Mathematics

Algebraic Geometry

An Introduction

Author: Daniel Perrin

Publisher: Springer Science & Business Media

ISBN: 9781848000568

Category: Mathematics

Page: 263

View: 3616

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.
Mathematics

Complex Geometry

An Introduction

Author: Daniel Huybrechts

Publisher: Springer Science & Business Media

ISBN: 3540266879

Category: Mathematics

Page: 309

View: 2778

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)
Mathematics

Algebraic Geometry

A Concise Dictionary

Author: Elena Rubei

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110316234

Category: Mathematics

Page: 239

View: 8748

Algebraic geometry has a complicated, difficult language. This book contains a definition, several references and the statements of the main theorems (without proofs) for every of the most common words in this subject. Some terms of related subjects are included. It helps beginners that know some, but not all, basic facts of algebraic geometry to follow seminars and to read papers. The dictionary form makes it easy and quick to consult.
Mathematics

Algebraic Geometry

A Problem Solving Approach

Author: Thomas A. Garrity

Publisher: American Mathematical Soc.

ISBN: 0821893963

Category: Mathematics

Page: 335

View: 3917

Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex
Mathematics

Algebra

Author: Siegfried Bosch

Publisher: Springer-Verlag

ISBN: 3642395678

Category: Mathematics

Page: 370

View: 8765

Eine verständliche, konzise und immer flüssige Einführung in die Algebra, die insbesondere durch ihre sorgfältige didaktische Aufbereitung bei vielen Studierenden Freunde findet. Die vorliegende Auflage bietet neben zahlreichen Aufgaben (mit Lösungshinweisen) sowie einführenden und motivierenden Vorbemerkungen auch Ausblicke auf neuere Entwicklungen. Auch selten im Lehrbuch behandelte Themen wie Resultanten, Diskriminanten, Kummer-Theorie und Witt-Vektoren werden angesprochen. Die berühmten Formeln aus dem 16. Jahrhundert zur Auflösung von Gleichungen dritten und vierten Grades werden ausführlich erläutert und in den Rahmen der Galois-Theorie eingeordnet. Ein klares, modernes und inhaltsreiches Lehrbuch, das für das Studium der Algebra unentbehrlich ist.
Mathematics

An Invitation to Algebraic Geometry

Author: Karen E. Smith,Lauri Kahanpää,Pekka Kekäläinen,William Traves

Publisher: Springer Science & Business Media

ISBN: 1475744978

Category: Mathematics

Page: 164

View: 8756

This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.
Mathematics

An Introduction to Algebraic Topology

Author: Joseph Rotman

Publisher: Springer Science & Business Media

ISBN: 9780387966786

Category: Mathematics

Page: 438

View: 7565

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.
Mathematics

An Introduction to Manifolds

Author: Loring W. Tu

Publisher: Springer Science & Business Media

ISBN: 1441974008

Category: Mathematics

Page: 410

View: 7819

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Mathematics

Vorlesungen Über die Zahlentheorie der Quaternionen

Author: Adolf Hurwitz

Publisher: Springer-Verlag

ISBN: 3642475361

Category: Mathematics

Page: 76

View: 4929

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Mathematics

An Algebraic Introduction to Complex Projective Geometry

Commutative Algebra

Author: Christian Peskine,Peskine Christian

Publisher: Cambridge University Press

ISBN: 9780521480727

Category: Mathematics

Page: 244

View: 7916

In this introduction to commutative algebra, the author choses a route that leads the reader through the essential ideas, without getting embroiled in technicalities. He takes the reader quickly to the fundamentals of complex projective geometry, requiring only a basic knowledge of linear and multilinear algebra and some elementary group theory. The author divides the book into three parts. In the first, he develops the general theory of noetherian rings and modules. He includes a certain amount of homological algebra, and he emphasizes rings and modules of fractions as preparation for working with sheaves. In the second part, he discusses polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalization lemma and Hilbert's Nullstellensatz, the author introduces affine complex schemes and their morphisms; he then proves Zariski's main theorem and Chevalley's semi-continuity theorem. Finally, the author's detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.
Mathematics

Quod erat knobelandum

Themen, Aufgaben und Lösungen des Schülerzirkels Mathematik der Universität Regensburg

Author: Clara Löh,Stefan Krauss,Niki Kilbertus

Publisher: Springer-Verlag

ISBN: 3662489562

Category: Mathematics

Page: 279

View: 9947

Fünfzehn ausgewählte mathematische Themen mit Aufgaben und Lösungen laden zum Entdecken und Knobeln ein und bieten Einblicke in die faszinierende Welt der Mathematik - von A wie Aussagenlogik bis Z wie Zahlentheorie. Die Themen wecken so die Neugierde für Mathematik und fördern die Begeisterung von Schülerinnen und Schülern ab Klasse 7. Anleitungen zum mathematischen Problemlösen und Beweisen erleichtern dabei den Einstieg. Das vorliegende Buch enthält das überarbeitete und ergänzte Material des Schülerzirkels Mathematik der Fakultät für Mathematik an der Universität Regensburg aus den Schuljahren 2012/13 bis 2014/15. Stimme zum Buch: "Es ist erfreulich, dass die Aufgaben und Lösungen aus dem Schülerzirkel Mathematik der Universität Regensburg einem breiten Leserkreis zur Verfügung gestellt werden. Die Verbindung von pfiffigen Knobelaufgaben als Einstieg in ein Thema mit der Vermittlung des mathematischen Hintergrundwissens wird sicher vielen Schülerinnen und Schülern den Weg in die Welt der Mathematik ebnen." Hanns-Heinrich Langmann, Projektleiter Bundesweite Mathematik-Wettbewerbe bei Bildung & Begabung
Mathematics

Compact Riemann Surfaces

An Introduction to Contemporary Mathematics

Author: Jürgen Jost

Publisher: Springer Science & Business Media

ISBN: 3662034468

Category: Mathematics

Page: 295

View: 6852

This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

A Course on Rough Paths

With an Introduction to Regularity Structures

Author: Peter K. Friz,Martin Hairer

Publisher: N.A

ISBN: 9783319083339

Category:

Page: 268

View: 4841

Mathematics

Higher-Dimensional Algebraic Geometry

Author: Olivier Debarre

Publisher: Springer Science & Business Media

ISBN: 9780387952277

Category: Mathematics

Page: 234

View: 4371

The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authors goal is to provide an easily accessible introduction to the subject. The book starts with preparatory and standard definitions and results, then moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Moris minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction.
Technology & Engineering

Geometrische Methoden in der Invariantentheorie

Author: Hanspeter Kraft

Publisher: Springer-Verlag

ISBN: 3663101436

Category: Technology & Engineering

Page: 308

View: 5801

In dieser Einführung geht es vor allem um die geometrischen Aspekte der Invariantentheorie. Die hauptsächliche Motivation bildet das Studium von Klassifikations- und Normalformenproblemen, die auch historisch der Ausgangspunkt für invariantentheoretische Untersuchungen waren.