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Handbook of Geometry and Topology of
Singularities VIII

Handbook of Geometry and Topology of Singularities VIII

Eine Einführung in moderne Verfahren. Mit MATLAB®-Implementierungen von C. Vömel

Numerik linearer Gleichungssysteme

Dieses sorgfältig verfasste Lehrbuch bietet eine zugängliche Einführung in die Darstellungstheorie von Algebren, einschließlich Darstellungen von Köchern.Das Buch beginnt mit grundlegenden Themen zu Algebren und Moduln und behandelt fundamentale Ergebnisse wie den Satz von Jordan-Hölder über Kompositionsreihen, den Satz von Artin-Wedderburn über die Struktur halbeinfacher Algebren und den Satz von Krull-Schmidt über unzerlegbare Moduln. Die Autoren behandeln anschließend detailliert Darstellungen von Köchern bis hin zu einem vollständigen Beweis von Gabriels berühmtem Satz, der die Darstellungstypen von Köchern anhand von Dynkin-Diagrammen charakterisiert.Das Lehrbuch benötigt nur Grundkenntnisse über lineare Algebra sowie Gruppen, Ringe und Körper und richtet sich an Studierende ab dem dritten Studienjahr. Mit zahlreichen Beispielen, die abstrakte Konzepte veranschaulichen, und mehr als 200 Übungen (mit Lösungen zu etwa einem Drittel davon), bietet das Buch eine beispielorientierte Einführung, die sich sowohl für das Selbststudium als auch zur Begleitung von Vorlesungen eignet.

Algebren und Darstellungstheorie

Als Spezialangebot erhalten Sie «Formeln» (ISBN 978-3-0355-1392-9) und «Algebra» (ISBN 978-3-0355-2814-5) als Paket zum Sonderpreis von CHF 83.– (statt CHF 90.–).&nbsp;

Spezialangebot «Formeln» und «Algebra»

VON NULL AUF MATHE

Auf geradem Weg: lineare Gleichungen und Funktionen

This book deals with the problem of bounding numerical invariants of nonsingular projective algebraic varieties from a unified point of view. Starting with a new insightful proof of the Castelnuovo theorem, the author proceeds with giving (sharp) bounds for basic numerical invariants (such as Betti, Hodge, and Chern numbers) of algebraic varieties of arbitrary dimension and classifying the varieties on the boundary. Many important results are proved in several different ways underlining different aspects of the topic. However, studying numerical invariants is just a pretext for the exploration of the rich and versatile interplay between geometry and topology of projective algebraic varieties which forms the core of the book. A special role in this study is played by the dual varieties and their degrees classically called classes. While making an extensive use of Lefschetz theory (which is now also available for varieties over an algebraically closed field of positive characteristic), the author also develops a new variant of Morse theory which yields statements (including bounds) on the level of CW-complexes and provides bounds for the homology of real algebraic varieties. In this way one also gets stronger forms of some classical results on the topology of projective varieties, such as weak and hard Lefschetz theorems, Hopf type formula etc. A detailed outline of the exciting centennial history of this topic and a list of intriguing open problems contribute to the value of the book. The exposition is accessible to students with only basic knowledge of algebraic geometry and topology.

Bounding Numerical Invariants Of Algebraic Varieties

This textbook has been designed to support the initial study of Complex Analysis, progressing to Complex Dynamics. It focuses on the fundamental aspects of one-variable complex functions, covering the geometric theory and dynamics of iterations of rational mappings. Following the standard material, the book delves into an extensive range of advanced topics, encompassing the requirements for a one-year graduate-level course or a preliminary exam.In this work, the reader will discover three distinctive characteristics: it simplifies and unifies ideas and concepts that might appear disparate or complicated in real analysis; it contributes to the development of other areas in mathematics; and it showcases relevance for applications in Science and Engineering, with many exercises. Historical notes throughout the text help to contextualize the theory.With its flexible structure, this textbook provides a solid foundation for a first course in Complex Analysis and for a second more advanced course, establishing a robust basis for subsequent studies.

