Projective Geometry - Volume I
Publisher: Potter Press | 2007-03-15 | ISBN:1406747173 | Pages:352 | DJVU | 4 MB
PEOJECTIVE GEOMETRY BY OSWALD VEBLEN PROFESSOR OP MATHEMATICS, PRINCETON UNIVERSITY AND JOHN WESLEY YOUNG PROFESSOR OF MATHEMATICS, UNIVERSITY OF KANSAS VOLUME I GINN AND COMPANY BOSTON NEW YORK CHICAGO LONDON PREFACE Geometry, which had been for centuries the most perfect example of a deductive science, during the creative period of the nineteenth century outgrew its old logical forms. The most recent period has however brought a clearer understanding of the logical foundations of mathematics and thus has made it possible for the exposition of geometry to resume the purely deductive form. But the treatment in the books which have hitherto appeared makes the work of lay ing the foundations seem so formidable as either to require for itself a separate treatise, or to be passed over without attention to more than the outlines. This is partly due to the fact that in giving the complete foundation for ordinary real or complex geometry, it is necessary to make a study of linear order and continuity, a study which is not only extremely delicate, but whose methods are those of the theory of functions of a real variable rather than of elemen tary geometry. The present work, which is to consist of two volumes and is in tended to be available as a text in courses offered in American uni versities to upper-class and graduate students, seeks to avoid this difficulty by deferring the study of order and continuity to the sec ond volume. The more elementary part of the subject rests on a very simple set of assumptions which characterize what may be called general protective geometry. It will be found that the theorems selected on this basis of logical simplicity are also elemen tary in the sense of being easily comprehended and often used. Even the limited space devoted in this volume to the foundations may seem a drawback from the pedagogical point of view of some mathematicians. To this we can only reply that, in our opinion, an adequate knowledge of geometry cannot be obtained without attention to the foundations. We believe, moreover, that the abstract treatment is peculiarly desirable in protective geometry, because it is through the latter that the other geometric disciplines are most readily coordinated. Read More »
Steven G. Krantz, “Geometric Function Theory: Explorations in Complex Analysis”
Birkhäuser Boston; 1 edition (September 20, 2005) | ISBN: 0817643397 | 314 pages | PDF | 2 Mb
Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous CauchyRiemann equations, and the corona problem.
The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme.
Jérôme Dedecker), Paul Doukhan, Gabriel Lang and oth.”Weak Dependence: With Examples and Applications”
Springer; 1 edition (July 18, 2007) | ISBN: 0387699511 | 322 pages | PDF | 2,3 Mb
This monograph is aimed at developing Doukhan/Louhichi’s (1999) idea to measure asymptotic independence of a random process. The authors propose various examples of models fitting such conditions such as stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Most of the commonly used stationary models fit their conditions. The simplicity of the conditions is also their strength.
The main existing tools for an asymptotic theory are developed under weak dependence. They apply the theory to nonparametric statistics, spectral analysis, econometrics, and resampling. The level of generality makes those techniques quite robust with respect to the model. The limit theorems are sometimes sharp and always simple to apply.
The theory (with proofs) is developed and the authors propose to fix the notation for future applications. A large number of research papers deals with the present ideas; the authors as well as numerous other investigators participated actively in the development of this theory. Several applications are still needed to develop a method of analysis for (nonlinear) times series and they provide here a strong basis for such studies.
Brain Dynamics:Synchronization and Activity Patterns in Pulse-Coupled Neural Nets with Delays and Noise
Publisher:Springer | 2006-11-02 | ISBN 3540462821 | Pages: 245 | PDF | 2.5 MB
This book addresses a large variety of models in mathematical and computational neuroscience. It is written for the experts as well as for graduate students wishing to enter this fascinating field of research. The author studies the behaviour of large neural networks composed of many neurons coupled by spike trains. He devotes the main part to the synchronization problem. He presents neural net models more realistic than the conventional ones by taking into account the detailed dynamics of axons, synapses and dendrites, allowing rather arbitrary couplings between neurons. He gives a complete stabile analysis that goes significantly beyond what has been known so far. He also derives pulse-averaged equations including those of the Wilson-Cowan and the Jirsa-Haken-Nunez types and discusses the formation of spatio-temporal neuronal activity pattems. An analysis of phase locking via sinusoidal couplings leading to various kinds of movement coordination is included.
Basic Training in Mathematics: A Fitness Program for Science Students
Springer; 1 edition | ISBN: 0306450356 | 388 pages | June 30, 1995 | djvu | 4 Mb
Entering a program in the physical sciences?
A high school student who has taken most of the offered courses, and looking for a glimpse of college mathematics?
Engaged in self-study to hone your mathematical skills?
Then R. Shankar’s Basic Training in Mathematics: A Fitness Program for Science Students is written for you. Based on the author’s course at Yale University, the book addresses the widening gap found by Professor Shankar and his colleagues between the mathematics needed for upper-level science study and the knowledge possessed by incoming students.
This superb text organizes the necessary mathematics background into a one-semester course covering such topics as:
- A review of calculus
- Infinite series
- Functions of a complex variable
- Vector calculus
- Linear vector spaces
- Differential equations
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Morris W. Hirsch, Stephen Smale, Robert Devaney, “Differential Equations, Dynamical Systems, and an Introduction to Chaos”
Academic Press; 2 edition | ISBN:0123497035 | 425 pages | PDF | 2,9 Mb
“The exposition is excellent. I particularly liked how the proofs are fairly easy to follow…a readable and informative text.” - Gareth Roberts, Holy Cross
“..from three mathematicians who are…among the world’s most prominent experts in dynamical systems…[and] the world’s best mathematical expositors.”
- Bruce Peckham, University of Minnesota
” (…) a standard on mathematical bookshelves (…). Readers familiar with the first edition will find much that is familiar, but with an increased emphasis on the behaviour of families of solutions”. Annalisa Cranell, MAA Online, Feb 2005
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S.D. Iliadis, ” Universal Spaces and Mappings, Volume 198 (North-Holland Mathematics Studies)”
North Holland; 1 edition (March 8, 2005) | ISBN: 0444515860 | 575 pages | Djvu | 3,3 Mb
The book is devoted to universality problems.
A new approach to these problems is given using some specific spaces. Since the construction of these specific spaces is set-theoretical, the given theory can be applied to different topics of Topology such as:
universal mappings, dimension theory, action of groups, inverse spectra, isometrical embeddings, and so on.
· Universal spaces
· Universal mappings
· Dimension theory
· Actions of groups
· Isometric Universal Spaces
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