This includes both thinkers who recognized the relevance of mathematics to their own work as well as those who chose to completely ignore its many achievements.The essays offer insight into the role that mathematics played in the formation of each included philosopher’s doctrine as well as the impact its remarkable expansion had on the philosophical systems each erected. Conversely, the authors also highlight the ways that philosophy contributed to the growth and transformation of mathematics. Throughout, significant historical examples help to illustrate these points in a vivid way. Mathematics has often been a favored interlocutor of philosophers and a major source of inspiration. This book is the outcome of an international conference held in honor of Roshdi Rashed, a renowned historian of mathematics. It provides researchers, students, and interested readers with remarkable insights into the history of an important relationship throughout the ages.
Автор: Russell Bertrand Название: Principles of Mathematics ISBN: 0415487412 ISBN-13(EAN): 9780415487412 Издательство: Taylor&Francis Рейтинг: Цена: 2908.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A precursor to Russell`s famous Principa Mathematica, this is one of the most original and comprehensive treatises on the logical foundation of mathematics available today.
Описание: This Unique Volume Summarizes With A Historical Perspective Several Of The Major Scientific Achievements Of Ludwig Faddeev, With A Foreword By Nobel Laureate C N Yang. The Volume That Spans Over Fifty Years Of Faddeev'S Career Begins Where He Started His Own Scientific Research, In The Subject Of Scattering Theory And The Three-Body Problem. It Then Continues To Describe Faddeev'S Contributions To Automorphic Functions, Followed By An Extensive Account Of His Many Fundamental Contributions To Quantum Field Theory Including His Original Article On Ghosts With Popov. Faddeev'S Contributions To Soliton Theory And Integrable Models Are Then Described, Followed By A Survey Of His Work On Quantum Groups. The Final Scientific Section Is Devoted To Faddeev'S Contemporary Research Including Articles On His Long-Term Interest In Constructing Knotted Solitons And Understanding Confinement. The Volume Concludes With His Personal View On Science And Mathematical Physics In Particular.
The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography--the science of sending secret messages. Most books about cryptography are organized historically, or around how codes and ciphers have been used, such as in government and military intelligence or bank transactions. Joshua Holden instead shows how mathematical principles underpin the ways that different codes and ciphers operate. Holden focuses on both code making and code breaking and he discusses the majority of ancient and modern ciphers currently known.
Holden begins by looking at substitution ciphers, built by substituting one letter or block of letters for another. Explaining one of the simplest and historically well-known ciphers, the Caesar cipher, Holden establishes the key mathematical idea behind the cipher and discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, including one developed by the Spartans, connections between ciphers and computer encryption, stream ciphers, and ciphers involving exponentiation. He also examines public-key ciphers, where the methods used to encrypt messages are public knowledge, and yet, intended recipients are still the only ones who are able to read the message. He concludes with a look at the future of ciphers and where cryptography might be headed. Only basic mathematics up to high school algebra is needed to understand and enjoy the book.
With a plethora of historical anecdotes and real-world examples, The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages.
Автор: Powers, Joseph M. (University of Notre Dame, Indiana) Sen, Mihir (University of Notre Dame, Indiana) Название: Mathematical Methods in Engineering ISBN: 1107037042 ISBN-13(EAN): 9781107037045 Издательство: Cambridge Academ Рейтинг: Цена: 10138.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is designed for engineering graduate students. It connects mathematics to a variety of methods used for engineering problems by walking the reader stepwise through examples that have been worked in detail, followed by numerous homework problems to reinforce learning and connect the subject matter to engineering applications.
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