Download or read book Calculus for Cranks written by Nets Hawk Katz and published by Yale University Press. This book was released on 2021-01-26 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the foundations of single variable calculus, based on the introductory course taught at Caltech In mathematics, "cranks" are people who insist they understand something new about math even when the world tells them they are doing it wrong. This introduction to calculus is written with those cranks in mind, based on the foundational course that Nets Katz teaches at Caltech. It emphasizes the practical purposes of the foundations, such as tracking errors in calculations. In addition to covering the basics of single variable calculus, the book outlines the mathematical method--the ability to express oneself with absolute precision and then to use logical proofs to establish that certain statements are universally true. Katz emphasizes conceptual clarity, as well as testing hypotheses and writing complete proofs. The result is a rigorous calculus book of use not only to future mathematicians but also to scientists and engineers.

Download or read book Mathematical Cranks written by Underwood Dudley and published by American Mathematical Soc.. This book was released on 2019-07-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A delightful collection of articles about people who claim they have achieved the mathematically impossible (squaring the circle, duplicating the cube); people who think they have done something they have not (proving Fermat's Last Theorem); people who pray in matrices; people who find the American Revolution ruled by the number 57; people who have in common eccentric mathematical views, some mild (thinking we should count by 12s instead of 10s), some bizarre (thinking that second-order differential equations will solve all problems of economics, politics and philosophy). This is a truly uniqu.

Download or read book Calculus for Cranks written by Nets Hawk Katz and published by Yale University Press. This book was released on 2021-01-26 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the foundations of single variable calculus, based on the introductory course taught at Caltech In mathematics, "cranks" are people who insist they understand something new about math even when the world tells them they are doing it wrong. This introduction to calculus is written with those cranks in mind, based on the foundational course that Nets Katz teaches at Caltech. It emphasizes the practical purposes of the foundations, such as tracking errors in calculations. In addition to covering the basics of single variable calculus, the book outlines the mathematical method--the ability to express oneself with absolute precision and then to use logical proofs to establish that certain statements are universally true. Katz emphasizes conceptual clarity, as well as testing hypotheses and writing complete proofs. The result is a rigorous calculus book of use not only to future mathematicians but also to scientists and engineers.

Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

Download or read book Good Math written by Mark C. Chu-Carroll and published by Pragmatic Bookshelf. This book was released on 2013-07-18 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you. Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird. Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing. If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.

Download or read book Elementary Calculus written by H. Jerome Keisler and published by Orange Groove Books. This book was released on 2009-09-01 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Mathematical Experience Study Edition written by Philip Davis and published by Springer Science & Business Media. This book was released on 2011-10-28 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.

Download or read book Theory and Applications of Special Functions written by Mourad E. H. Ismail and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles on various aspects of q-series and special functions dedicated to Mizan Rahman. It also includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject.

Download or read book The Cognitive Theoretic Model of the Universe A New Kind of Reality Theory written by Christopher Michael Langan and published by Mega Foundation Press. This book was released on 2002-06-01 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paperback version of the 2002 paper published in the journal Progress in Information, Complexity, and Design (PCID). ABSTRACT Inasmuch as science is observational or perceptual in nature, the goal of providing a scientific model and mechanism for the evolution of complex systems ultimately requires a supporting theory of reality of which perception itself is the model (or theory-to-universe mapping). Where information is the abstract currency of perception, such a theory must incorporate the theory of information while extending the information concept to incorporate reflexive self-processing in order to achieve an intrinsic (self-contained) description of reality. This extension is associated with a limiting formulation of model theory identifying mental and physical reality, resulting in a reflexively self-generating, self-modeling theory of reality identical to its universe on the syntactic level. By the nature of its derivation, this theory, the Cognitive Theoretic Model of the Universe or CTMU, can be regarded as a supertautological reality-theoretic extension of logic. Uniting the theory of reality with an advanced form of computational language theory, the CTMU describes reality as a Self Configuring Self-Processing Language or SCSPL, a reflexive intrinsic language characterized not only by self-reference and recursive self-definition, but full self-configuration and self-execution (reflexive read-write functionality). SCSPL reality embodies a dual-aspect monism consisting of infocognition, self-transducing information residing in self-recognizing SCSPL elements called syntactic operators. The CTMU identifies itself with the structure of these operators and thus with the distributive syntax of its self-modeling SCSPL universe, including the reflexive grammar by which the universe refines itself from unbound telesis or UBT, a primordial realm of infocognitive potential free of informational constraint. Under the guidance of a limiting (intrinsic) form of anthropic principle called the Telic Principle, SCSPL evolves by telic recursion, jointly configuring syntax and state while maximizing a generalized self-selection parameter and adjusting on the fly to freely-changing internal conditions. SCSPL relates space, time and object by means of conspansive duality and conspansion, an SCSPL-grammatical process featuring an alternation between dual phases of existence associated with design and actualization and related to the familiar wave-particle duality of quantum mechanics. By distributing the design phase of reality over the actualization phase, conspansive spacetime also provides a distributed mechanism for Intelligent Design, adjoining to the restrictive principle of natural selection a basic means of generating information and complexity. Addressing physical evolution on not only the biological but cosmic level, the CTMU addresses the most evident deficiencies and paradoxes associated with conventional discrete and continuum models of reality, including temporal directionality and accelerating cosmic expansion, while preserving virtually all of the major benefits of current scientific and mathematical paradigms.

