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 : 41. 61 MB
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An introductory treatment of infinite series of real numbers, from basic definitions and tests to advanced results.

A Primer Of Real Functions

Author : Ralph P. Boas
ISBN : 088385029X
Genre : Mathematics
File Size : 34. 42 MB
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Revised edition of a classic Carus monograph with a new chapter on integration and its applications.

A Radical Approach To Real Analysis

Author : David M. Bressoud
ISBN : 0883857472
Genre : Mathematics
File Size : 26. 17 MB
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Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.

Number Theory Through Inquiry

Author : David C. Marshall
ISBN : 9780883857519
Genre : Mathematics
File Size : 75. 43 MB
Format : PDF
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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 : 77. 56 MB
Format : PDF, ePub
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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.

Real Analysis

Author : Saul Stahl
ISBN : 9781118096857
Genre : Mathematics
File Size : 43. 52 MB
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A provocative look at the tools and history of real analysis This new edition of Real Analysis: A Historical Approach continues to serve as an interesting read for students of analysis. Combining historical coverage with a superb introductory treatment, this book helps readers easily make the transition from concrete to abstract ideas. The book begins with an exciting sampling of classic and famous problems first posed by some of the greatest mathematicians of all time. Archimedes, Fermat, Newton, and Euler are each summoned in turn, illuminating the utility of infinite, power, and trigonometric series in both pure and applied mathematics. Next, Dr. Stahl develops the basic tools of advanced calculus, which introduce the various aspects of the completeness of the real number system as well as sequential continuity and differentiability and lead to the Intermediate and Mean Value Theorems. The Second Edition features: A chapter on the Riemann integral, including the subject of uniform continuity Explicit coverage of the epsilon-delta convergence A discussion of the modern preference for the viewpoint of sequences over that of series Throughout the book, numerous applications and examples reinforce concepts and demonstrate the validity of historical methods and results, while appended excerpts from original historical works shed light on the concerns of influential mathematicians in addition to the difficulties encountered in their work. Each chapter concludes with exercises ranging in level of complexity, and partial solutions are provided at the end of the book. Real Analysis: A Historical Approach, Second Edition is an ideal book for courses on real analysis and mathematical analysis at the undergraduate level. The book is also a valuable resource for secondary mathematics teachers and mathematicians.

Infinite Sequences And Series

Author : Konrad Knopp
ISBN : 9780486152042
Genre : Mathematics
File Size : 43. 72 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.

An Invitation To Real Analysis

Author : Luis F. Moreno
ISBN : 9781939512055
Genre : Mathematics
File Size : 90. 9 MB
Format : PDF
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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.

Theory And Application Of Infinite Series

Author : Konrad Knopp
ISBN : 9780486318615
Genre : Mathematics
File Size : 53. 31 MB
Format : PDF, Kindle
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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.

Playing With Infinity

Author : Rózsa Péter
ISBN : 9780486150055
Genre : Mathematics
File Size : 84. 3 MB
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Popular account ranges from counting to mathematical logic and covers many concepts related to infinity: graphic representation of functions; pairings, other combinations; prime numbers; logarithms, circular functions; more. 216 illustrations.

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