Download or read book More Almost Impossible Integrals Sums and Series written by Cornel Ioan Vălean and published by Springer Nature. This book was released on 2023-05-24 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the much-anticipated sequel to (Almost) Impossible, Integrals, Sums, and Series, presents a whole new collection of challenging problems and solutions that are not commonly found in classical textbooks. As in the author’s previous book, these fascinating mathematical problems are shown in new and engaging ways, and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Classical problems are shown in a fresh light, with new, surprising or unconventional ways of obtaining the desired results devised by the author. This book is accessible to readers with a good knowledge of calculus, from undergraduate students to researchers. It will appeal to all mathematical puzzlers who love a good integral or series and aren’t afraid of a challenge.

Download or read book Almost Impossible Integrals Sums and Series written by Cornel Ioan Vălean and published by Springer. This book was released on 2019-05-10 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.

Download or read book Irresistible Integrals written by George Boros and published by Cambridge University Press. This book was released on 2004-06-21 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2004, uses the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics.

Download or read book Inside Interesting Integrals written by Paul J. Nahin and published by Springer Nature. This book was released on 2020-06-27 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: What’s the point of calculating definite integrals since you can’t possibly do them all? What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book, now in its second edition, is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you. New material in the second edition includes 25 new challenge problems and solutions, 25 new worked examples, simplified derivations, and additional historical discussion.

Download or read book The Essence of Numbers written by Frédéric Patras and published by Springer Nature. This book was released on 2020-10-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.

Download or read book Probability Through Problems written by Marek Capinski and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book of problems is designed to challenge students learning probability. Each chapter is divided into three parts: Problems, Hints, and Solutions. All Problems sections include expository material, making the book self-contained. Definitions and statements of important results are interlaced with relevant problems. The only prerequisite is basic algebra and calculus.

Download or read book Limits Series and Fractional Part Integrals written by Ovidiu Furdui and published by Springer Science & Business Media. This book was released on 2013-05-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features challenging problems of classical analysis that invite the reader to explore a host of strategies and tools used for solving problems of modern topics in real analysis. This volume offers an unusual collection of problems — many of them original — specializing in three topics of mathematical analysis: limits, series, and fractional part integrals. The work is divided into three parts, each containing a chapter dealing with a particular problem type as well as a very short section of hints to select problems. The first chapter collects problems on limits of special sequences and Riemann integrals; the second chapter focuses on the calculation of fractional part integrals with a special section called ‘Quickies’ which contains problems that have had unexpected succinct solutions. The final chapter offers the reader an assortment of problems with a flavor towards the computational aspects of infinite series and special products, many of which are new to the literature. Each chapter contains a section of difficult problems which are motivated by other problems in the book. These ‘Open Problems’ may be considered research projects for students who are studying advanced calculus, and which are intended to stimulate creativity and the discovery of new and original methods for proving known results and establishing new ones. This stimulating collection of problems is intended for undergraduate students with a strong background in analysis; graduate students in mathematics, physics, and engineering; researchers; and anyone who works on topics at the crossroad between pure and applied mathematics. Moreover, the level of problems is appropriate for students involved in the Putnam competition and other high level mathematical contests.

Download or read book Proof Analysis written by Sara Negri and published by Cambridge University Press. This book was released on 2011-09-29 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.

Download or read book Pell s Equation written by Edward J. Barbeau and published by Springer Science & Business Media. This book was released on 2006-05-04 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields. It is an ideal topic to lead college students, as well as some talented and motivated high school students, to a better appreciation of the power of mathematical technique. Even at the specific level of quadratic diophantine equations, there are unsolved problems, and the higher degree analogues of Pell's equation, particularly beyond the third, do not appear to have been well studied. In this focused exercise book, the topic is motivated and developed through sections of exercises which will allow the readers to recreate known theory and provide a focus for their algebraic practice. There are several explorations that encourage the reader to embark on their own research. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have (or have forgotten) a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.

Download or read book Advanced Calculus of Several Variables written by C. H. Edwards and published by Academic Press. This book was released on 2014-05-10 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence.

Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.

Download or read book 40 Puzzles and Problems in Probability and Mathematical Statistics written by Wolf Schwarz and published by Springer Science & Business Media. This book was released on 2007-11-25 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the view that cognitive skills are best acquired by solving challenging, non-standard probability problems. Many puzzles and problems presented here are either new within a problem solving context (although as topics in fundamental research they are long known) or are variations of classical problems which follow directly from elementary concepts. A small number of particularly instructive problems is taken from previous sources which in this case are generally given. This book will be a handy resource for professors looking for problems to assign, for undergraduate math students, and for a more general audience of amateur scientists.

Download or read book Measure Probability and Mathematical Finance written by Guojun Gan and published by John Wiley & Sons. This book was released on 2014-04-07 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models. The authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features: A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.

Download or read book Examples and Problems in Advanced Calculus Real Valued Functions written by Bijan Davvaz and published by Springer Nature. This book was released on 2020-12-11 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes over 500 most challenging exercises and problems in calculus. Topical problems and exercises are discussed on set theory, numbers, functions, limits and continuity, derivative, integral calculus, Rolle’s theorem, mean value theorem, optimization problems, sequences and series. All the seven chapters recall important definitions, theorems and concepts, making this book immensely valuable to undergraduate students of engineering, mathematics, statistics, computer science and basic sciences.

Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Download or read book An Introduction to Measure Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2021-09-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Download or read book Hilbert Space written by Edited by Paul F. Kisak and published by Createspace Independent Publishing Platform. This book was released on 2016-01-07 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer)-and ergodic theory, which forms the mathematical underpinning of thermodynamics. John von Neumann coined the term Hilbert space for the abstract concept that underlies many of these diverse applications. The success of Hilbert space methods ushered in a very fruitful era for functional analysis. Apart from the classical Euclidean spaces, examples of Hilbert spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized functions, and Hardy spaces of holomorphic functions. This book gives a mathematical overview of the definition and use of Hilbert Space.