Complex Analysis and Dynamics in One Variable with Applications

Princeton Mathematical Series

"A natural question that sits at the nexus of algebraic geometry, differential geometry, and geometric group theory is: which groups can be realized as fundamental groups of compact Kèahler manifolds, called "Kèahler groups"? Roughly speaking, the fundamental group of a manifold measures the number of "holes." Many restrictions are known, and many examples are known; but mathematicians are far from having a precise conjecture about which groups are Kèahler. The question serves as a fruitful connection between several major areas of geometry and complex analysis. Py's book is an up-to-date pedagogical survey of the central theorems and methods for the study of Kèahler groups including, where illuminating, detailed proofs. It includes results of Gromov, Schoen, Napier, Ramachandran, Corlette, Simpson, Delzant, Arapura, and Nori. The charm of the subject is that different methods yield information of different flavors, and the challenge is to draw these threads together. This book leans toward geometric group theory, but it gives a coherent account of great value to anyone interested in Kèahler groups - and in Kèahler manifolds more broadly. The emphasis is on unity and cross-fertilization among approaches"--

An introduction to the state of the art in the study of Kähler groups This book gives an authoritative and up-to-date introduction to the study of fundamental groups of compact Kähler manifolds, known as Kähler groups. Approaching the subject from the perspective of a geometric group theorist, Pierre Py equips readers with the necessary background in both geometric group theory and Kähler geometry, covering topics such as the actions of Kähler groups on spaces of nonpositive curvature, the large-scale geometry of infinite covering spaces of compact Kähler manifolds, and the topology of level sets of pluriharmonic functions. Presenting the most important results from the past three decades, the book provides graduate students and researchers with detailed original proofs of several central theorems, including Gromov and Schoen’s description of Kähler group actions on trees; the study of solvable quotients of Kähler groups following the works of Arapura, Beauville, Campana, Delzant, and Nori; and Napier and Ramachandran’s work characterizing covering spaces of compact Kähler manifolds having many ends. It also describes without proof many of the recent breakthroughs in the field. Lectures on Kähler Groups also gives, in eight appendixes, detailed introductions to such topics as the study of ends of groups and spaces, groups acting on trees and Hilbert spaces, potential theory, and L2 cohomology on Riemannian manifolds.

Lectures on Kähler Groups

Science Networks. Historical Studies

Volume I: A-I

A Historical Dictionary of Mathematical Terms

An accessible, motivated introduction to one of the most dynamic areas of mathematicsDecades ago, Mumford wrote that algebraic geometry "seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics." The revolution has now fully come to pass and has fundamentally changed how we think about many fields of mathematics. This book provides a thorough foundation in the powerful ideas that now shape the landscape, with an informal yet rigorous exposition that builds intuition for the formidable machinery. It begins with a discussion of categorical thinking and sheaves and then develops the notion of schemes and varieties as examples of "geometric spaces" before discussing their specific aspects. The book goes on to cover topics such as dimension and smoothness, vector bundles and their natural generalizations, and important cohomological tools and their applications. Important optional topics are included in starred sections. A comprehensive introduction certain to become the standard book on the subjectFeatures a wealth of exercises that enable students to learn by doingRequires few prerequisites, developing the tools students need to succeed, from category theory and sheaf theory to commutative and homological algebraUses an example-driven approach that builds mathematical intuitionA self-contained textbook for graduate students and an essential reference for researchers

Foundations of Algebraic Geometry

The Rising Sea

Cambridge Monographs on Applied and Computational Mathematics

Cubature rules are indispensable tools in scientific computing and applied sciences whenever evaluating or discretizing integrals is needed. This monograph is the first comprehensive resource devoted to cubature rules in English since Stroud's classic 1971 book, and the first book about minimal cubature rules. The book explores the subject's theoretical side, which intersects with many branches of mathematics. Minimal cubature rules are intimately connected with common zeros of orthogonal polynomials, which can be described via the polynomial ideals and varieties. Many prominent or practical cubature rules are invariant under a finite group, and some involve symmetric functions and the discrete Fourier transform. Based on state-of-the-art research, the book systematically studies Gauss and minimal cubature rules, and includes a chapter on the practical aspects of construction cubature rules on triangles and simplexes. This comprehensive guide is ideal for researchers and advanced graduate students across the computational and applied mathematics community.

Theory and Practice

Minimal Cubature Rules

Synthesis Lectures on Mathematics & Statistics

Advanced Fractional Dynamic Equations on Time Scales

Boundary Value Problems

This book presents in-depth explanations of well-known and recognized behaviors of neural networks in machine learning.&nbsp; In addition, the author provides novel technical analyses of behaviors of discrete-time dynamical systems modeled as difference equations. &nbsp;These analyses and their outcomes are closely related to models of very well-known neural networks such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) neural networks, which are widely used in machine learning and artificial intelligence (AI) applications.&nbsp; The author also discusses difference equations and their relevance to neural networks, machine learning, and AI.
&nbsp;In addition, this book:
<ul>
<li>Includes characterizations of difference equations and technical prospectives of discrete-time systems</li>
<li>Provides new insights into the dynamical behaviors of some of the most popular neural networks used in machine learning</li>
<li>Discusses novel technical analyses of discrete-time dynamical systems modeled as difference equations</li>
</ul>

Difference Equations and Machine Learning

Handbook of Geometry and Topology of Singularities VIII

Weitere Titel zum Thema