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Introductory Notes On Valuation Rings And Function Fields In One Variable
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Book Synopsis Introductory Notes on Valuation Rings and Function Fields in One Variable by : Renata Scognamillo
Download or read book Introductory Notes on Valuation Rings and Function Fields in One Variable written by Renata Scognamillo and published by Springer. This book was released on 2014-07-01 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with the (elementary and introductory) theory of valuation rings. As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. The correspondences of this with other viewpoints (e.g. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results. Links with arithmetic are also often indicated. There are three appendices, concerning Hilbert’s Nullstellensatz (for which several proofs are provided), Puiseux series and Dedekind domains. There are also several exercises, often accompanied by hints, which sometimes develop further results not included in full for brevity reasons.
Book Synopsis Lectures on Elliptic Partial Differential Equations by : Luigi Ambrosio
Download or read book Lectures on Elliptic Partial Differential Equations written by Luigi Ambrosio and published by Springer. This book was released on 2019-01-10 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.
Book Synopsis Transcriptome Analysis by : Alessandro Cellerino
Download or read book Transcriptome Analysis written by Alessandro Cellerino and published by Springer. This book was released on 2018-06-14 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to be an accessible guide for undergraduate and graduate students to the new field of data-driven biology. Next-generation sequencing technologies have put genome-scale analysis of gene expression into the standard toolbox of experimental biologists. Yet, biological interpretation of high-dimensional data is made difficult by the lack of a common language between experimental and data scientists. By combining theory with practical examples of how specific tools were used to obtain novel insights in biology, particularly in the neurosciences, the book intends to teach students how to design, analyse, and extract biological knowledge from transcriptome sequencing experiments. Undergraduate and graduate students in biomedical and quantitative sciences will benefit from this text as well as academics untrained in the subject.
Book Synopsis Symmetry Breaking in the Standard Model by : Franco Strocchi
Download or read book Symmetry Breaking in the Standard Model written by Franco Strocchi and published by Springer. This book was released on 2019-07-03 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a non-perturbative approach to the symmetry breaking in the standard model, in this way avoiding the critical issues which affect the standard presentations. The debated empirical meaning of global and local gauge symmetries is clarified. The absence of Goldstone bosons in the Higgs mechanism is non-perturbatively explained by the validity of Gauss laws obeyed by the currents which generate the relatedglobal gauge symmetry. The solution of the U(1) problem and the vacuum structure in quantum chromodynamics (QCD) are obtained without recourse to the problematic semiclassical instanton approximation, by rather exploiting the topology of the gauge group.
Book Synopsis Interpolation Theory by : Alessandra Lunardi
Download or read book Interpolation Theory written by Alessandra Lunardi and published by Springer. This book was released on 2018-05-05 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.
Book Synopsis Fractional Elliptic Problems with Critical Growth in the Whole of $\R^n$ by : Serena Dipierro
Download or read book Fractional Elliptic Problems with Critical Growth in the Whole of $\R^n$ written by Serena Dipierro and published by Springer. This book was released on 2017-03-14 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary. The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.
Book Synopsis Valued Fields by : Antonio J. Engler
Download or read book Valued Fields written by Antonio J. Engler and published by Springer Science & Business Media. This book was released on 2005-12-28 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.
Book Synopsis Algebraic Numbers and Algebraic Functions by : P.M. Cohn
Download or read book Algebraic Numbers and Algebraic Functions written by P.M. Cohn and published by CRC Press. This book was released on 2018-01-18 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.
Book Synopsis Lecture Notes Series by : Aarhus universitet. Matematisk institut
Download or read book Lecture Notes Series written by Aarhus universitet. Matematisk institut and published by . This book was released on 2001 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Closure of Ideals, Rings, and Modules by : Craig Huneke
Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Book Synopsis Algebraic Curves by : William Fulton
Download or read book Algebraic Curves written by William Fulton and published by . This book was released on 2008 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these notes is to develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideals and polynomials, such as is often covered in a one-semester course in modern algebra; additional commutative algebra is developed in later sections.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1078 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Numbers and Algebraic Functions by : Emil Artin
Download or read book Algebraic Numbers and Algebraic Functions written by Emil Artin and published by CRC Press. This book was released on 1967 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometrie algebrique reelle et formes quadratiques by : J.-L. Colliot-Thelene
Download or read book Geometrie algebrique reelle et formes quadratiques written by J.-L. Colliot-Thelene and published by Springer. This book was released on 2006-11-15 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction To Commutative Algebra by : Michael F. Atiyah
Download or read book Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.
Download or read book Simon Stevin written by and published by . This book was released on 1992 with total page 938 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Commutative Rings and Their Applications by : Gilberto Bini
Download or read book Finite Commutative Rings and Their Applications written by Gilberto Bini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.
