By Reinhold Remmert
Diese dritte Auflage wurde zusammen mit dem zweitgenannten Autor kritisch durchgesehen, ergänzt und verbessert. Ein weiteres Kapitel über geometrische Funktionentheorie und schlichte Funktionen enthält einen Beweis der Bieberbachschen Vermutung.
"Der ... vorliegende zweite Band der Funktionentheorie erfüllt voll die Erwartungen, die der erste Band geweckt hat. Wieder beeindrucken vor allem die hochinteressanten historischen Bemerkungen zu den einzelnen Themenkreisen, als besonderer Leckerbissen wird das Gutachten von Gauß über Riemanns Dissertation vorgestellt... Jedes einzelne Kapitel enthält ausführliche Literaturangaben. Ferner werden oft sehr aufschlussreiche Hinweise auf die Funktionentheorie mehrerer Veränderlicher gegeben. Die vielen Beispiele und Übungsaufgaben bilden eine wertvolle Ergänzung der brillant dargelegten Theorie. Der Rezensent bedauert, dass ihm nicht schon als pupil ein derartig umfassendes, qualitativ hochstehendes Lehrbuch zur Verfügung stand."
Monatshefte für Mathematik
By Michel Coornaert
Translated from the preferred French version, the objective of the publication is to supply a self-contained advent to intend topological measurement, an invariant of dynamical platforms brought in 1999 by way of Misha Gromov. The ebook examines how this invariant used to be effectively utilized by Elon Lindenstrauss and Benjamin Weiss to respond to a long-standing open query approximately embeddings of minimum dynamical structures into shifts.
A huge variety of revisions and additions were made to the unique textual content. bankruptcy five comprises a wholly new part dedicated to the Sorgenfrey line. chapters have additionally been extra: bankruptcy nine on amenable teams and bankruptcy 10 on suggest topological size for non-stop activities of countable amenable teams. those new chapters comprise fabric that experience by no means ahead of seemed in textbook shape. The bankruptcy on amenable teams relies on Følner’s characterization of amenability and should be learn independently from the remainder of the book.
Although the contents of this booklet lead on to numerous energetic components of present examine in arithmetic and mathematical physics, the necessities wanted for interpreting it stay modest; primarily a few familiarities with undergraduate point-set topology and, with a view to entry the ultimate chapters, a few acquaintance with uncomplicated notions in crew concept. Topological size and Dynamical Systems is meant for graduate scholars, in addition to researchers drawn to topology and dynamical platforms. many of the subject matters taken care of within the booklet at once result in learn components that stay to be explored.
By Uri Kirsch (auth.), Prof. Martin Philip Bendsøe, Prof. Carlos A. Mota Soares (eds.)
The effective use of fabrics is of significant significance, and the alternative of the fundamental topology for the layout of buildings and mechanical components is important for the functionality of sizing of form optimization.
This quantity offers a accomplished assessment of the cutting-edge in topology layout, spanning basic mathematical, mechanical and implementation matters. Topology layout of discrete constructions consists of huge scale computational difficulties and the necessity to pick out structural parts from a discrete set of percentages. The formula and resolution of discrete layout difficulties are defined, together with new purposes of genetic algorithms and twin equipment. For continuum difficulties the emphasis is at the `homogenization method', which employs composite fabrics because the foundation for outlining form by way of fabric density, unifying macroscopic structural layout optimization and micromechanics. All elements of this box are coated, together with computational features and using the homogenization strategy in a computer-aided layout setting.
By Marcelo Aguilar, Samuel Gitler, Carlos Prieto
The authors current introductory fabric in algebraic topology from a unique perspective in utilizing a homotopy-theoretic strategy. This conscientiously written e-book could be learn through any pupil who is familiar with a few topology, supplying an invaluable strategy to quick research this novel homotopy-theoretic viewpoint of algebraic topology.
From the reviews:
"This is a easy direction on algebraic topology and … it really is excellently written and composed and will be strongly instructed to anyone wishing to profit the sector. The reader can locate many examples, calculations, and likewise a few routines. … The publication has appendices, … references together with eighty three goods and an extended checklist of symbols. there are various comments and reviews making the orientation of the reader within the box of algebraic topology more straightforward … ." (EMS, June, 2004)
"The modus operandi of algebraic topology is to affiliate algebraic invariants, resembling teams or jewelry, to a topological area in this kind of means that identical areas express isomorphic invariants; the following, ‘equivalent’ can be selected to slot the geometry of the matter. during this ebook, ‘equivalent’ ability homotopy identical … . For its readability and directness, a welcome boost to complex arithmetic collections. Upper-division undergraduates via faculty." (J. McCleary, selection, December, 2002)
"The function of this e-book is to introduce algebraic topology utilizing the radical procedure of homotopy thought … . the elemental thoughts of homotopy concept … are used to build singular homology and cohomology, in addition to K-theory. … during the textual content many different basic options are brought … ." (L’Enseignement Mathematique, Vol. forty eight (3-4), 2002)
“The publication of Aguilar, Gitler and Prieto supplies an attractive new strategy for a primary path in algebraic topology. … what's additionally very fascinating is the truth that the ebook includes a exact presentation of a few deep result of algebraic topology no longer often coated by way of a primary ebook in algebraic topology … . The textual content is thoroughly good written. … the scholar in algebraic topology will locate within the e-book loads of attention-grabbing well-exposed material.” (Yves Félix, Bulletin of the Belgian Mathematical Society, 2007)
From the again Cover
The function of this publication is to introduce algebraic topology utilizing the unconventional strategy of homotopy thought, an procedure with transparent purposes in algebraic geometry as understood via Lawson and Voevodsky. this technique permits the authors to hide the fabric extra successfully than the extra universal strategy utilizing homological algebra. the elemental thoughts of homotopy thought, equivalent to fibrations and cofibrations, are used to build singular homology and cohomology, in addition to K-theory. in the course of the textual content many different primary options are brought, together with the development of the attribute periods of vector bundles. even supposing functors look regularly through the textual content, no wisdom approximately type concept is anticipated from the reader. This e-book is meant for complex undergraduates and graduate scholars with a simple wisdom of aspect set topology in addition to workforce thought and will be utilized in a semester course.
Marcelo Aguilar and Carlos Prieto are Professors on the Instituto de Matemticas, Universidad Nacional Autónoma de México, and Samuel Gitler is a member of El Colegio Nacional and professor on the Centro de Investigación y Estudios Avanzados del IPN.
By Albert Wilansky
Beginning with the 1st ideas of topology, this quantity advances to normal research. 3 degrees of examples and difficulties make it applicable for college students and execs. ample routines, ordered and numbered through measure of hassle, illustrate very important ideas, and a 40-page appendix comprises tables of theorems and counterexamples. 1970 version.
By S.Dale Cutkosky, Dan Edidin, Zhenbo Qin, Qi Zhang
This quantity comprises thirteen papers from the convention on 'Hilbert Schemes, Vector Bundles and Their interaction with illustration Theory'. The papers are written by way of top mathematicians in algebraic geometry and illustration idea and current the most recent advancements within the box. between different contributions, the amount comprises a number of very notable and chic theorems in illustration concept by way of R. Friedman and J. W. Morgan, convolution on homology teams of moduli areas of sheaves on K3 surfaces via H. Nakajima, and computation of the $S^1$ fastened issues in Quot-schemes and reflect precept computations for Grassmannians through S.T. Yau, et al. The publication is of curiosity to graduate scholars and researchers in algebraic geometry, illustration concept, topology and their functions to excessive power physics