Ralph P. Boas's Books

A Primer of Real Functions: Fourth Edition

By: Ralph P. Boas,Harold P. Boas

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A Primer of Real Functions: Fourth Edition

By: Ralph P. Boas,Harold P. Boas

This is a revised, updated, and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications. The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is, thus, suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: e.g., the existence of continuous everywhere-oscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series. This book recaptures the sense of wonder that was associated with the subject in its early days. It is a must for mathematics libraries.

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Page Count

321

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470454327

ISBN 13

9781470454326

Lion Hunting & Other Mathematical Pursuits: A Collection of Mathematics, Verse and Stories

By: Ralph P. Boas Jr.

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Lion Hunting & Other Mathematical Pursuits: A Collection of Mathematics, Verse and Stories

By: Ralph P. Boas Jr.

In the famous paper of 1938, “A Contribution to the Mathematical Theory of Big Game Hunting”, written by Ralph Boas along with Frank Smithies, using the pseudonym H. Pétard, Boas describes sixteen methods for hunting a lion. This marvelous collection of Boas memorabilia contains not only the original article, but also several additional articles, as late as 1985, giving many further methods. But once you are through with lion hunting, you can hunt through the remainder of the book to find numerous gems by and about this remarkable mathematician. Not only will you find his biography of Bourbaki along with a description of his feud with the French mathematician, but also you will find a lucid discussion of the mean value theorem. There are anecdotes Boas told about many famous mathematicians, along with a large collection of his mathematical verses. You will find mathematical articles like a proof of the fundamental theorem of algebra and pedagogical articles giving Boas' views on making mathematics intelligible.

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308

Publisher

American Mathematical Soc.

ISBN 10

147045839X

ISBN 13

9781470458393

Invitation to Complex Analysis

By: Ralph P. Boas

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Invitation to Complex Analysis

By: Ralph P. Boas

Ideal for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written at a level accessible to advanced undergraduates and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of intriguing topics that are uncommon in a book at this level. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, one-term course or to a comprehensive, full-year course. Detailed solutions of the exercises both serve as models for students and facilitate independent study. Supplementary exercises, not solved in the book, provide an additional teaching tool. This second edition has been painstakingly revised by the author's son, himself an award-winning mathematical expositor.

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343

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0883857642

ISBN 13

9780883857649

Polynomial expansions of analytic functions

By: Ralph P. Boas,Robert Creighton Buck

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Polynomial expansions of analytic functions

By: Ralph P. Boas,Robert Creighton Buck

This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1], voi. III, chap. 19) and in TRUESDELL [1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series ,Lc,. p,. (z), where {p,. } is a prescribed sequence of functions, and the connections between the function f and the coefficients c,. . BIEBERBACH's mono graph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p,. (z) =z", and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M.

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Springer Science & Business Media

Published Date

ISBN 10

3662251701

ISBN 13

9783662251706

Mathematics for Secondary School Teachers

By: Elizabeth G. Bremigan,Ralph J. Bremigan,John D. Lorch

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Mathematics for Secondary School Teachers

By: Elizabeth G. Bremigan,Ralph J. Bremigan,John D. Lorch

Discusses topics of central importance in the secondary school mathematics curriculum, including functions, polynomials, trigonometry, exponential and logarithmic functions, number and operation, and measurement. This volume is primarily intended as the text for a bridge or capstone course for pre-service secondary school mathematics teachers.

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Page Count

444

Publisher

MAA

Published Date

ISBN 10

0883857731

ISBN 13

9780883857731

Integrability Theorems for Trigonometric Transforms

By: Ralph P.Jr. Boas

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Integrability Theorems for Trigonometric Transforms

By: Ralph P.Jr. Boas

This monograph is areport on the present state of a fairly coherent collection of problems about which a sizeable literature has grown up in recent years. In this literature, some of the problems have, as it happens, been analyzed in great detail, whereas other very similar ones have been treated much more superficially. I have not attempted to improve on the literature by making equally detailed presentations of every topic. I have also not aimed at encyclopedic completeness. I have, however, pointed out some possible generalizations by stating a number of questions; some of these could doubtless be disposed of in a few minutes; some are probably quite difficult. This monograph was written at the suggestion of B. SZ.-NAGY. I take this opportunity of pointing out that his paper [1] inspired the greater part of the material that is presented here; in particular, it contains the happy idea of focusing Y attention on the multipliers nY-i, x- . R. ASKEY, P. HEYWOOD, M. and S. IZUMI, and S. WAINGER have kindly communicated some of their recent results to me before publication. I am indebted for help on various points to L. S. BOSANQUET, S. M. EDMONDS, G. GOES, S. IZUMI, A. ZYGMUND, and especially to R. ASKEY. My work was supported by the National Science Foundation under grants GP-314, GP-2491, GP-3940 and GP-5558. Evanston, Illinois, February, 1967 R. P. Boas, Jr. Contents Notations ... § 1. Introduetion 3 §2. Lemmas .. 7 § 3. Theorems with positive or decreasing functions .

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Springer Science & Business Media

Published Date

ISBN 10

3642871089

ISBN 13

9783642871085

Invitation to Complex Analysis

By: Ralph P. Boas

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Invitation to Complex Analysis

By: Ralph P. Boas

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Solve jigsaw puzzle

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343

Publisher

American Mathematical Soc.

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ISBN 10

0883857642

ISBN 13

9780883857649

Book's by Ralph P. Boas

A Primer of Real Functions: Fourth Edition

A Primer of Real Functions: Fourth Edition

Lion Hunting & Other Mathematical Pursuits: A Collection of Mathematics, Verse and Stories

Lion Hunting & Other Mathematical Pursuits: A Collection of Mathematics, Verse and Stories

Invitation to Complex Analysis

Invitation to Complex Analysis

Polynomial expansions of analytic functions

Polynomial expansions of analytic functions

Mathematics for Secondary School Teachers

Mathematics for Secondary School Teachers

Integrability Theorems for Trigonometric Transforms

Integrability Theorems for Trigonometric Transforms

Invitation to Complex Analysis

Invitation to Complex Analysis

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