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Mathematics in the Age of the Turing Machine
Mathematical models and algorithms rule the quantitative world. Without applied mathematics, we would be bereft of Shor’s factorization algorithm for quantum com-puters, Yang-Mills theories of strong interactions in physics, invisibility cloaks, Radon transforms for medical imaging, models of epidemiology, risk analysis in insurance, stochastic pricing models of financial derivatives, RSA encryption of sensitive data, Navier-Stokes modeling of fluids, and models of climate change. Without it, entire fields of engineering from Control Engineering to Operations Research would close their doors. The early icon of mathematical computing, Von Neumann, divided his final years between meteorology and hydrogen bomb calculations. Today, applications fuel the economy: in 2011 rankings, the first five of the “10 best jobs” are math or computer related: software engineer, mathematician, actuary, statistician, and computer systems analys.
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Matrix Analysis and Algorithms
The book contains an introduction to matrix analysis, and to the basic algorithms of numerical linear algebra. Further results can be found in many text books. The book of Horn and Johnson is an excellent reference for theoretical results about matrix analysis. The subject of linear algebra, and matrix analysis in particular, is treated in an original and illuminating fashion in [Lax97]. For a general introduction to the subject of numerical linear algebra we recommend the book by Trefethen and Bau; more theoretical treatments of the subject can be found in Demmel, Golub and Van Loan and in Stoer and Bulirsch. Higham's book contains a wealth of information about stability and the effect of rounding errors in numerical algorithms; it is this source that we used for almost all theorems we state concerning backward error analysis. The book of Saad covers the subject of iterative methods for linear systems. The symmetric eigenvalue problem is analysed in Parlett.
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Metamath: A Computer Language for Pure Mathematics
Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs at a very detailed level. The Metamath language incorporates no mathematics per se but treats all mathematical statements as mere sequences of symbols. You provide Metamath with certain special sequences (axioms) that tell it what rules of inference are allowed. Metamath is not limited to any specific field of mathematics. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and I believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor.
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Академические письмо. От исследования к тесту
В учебнике излагаются теоретические основы методологии исследования, описаны стандарты изложения результатов исследования и оформления академических текстов, приводятся практические рекомендации по написанию научных работ. Каждая глава снабжена практикумом, содержащим разнообразные задания по каждому разделу темы.
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Adventurous math for the playground crowd
How do you want your child to feel about math? Confident, curious and deeply connected? Then Moebius Noodles is for you. It offers advanced math activities to fit your child’s personality, interests, and needs.Can you enjoy playful math with your child? Yes! The book shows you how to go beyond your own math limits and anxieties to do so. It opens the door to a supportive online community that will answer your questions and give you ideas along the way.Learn how you can create an immersive rich math environment for your baby. Find out ways to help your toddler discover deep math in everyday experiences. Play games that will develop your child’s sense of happy familiarity with mathematics.A five-year-old once asked us, “Who makes math?” and jumped for joy at the answer, “You!” Moebius Noodles helps you take small, immediate steps toward the sense of mathematical power.You and your child can make math your own. Together, make your own math!
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ЭЛЕКТРОХИМИЯ
Учебник содержит все традиционные разделы курса электрохимии. В нем приведены примеры использования количественных соотношений электро химической термодинамики и кинетики для описания и прогнозирования свойств реальных систем. Даны основы научного подхода к решению задач, связанных с практическим применением электрохимических систем. Рассмотрены последние достижения в области разработки новых матери алов для электрохимических систем, современное состояние физических пред ставлений об элементарных явлениях в электрохимических процессах, фи зические методы исследования растворов, межфазных границ и электродных материалов.
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Әдебияттаныў
Әдебияттаныў атлы колланба окыу куралы каракалпак тилинде биринши мартебе жарияланып отыр. Бул колланба окыу куралын доретиуде Л. Тимофеевтин «Адебият теориясынын тийкарлары», «Адебият теориясы» университетлерге арналган «Адебияттаныу илимине кирисиу», озбек тилинде шыккап «Адебият теориясы» (еки томнан), И. Султанов «Адебият теориясы», 3. Кабдоловтын «Соз онери» китапларынан пайдаланылды, авторлар олардын курылысы, айырым теориялык пикирлерине суйенди. Теориялык маселелерди тусиндириуде каракалпак фольклоры, классикалык адебияты, бурынгы дауирдеги шыгармалар мумкин болганынша негиз етип алынды.
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Neutrality and Many-Valued Logics
This book written by A. Schumann & F. Smarandache is devoted to advances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes’ axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0, 1] which are larger than zero. In this book, we consider various many-valued logics: standard, linear, hy-perbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert’s style, sequent, and hypersequent.
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ОБЩАЯ И НЕОРГАНИЧЕСКАЯ ХИМИЯ
В книге рассмотрены основные понятия н законы химии: строение вещества, химическая связь (метод молекулярных орбиталей, метод валентных связей, зонная теория кристаллов), важнейшие положения химической термодинамики и химиче ской кинетики, методы исследования структуры веществ. Химия элементов изложена на основе периодического закона Д. И. Мен делеева с привлечением структурных и термодинамических представлений. Учебник предназначен для студентов, аспирантов и препода вателей химических факультетов университетов, а также химико технологических вузов
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Notes on Differential Equations
These Notes on Differential Equations are an introduction and invitation. The focus is on. Important models. Calculus in applied contexts. I may point out that the title is not Solving Differential Equations; we derive them, discuss them, review calculus background for them, apply them, sketch and compute them, and also solve them and interpret the solutions. This breadth is new to many students. The notes, available for many years on my web page, have evolved from lectures I have given while teaching the Engineering Mathematics courses at Cornell University. They could be used for an introductory unified course on ordinary and partial differential equations. There is minimal manipulation and a lot of emphasis on the teaching of concepts by example.
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“Metrology – in short” 3rd edition
The content of this handbook is a description of scientific, industrial and legal metrology. The technical subject fields of metrology and metrological units are described. The international metrology infrastructure is detailed, including the regional metrology organisations such as EURAMET.
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Metal Forming
This book is designed to help the engineer understand the principles of metal forming and analyze forming problems – both the mechanics of forming processes and how the properties of metals interact with the processes. The first third of the book is devoted to fundamentals of mechanics and materials; the middle to analyses of bulk forming processes such as drawing, extrusion, and rolling; and the last third covers sheet forming processes.
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Measurement and Instrumentation
Ideally, the principles of good measurement and instrumentation practice should be taught throughout the duration of engineering courses, starting at an elementary level and moving on to more advanced topics as the course progresses. With this in mind, the material contained in this book is designed both to support introductory courses in measurement and instrumentation, and also to provide in-depth coverage of advanced topics for higher-level courses.
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Разведочное бурение
В книге дана краткая характеристика физико-механических свойств горных пород с точки зрения их разрушения при бурении и описаны различные способы бурения скважин для различных целей и на разные глубины. Основное внимание уделено технологии бурения. Более детально описаны способы бурения, применяемые для разведочных целей, особенно колонковое бурение. Приведены данные по борьбе с искривлением скважин и авариями. Буровые станки описаны схематично. Книга является учебным пособием для студентов геологоразведочных вузов по специальности «Геология и разведка месторождений полезных ископаемых».
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Исследования мостовых конструкции
Важной особенностью предлагаемой методики расчета является представление воздействия сил регулирования (натяжения вант) на систему в виде векторе или матрицы перемещений по направлению неизвестных усилий в связях, с помощью которых производится регулирование. Это позволяет определять усилия и перемещения исходя из однократного расчета лишь заданной системы и в едином алгоритме расчета получать как необходимые усилия натяжения вант.