Download or read book Tales of Impossibility written by David S. Richeson and published by Princeton University Press. This book was released on 2021-11-02 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.

Download or read book Appleton s Dictionary of Machines Mechanics Engine work and Engineering written by and published by . This book was released on 1873 with total page 1082 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Trisectors written by Underwood Dudley and published by American Mathematical Soc.. This book was released on 2019-07-01 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Underwood Dudley is well known for his collection of books on mathematical cranks. Here he offers yet another--angle trisectors. It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. According to Dudley: ""Hardly any mathematical training is necessary to read this book. There is a little trigonometry here and there, but it may be safely skipped. There are hardly any equations. There are no exercises and there will be no final examination. The worst victim o.

Download or read book Invisible in the Storm written by Ian Roulstone and published by Princeton University Press. This book was released on 2013-02-24 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: They explore how weather forecasters today formulate their ideas through state-of-the-art mathematics, taking into account limitations to predictability.

Download or read book Metamath A Computer Language for Mathematical Proofs written by Norman Megill and published by Lulu.com. This book was released on 2019 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the "Formalizing 100 Theorems" challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database.

Download or read book Numerology Or What Pythagoras Wrought written by Underwood Dudley and published by Cambridge University Press. This book was released on 1997 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Numerology is about numerology, which is the delusion that numbers have power over events. ... The message of the book is that numbers indeed have power, but the power is not over events, it is over the human minds. It is intended for anyone interested in human folly and requires no mathematical knowledge beyond arithmetic to understand."--Cover

Download or read book Reciprocating Machinery Dynamics written by Abdulla S. Rangwala and published by New Age International. This book was released on 2006 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Book Primarily Written To Meet The Needs Of Practicing Engineers In A Large Variety Of Industries Where Reciprocating Machines Are Used, Although All Of The Material Is Suitable For College Undergraduate Level Design Engineering Courses. It Is Expected That The Reader Is Familiar With Basic To Medium Level Calculus Offered At The College Undergraduate Level.The First Chapter Of The Book Deals With Classical Vibration Theory, Starting With A Single Degree Of Freedom System, To Develop Concepts Of Damping, Response And Unbalance. The Second Chapter Deals With Types And Classification Of Reciprocating Machines, While The Third Chapter Discusses Detail-Design Aspects Of Machine Components. The Fourth Chapter Introduces The Dynamics Of Slider And Cranks Mechanism, And Provides Explanation Of The Purpose And Motion Of Various Components.The Fifth Chapter Looks Into Dynamic Forces Created In The System, And Methods To Balance Gas Pressure And Inertia Loads. The Sixth Chapter Explains The Torsional Vibration Theory And Looks At The Different Variables Associated With It. Chapter Seven Analyzes Flexural Vibrations And Lateral Critical Speed Concepts, Together With Journal Bearings And Their Impact On A Rotating System. Advanced Analytical Techniques To Determine Dynamic Characteristics Of All Major Components Of Reciprocating Machinery Are Presented In Chapter Eight. Methods To Mitigate Torsional Vibrations In A Crankshaft Using Absorbers Are Analyzed In Close Detail. Various Mechanisms Of Flexural Excitation Sources And Their Response On A Rotor-Bearing System Are Explored. Stability Of A Rotor And Different Destabilizing Mechanisms Are Also Included In This Chapter.Techniques In Vibration Measurement And Balancing Of Reciprocating And Rotating Systems Are Presented In Chapter Nine. Chapter Ten Looks At Computational Fluid Dynamics Aspects Of Flow Through Intake And Exhaust Manifolds, As Well As Fluid Flow Induced Component Vibrations. Chapter Eleven Extends This Discussion To Pressure Pulsations In Piping Attached To Reciprocating Pumps And Compressors. Chapter Twelve Considers The Interaction Between The Structural Dynamics Of Components And Noise, Together With Methods To Improve Sound Quality. Optimized Design Of Components Of Reciprocating Machinery For Specified Parameters And Set Target Values Is Investigated At Length In Chapter Thirteen. Practicing Engineers Interested In Applying The Theoretical Model To Their Own Operating System Will Find Case Histories Shown In Chapter FourteenUseful.

Download or read book Mechanics written by J. P. Den Hartog and published by Courier Corporation. This book was released on 2013-03-13 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introductory text features hundreds of applications and design problems that illuminate fundamentals of trusses, loaded beams and cables, and related areas. Includes 334 answered problems.