A Short Book on Long Sums

Download A Short Book on Long Sums PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3031375572
Total Pages : 153 pages
Book Rating : 4.0/5 (313 download)

DOWNLOAD NOW!


Book Synopsis A Short Book on Long Sums by : Fernando Q. Gouvêa

Download or read book A Short Book on Long Sums written by Fernando Q. Gouvêa and published by Springer Nature. This book was released on 2023-12-07 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series—and infinite series in general—are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural. Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor’s guide with solutions to all the problems is available. The book is intended as a supplementary textbook for calculus courses; lecturers and instructors will find innovative and engaging ways to teach this topic. The informal and conversational tone make the book useful to any student seeking to understand this essential aspect of analysis.

Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition

Download Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition PDF Online Free

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 147046456X
Total Pages : 331 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!


Book Synopsis Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition by : William P. Berlinghoff

Download or read book Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition written by William P. Berlinghoff and published by American Mathematical Soc.. This book was released on 2021-04-29 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.

Concrete Mathematics

Download Concrete Mathematics PDF Online Free

Author :
Publisher : Addison-Wesley Professional
ISBN 13 : 0134389980
Total Pages : 811 pages
Book Rating : 4.1/5 (343 download)

DOWNLOAD NOW!


Book Synopsis Concrete Mathematics by : Ronald L. Graham

Download or read book Concrete Mathematics written by Ronald L. Graham and published by Addison-Wesley Professional. This book was released on 1994-02-28 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.

(Almost) Impossible Integrals, Sums, and Series

Download (Almost) Impossible Integrals, Sums, and Series PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3030024628
Total Pages : 572 pages
Book Rating : 4.0/5 (3 download)

DOWNLOAD NOW!


Book Synopsis (Almost) Impossible Integrals, Sums, and Series by : Cornel Ioan Vălean

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 572 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.

Short Calculus

Download Short Calculus PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461300770
Total Pages : 276 pages
Book Rating : 4.4/5 (613 download)

DOWNLOAD NOW!


Book Synopsis Short Calculus by : Serge Lang

Download or read book Short Calculus written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews "This is a reprint of the original edition of Lang’s ‘A First Course in Calculus’, which was first published in 1964....The treatment is ‘as rigorous as any mathematician would wish it’....[The exercises] are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging....There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." --Mathematical Gazette

An Introduction to Infinite Products

Download An Introduction to Infinite Products PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3030906469
Total Pages : 258 pages
Book Rating : 4.0/5 (39 download)

DOWNLOAD NOW!


Book Synopsis An Introduction to Infinite Products by : Charles H. C. Little

Download or read book An Introduction to Infinite Products written by Charles H. C. Little and published by Springer Nature. This book was released on 2022-01-10 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.

p-adic Numbers

Download p-adic Numbers PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3662222787
Total Pages : 285 pages
Book Rating : 4.6/5 (622 download)

DOWNLOAD NOW!


Book Synopsis p-adic Numbers by : Fernando Q. Gouvea

Download or read book p-adic Numbers written by Fernando Q. Gouvea and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.

Sums of Squares of Integers

Download Sums of Squares of Integers PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1584884568
Total Pages : 368 pages
Book Rating : 4.5/5 (848 download)

DOWNLOAD NOW!


Book Synopsis Sums of Squares of Integers by : Carlos J. Moreno

Download or read book Sums of Squares of Integers written by Carlos J. Moreno and published by CRC Press. This book was released on 2005-12-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares. The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.

Advanced Calculus (Revised Edition)

Download Advanced Calculus (Revised Edition) PDF Online Free

Author :
Publisher : World Scientific Publishing Company
ISBN 13 : 9814583952
Total Pages : 595 pages
Book Rating : 4.8/5 (145 download)

DOWNLOAD NOW!


Book Synopsis Advanced Calculus (Revised Edition) by : Lynn Harold Loomis

Download or read book Advanced Calculus (Revised Edition) written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 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.

Calculus For Dummies

Download Calculus For Dummies PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119297435
Total Pages : 446 pages
Book Rating : 4.1/5 (192 download)

DOWNLOAD NOW!


Book Synopsis Calculus For Dummies by : Mark Ryan

Download or read book Calculus For Dummies written by Mark Ryan and published by John Wiley & Sons. This book was released on 2016-05-18 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be. Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is—simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win. Includes foundations in algebra, trigonometry, and pre-calculus concepts Explores sequences, series, and graphing common functions Instructs you how to approximate area with integration Features things to remember, things to forget, and things you can't get away with Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.

Calculus Made Easy

Download Calculus Made Easy PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.A/5 ( download)

DOWNLOAD NOW!


Book Synopsis Calculus Made Easy by : Silvanus Phillips Thompson

Download or read book Calculus Made Easy written by Silvanus Phillips Thompson and published by . This book was released on 1911 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Problem Book in Real Analysis

Download A Problem Book in Real Analysis PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1441912967
Total Pages : 257 pages
Book Rating : 4.4/5 (419 download)

DOWNLOAD NOW!


Book Synopsis A Problem Book in Real Analysis by : Asuman G. Aksoy

Download or read book A Problem Book in Real Analysis written by Asuman G. Aksoy and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

Sum

Download Sum PDF Online Free

Author :
Publisher : Vintage
ISBN 13 : 0307378020
Total Pages : 128 pages
Book Rating : 4.3/5 (73 download)

DOWNLOAD NOW!


Book Synopsis Sum by : David Eagleman

Download or read book Sum written by David Eagleman and published by Vintage. This book was released on 2009-02-10 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: At once funny, wistful and unsettling, Sum is a dazzling exploration of unexpected afterlives—each presented as a vignette that offers a stunning lens through which to see ourselves in the here and now. In one afterlife, you may find that God is the size of a microbe and unaware of your existence. In another version, you work as a background character in other people’s dreams. Or you may find that God is a married couple, or that the universe is running backward, or that you are forced to live out your afterlife with annoying versions of who you could have been. With a probing imagination and deep understanding of the human condition, acclaimed neuroscientist David Eagleman offers wonderfully imagined tales that shine a brilliant light on the here and now.

The Joy of X

Download The Joy of X PDF Online Free

Author :
Publisher : Houghton Mifflin Harcourt
ISBN 13 : 0547517653
Total Pages : 333 pages
Book Rating : 4.5/5 (475 download)

DOWNLOAD NOW!


Book Synopsis The Joy of X by : Steven Henry Strogatz

Download or read book The Joy of X written by Steven Henry Strogatz and published by Houghton Mifflin Harcourt. This book was released on 2012 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."

The Reference Catalogue of Current Literature

Download The Reference Catalogue of Current Literature PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 1538 pages
Book Rating : 4.:/5 (334 download)

DOWNLOAD NOW!


Book Synopsis The Reference Catalogue of Current Literature by :

Download or read book The Reference Catalogue of Current Literature written by and published by . This book was released on 1906 with total page 1538 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reference Catalogue of Current Literature

Download Reference Catalogue of Current Literature PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 1532 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!


Book Synopsis Reference Catalogue of Current Literature by :

Download or read book Reference Catalogue of Current Literature written by and published by . This book was released on 1906 with total page 1532 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sessional Papers

Download Sessional Papers PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 876 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!


Book Synopsis Sessional Papers by : Great Britain. Parliament. House of Commons

Download or read book Sessional Papers written by Great Britain. Parliament. House of Commons and published by . This book was released on 1901 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: