May 13, 2020 Forthcoming
Textbook - 568 Pages - 3 B/W Illustrations
ISBN 9781138583610 - CAT# K376897
The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekindfs ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of differents, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse -Weil theorem represent the culminating point of the volume.
The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and it is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory.
A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal- and valuation-theoretic basis.
Several of the topics both in the number field and in the function field case were not presented before in this context.
Despite the wealth of presented advanced topics the text is easily readable.
Topological groups and infinite Galois theory. Cohomology of groups. Simple algebras. Local class field theory. Idels and holomorphy domains in global fields. Global class field theory. Artin L functions
May 12, 2020 Forthcoming
Textbook - 499 Pages - 13 B/W Illustrations
ISBN 9781138055117 - CAT# K33235
Basic Analysis IV: Measure Theory and Integration introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides.
* Can be used as a traditional textbook as well as for self-study
* Suitable for advanced students in mathematics and associated disciplines
* Emphasises learning how to understand the consequences of assumptions
using a variety of tools to provide the proofs of propositions
1.Introduction 2.An Overview Of Riemann Integration 3.Functions Of Bounded Variation 4.The Theory Of Riemann Integration 5.Further Riemann Integration Results 6.The Riemann-Stieltjes Integral 7.Further Riemann - Stieljes Results 8.Measurable Functions and Spaces 9.Measure And Integration 10.The Lp Spaces11.Constructing Measures 12.Lebesgue Measure 13.Cantor Set Experiments 14.Lebesgue Stieljes Measure 15.Modes Of Convergence 16. Decomposition Of Measures 17.Connections To Riemann Integration 18.Fubini Type Results 19.Differentiation 20.Summing It All Up. References. Index. Appendix A. Appendix B. Appendix C. Appendix D
This carefully-designed book covers multivariable and vector calculus, and is
appropriate either as a text of a one-semester course, or for self-study. It includes
many worked-through exercises, with answers to many of the basic
computational ones and hints to many of those that are more involved, as well as
lots of diagrams which illustrate the various theoretical concepts.
A detailed presentation of multivariable and vector calculus, ideal as course
material or for self study
Includes many exercises and diagrams
Of interest to students and lecturers alike
Joseph D. Fehribach, Worcester Polytechnic Institute, USA.
De Gruyter Textbook xiv, 165 pages, 20 Figures (bw), 50 Figures (c)
Paperback:
ISBN 978-3-11-066020-3
Language of Publication: English
Subjects: Analysis General Mathematics
Of interest to: Students and lecturers in mathematic
Concentration compactness methods are applied to PDE's that lack compactness
properties, typically due to the scaling invariance of the underlying problem.
This monograph presents a systematic functional-analytic presentation of
concentration mechanisms and is by far the most extensive and systematic
collection of mathematical tools for analyzing the convergence of functional
sequences via the mechanism of concentration.
A comprehensive monograph on the state of the art of concentration
compactness techniques
Summary of the last ten years of research on the topic
An authoritative overview of many deep results in modern functional analysis
Cyril Tintarev, Uppsala University, Sweden.
De Gruyter Series in Nonlinear Analysis and Applications 33
Approx. xii, 200 pages
Hardcover:
ISBN 978-3-11-053034-6
Date of Publication: February 2020
Language of Publication: English
Subjects: Analysis
Differential Equations and Dynamical Systems
Of interest to: Researchers and graduate students in mathematical analys
This book is a concise yet complete calculus textbook covering all essential
topics in multi-variable calculus, including geometry in three-dimensional space,
partial derivatives, maximum/minimum, multiple integrals and vector calculus
as well as a chapter for ODE. All the chapters are constructed in a logical way to
outline the essence of each topic and to address potential difficulties arising
from learning.
Covering key contents in multi-variable calculus in a concise way.
Providing a summary for each chapter.
Including exercises at the end of each chapter.
Adapting to students' learning behaviors.
Yinzhu Zou, Sichuan University, Chengdu, China
De Gruyter Textbook
Approx. x, 300 pages, 3 Figures (bw), 124 Figures (c)
Paperback:
ISBN 978-3-11-067414-9
Date of Publication: March 2020
Language of Publication: English
Subjects: Analysis
Of interest to: Students and lecturers in mathematics, physics and engineer
Documenta Mathematiques Volume: 17
2019; 630 pp; Softcover
MSC: Primary 55; 57; 14; 32;
Print ISBN: 978-2-85629-888-6
A note to readers: This book is in French.
This second volume of Rene Thom's complete mathematical works contains the 1959 Bonn lectures on singularities and the articles published between 1962 and 1971, together with previously unpublished texts and comments putting all into perspective. This includes Thom's impressive contribution to the topological classification of singularities of smooth maps and to the theory of stratified sets.
This volume, which also contains articles about the founding of catastrophe theory, begins with a bibliography of Thom's mathematical and nonmathematical works.
Graduate students and research mathematicians.