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Classical Theory of Algebraic Numbers
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's …
Basic Theory of Ordinary Differential Equations
The authors' aim is to provide the reader with the very basic knowledge necessary to begin research on differential equations with professional ability. The selection of topics …
The Calculus of Variations
The calculus of variations has a long history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly …
Intuitive Combinatorial Topology
Topology is a relatively young and very important branch of mathematics. It studies properties of objects that are preserved by deformations, twistings, and stretchings, but not …
Introduction to the Mori Program
Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational classification of higher dimensional algebraic …
Algebraic Topology from a Homotopical Viewpoint
The authors present introductory material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This carefully written book can be read by any …
Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli
"Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between …
Lectures on Analysis on Metric Spaces
Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. In particular, there have been important advances in …
An Introduction to Semiclassical and Microlocal Analysis
The following lecture notes correspond to a course taught for several years, first at the University of Paris-Nord (France) and then at the University of Bologna (Italy). They are …
Fourier and Wavelet Analysis
globalized Fejer's theorem; he showed that the Fourier series for any f E Ld-7I", 7I"] converges (C, 1) to f (t) a.e. The desire to do this was part of the reason that Lebesgue …
An Invitation to Algebraic Geometry
The aim of this book is to describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that …
A Course in Model Theory
Can we reproduce the inimitable, or give a new life to what has been af fected by the weariness of existence? Folks, what you have in your hands is a translation into English of a …