Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 131 (1989), No. 1

Fractals in Geophysics

Science & Math

Scholz, Christopher

Mathematics

Birkhäuser Boston

Variability in Response to Anti-Rheumatic Drugs (Agents & Actions Supplements)

Brooks, Peter

Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. 
Measure Theory provides a solid background for study in both harmonic analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are courses in topology and analysis.

Measure Theory

Donald L. Cohn

Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate.

Topics from the Theory of Numbers

Emil Grosswald

It has been estimated that, at the present stage of our knowledge, one could give a 200 semester course on commutative algebra and algebraic geometry without ever repeating himself. So any introduction to this subject must be highly selective. I first want to indicate what point of view guided the selection of material for this book. This introduction arose from lectures for students who had taken a basic course in algebra and could therefore be presumed to have a knowledge of linear algebra, ring and field theory, and Galois theory. The present text shouldn't require much more. In the lectures and in this text I have undertaken with the fewest possible auxiliary means to lead up to some recent results of commutative algebra and algebraic geometry concerning the representation of algebraic varieties as in tersections of the least possible number of hypersurfaces and- a closely related problem-with the most economical generation of ideals in Noetherian rings. The question of the equations needed to describe an algebraic variety was addressed by Kronecker in 1882. In the 1940s it was chiefly Perron who was interested in this question; his discussions with Severi made the problem known and contributed to sharpening the rei event concepts. Thanks to the general progress of commutative algebra many beautiful results in this circle of questions have been obtained, mainly after the solution of Serre's problem on projective modules. Because of their relatively elementary character they are especially suitable for an introduction to commutative algebra.

Introduction to Commutative Algebra and Algebraic Geometry

Ernst Kunz

Combinatorics and Commutative Algebra (Progress in Mathematics)

Stanley, R.P.

This book presents a historical overview of number theory. It examines texts that span some thirty-six centuries of arithmetical work, from an Old Babylonian tablet to Legendre’s Essai sur la Théorie des Nombres, written in 1798. Coverage employs a historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. The book also takes the reader into the workshops of four major authors of modern number theory: Fermat, Euler, Lagrange and Legendre and presents a detailed and critical examination of their work.

Number Theory: An approach through history From Hammurapi to Legendre

André Weil

History & Philosophy

Inner Exile: Recollections of a Life With Werner Heisenberg

Elisabeth Heisenberg

Physics

The central subject matter of this book is Einstein's special theory of relativiry. While it is a book that is written primarily for a lay audience this does not necessarily mean an audience not versed in the ways of doing science. Rather, this book is written for anyone wishing to consider the nature of the scientific enterprise: where ideas come from, how they become established and accepted, what the relationships are among theories, predictions, and measurements, or the relationship between ideas in a scientific theory and the values held to be important within the larger culture. Some readers will find it strange that I raise any of these issues. It is a common view in our culture that the status of knowledge within science is totally different from the status of knowledge in other areas of human endeavor. The word "science" stems from the Latin word meaning "to know" and indeed, knowledge which scientists acquire in their work is commonly held to be certain, unyielding, and absolute. Consider how we use the adjective "scientific. " There are investors and there are scientific investors. There are socialists and there are scientific socialists. There are exterminators and there are scientific exterminators. We all know how the modifier "scientific" inttudes in our daily life. It is the purpose of this book to challenge the belief that scientific knowledge is different from other kinds of knowledge.

Understanding Relativity: Origin and Impact of a Scientific Revolution

GOLDBERG

The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].

Minimal Surfaces and Functions of Bounded Variation (Monographs in Mathematics, 80)

Giusti, Enrico

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