Springer «18 Unconventional Essays on the Nature of Mathematics» by Reuben Hersh

Springer «18 Unconventional Essays on the Nature of Mathematics» by Reuben Hersh
English | Springer | 2006 | ISBN 0-387-25717-9 | True PDF | 346 pages | 1,4 Mb

This book collects some of the most interesting recent writings that are tackling, from various points of view, the problem of giving an accounting of the nature, purpose, and justification of real mathematical practice - mathematics as actually done by real live mathematicians. What is the nature of the objects being studied? What determines the directions and styles in which mathematics progresses (or, perhaps, degenerates)? What certifies its claim to certainty, or to a priori status, to independence of experience? Why is mathematics the same for all times and places, or is it really the same, or in what senses is it the same and in what senses different? Many of these writings were read at conferences in Europe and America under the heading of «history» or «cultural studies» as well as «philosophy». It is the editor’s hope to help foster healthy interdisciplinary mutual aid in this young and fertile area.

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Riddles in Math: Book of Paradoxes

Riddles in Math: Book of Paradoxes
Krieger | 262 Pages | 2001 | ISBN:0882752731 | PDF + DJVU | 15 MB

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Probability and Mathematical Statistics, Vol. 22: The Spectral Analysis of Time Series

Lambert Herman Koopmans, "Probability and Mathematical Statistics, Vol. 22: The Spectral Analysis of Time Series"
Academic Press | 1995-05 | ISBN: 0124192513 | 366 pages | PDF | 13 MB

To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series. This classic book provides an introduction to the techniques and theories of spectral analysis of time series. In a discursive style, and with minimal dependence on mathematics, the book presents the geometric structure of spectral analysis. This approach makes possible useful, intuitive interpretations of important time series parameters and provides a unified framework for an otherwise scattered collection of seemingly isolated results.
The books strength lies in its applicability to the needs of readers from many disciplines with varying backgrounds in mathematics. It provides a solid foundation in spectral analysis for fields that include statistics, signal process engineering, economics, geophysics, physics, and geology. Appendices provide details and proofs for those who are advanced in math. Theories are followed by examples and applications over a wide range of topics such as meteorology, seismology, and telecommunications.
Topics covered include Hilbert spaces; univariate models for spectral analysis; multivariate spectral models; sampling, aliasing, and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction.
Key Features
* Hilbert spaces
* univariate models for spectral analysis
* multivariate spectral models
* sampling, aliasing, and discrete-time models
* real-time filtering
* digital filters
* linear filters
* distribution theory
* sampling properties of spectral estimates
* linear prediction

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The Analysis of Linear Partial Differential Operators III: Pseudo-Differential Operators

Lars Hörmander, "The Analysis of Linear Partial Differential Operators III: Pseudo-Differential Operators"
Springer | 2007-03 | ISBN: 3540499377 | 525 pages | Djvu | 5 MB

"Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators."
L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987
"This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation."
J. Brüning in Zentralblatt MATH, 1987

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Calculus of Variations

I. M. Gelfand, S. V. Fomin, "Calculus of Variations"
Dover Publications | 2000-10-16 | ISBN: 0486414485 | 240 pages | Djvu | 2 MB

First six chapters include theory of fields and sufficient conditions for weak and strong extrema. Chapter 7 considers application of variation methods to systems with infinite degrees of freedom, and Chapter 8 deals with direct methods in the calculus of variations. Problems follow each chapter and the two appendices. Fresh, lively text is ideal for advanced undergraduate and graduate students in math and physics.

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Real Analysis: A Constructive Approach

Mark Bridger, "Real Analysis: A Constructive Approach"
Wiley-Interscience | 2006-11-28 | ISBN:0471792306 | 302 pages | DjVu | 2 Mb

This innovative text sets forth a thoroughly rigorous modern account of the theoretical underpinnings of calculus: continuity, differentiability, and convergence. Using a constructive approach, every proof of every result is direct and ultimately computationally verifiable. The ultimate consequence of this method is that it makes sense—whether you’re a math major or student in any branch of the sciences.


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