real infinite series mathematical association of america textbooks

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Real Infinite Series

Author : Daniel D. Bonar
ISBN : 0883857456
Genre : Mathematics
File Size : 51. 35 MB
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An introductory treatment of infinite series of real numbers, from basic definitions and tests to advanced results.

A Radical Approach To Real Analysis

Author : David M. Bressoud
ISBN : 0883857472
Genre : Mathematics
File Size : 22. 97 MB
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Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.

A Primer Of Real Functions

Author : Ralph P. Boas
ISBN : 088385029X
Genre : Mathematics
File Size : 84. 22 MB
Format : PDF, ePub
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Revised edition of a classic Carus monograph with a new chapter on integration and its applications.

Infinite Sequences And Series

Author : Konrad Knopp
ISBN : 9780486152042
Genre : Mathematics
File Size : 25. 59 MB
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Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.

The Art Of The Infinite

Author : Robert Kaplan
ISBN : 9781608198887
Genre : Mathematics
File Size : 53. 84 MB
Format : PDF
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A classic now available in a new, expanded edition-a witty, literate, and accessible tour of the world of mathematics. The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Robert and Ellen Kaplan guide us through the "Republic of Numbers,†? where we meet both its upstanding citizens and its more shadowy dwellers; and transport us across the plane of geometry into the unlikely realm where parallel lines meet. The journey is enriched by deft character studies of great mathematicians (and equally colorful lesser ones). And as we go deeper into infinity, we explore the most profound mystery of mathematics: Are its principles eternal truths that we discover? Or ones that we invent?

An Introduction To The Theory Of Infinite Series

Author : Thomas John I'Anson Bromwich
ISBN : 0821839764
Genre : Mathematics
File Size : 45. 24 MB
Format : PDF
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This edition consists largely of a reproduction of the first edition (which was based on lectures on Elementary Analysis given at Queen's College, Galway, from 1902-1907), with additional theorems and examples. Additional material includes a discussion of the solution of linear differential equations of the second order; a discussion of elliptic function formulae; expanded treatment of asymptomatic series; a discussion of trigonometrical series, including Stokes' transformation and Gibbs' phenomenon; and an expanded Appendix II that includes an account of Napier's invention of logarithms.

Number Theory Through Inquiry

Author : David C. Marshall
ISBN : 9780883857519
Genre : Mathematics
File Size : 79. 38 MB
Format : PDF, Kindle
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This innovative textbook leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. The first is to help students develop mathematical thinking skills, particularly theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for independent study, or for a course designed as an introduction to abstract mathematics. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method, which gives students a totally different experience compared to a standard lecture course. Students develop an attitude of personal reliance and a sense that they can think effectively about difficult problems; goals that are fundamental to the educational enterprise within and beyond mathematics.

Writing Proofs In Analysis

Author : Jonathan M. Kane
ISBN : 9783319309675
Genre : Mathematics
File Size : 33. 63 MB
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This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills. This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. To this end, all proofs presented in this text are preceded by detailed explanations describing the thought process one goes through when constructing the proof. Over 150 example proofs, templates, and axioms are presented alongside full-color diagrams to elucidate the topics at hand.

Theory And Application Of Infinite Series

Author : Konrad Knopp
ISBN : 9780486318615
Genre : Mathematics
File Size : 50. 19 MB
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Unusually clear and interesting classic covers real numbers and sequences, foundations of the theory of infinite series and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, other topics). Includes exercises.

An Invitation To Real Analysis

Author : Luis F. Moreno
ISBN : 9781939512055
Genre : Mathematics
File Size : 49. 19 MB
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An Invitation to Real Analysis is written both as a stepping stone to higher calculus and analysis courses, and as foundation for deeper reasoning in applied mathematics. This book also provides a broader foundation in real analysis than is typical for future teachers of secondary mathematics. In connection with this, within the chapters, students are pointed to numerous articles from The College Mathematics Journal and The American Mathematical Monthly. These articles are inviting in their level of exposition and their wide-ranging content. Axioms are presented with an emphasis on the distinguishing characteristics that new ones bring, culminating with the axioms that define the reals. Set theory is another theme found in this book, beginning with what students are familiar with from basic calculus. This theme runs underneath the rigorous development of functions, sequences, and series, and then ends with a chapter on transfinite cardinal numbers and with chapters on basic point-set topology. Differentiation and integration are developed with the standard level of rigor, but always with the goal of forming a firm foundation for the student who desires to pursue deeper study. A historical theme interweaves throughout the book, with many quotes and accounts of interest to all readers. Over 600 exercises and dozens of figures help the learning process. Several topics (continued fractions, for example), are included in the appendices as enrichment material. An annotated bibliography is included.

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