Journal ArticleDOI
A radical approach to real analysis, by David Bressoud. Pp328. $29. 1994. ISBN-0-88385-701-4 (Mathematical Association of America)
TLDR
This chapter discusses Fourier's series in detail, focusing on the summations of the Fourier series, which are concerned with the convergence of infinite series.Abstract:
Preface 1. Crisis in mathematics: Fourier's series 2. Infinite summations 3. Differentiability and continuity 4. The convergence of infinite series 5. Understanding infinite series 6. Return to Fourier series 7. Epilogue A. Explorations of the infinite B. Bibliography C. Hints to selected exercises.read more
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Journal ArticleDOI
The mathematics of the past: distinguishing its history from our heritage
TL;DR: The difference between these two approaches is discussed in this paper, with examples exhibited; these will include Euclid, set theory, limits, and applied mathematics in general, and examples of the difference between them are discussed.
Book
Classic Problems of Probability
TL;DR: The Classic Problems of Probability as discussed by the authors is a collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature.
Journal ArticleDOI
A Theory of Antenna Electromagnetic Near Field—Part II
Said Mikki,Yahia M. M. Antar +1 more
TL;DR: In this article, the rotational symmetry breaking of the scalar Greens function was studied from a source point of view, and a suitable mathematical machinery for dealing with the symmetry breaking procedure from the source point-of-view was developed in detail.
Problem Books in Mathematics
Peter Winkler,Edward J. Barbeau,Marcel Berger,Pierre Pansu,Jean-Pic Berry,Xavier Saint-Raymond,George W. Bluman,T. Cacoullos,Tomasz Zastawniak,David W. Cohen +9 more
TL;DR: The Problem-Solving Strategies (PS) series as mentioned in this paper is a collection of books devoted exclusively to problems challenging, difficult, but accessible problems that are intended to help at all levels in college, in graduate school, and in the profession.
Journal ArticleDOI
Nonstandard Student Conceptions About Infinitesimals
TL;DR: In this article, a case study of an undergraduate calculus student's nonstandard conceptions of the real number line is presented, and the similarities between these conceptions and those of G. W. Leibniz are discussed and illuminated by the formalization of infinitesimals in A. Robinson's non-standard analysis, suggesting that these student conceptions are not mere misconceptions, but are nonstandard knowledge that could be built into a system of real numbers proven to be as mathematically consistent and powerful as the standard system.