Peyret, R., Universite de Nice-Sophia, Nice, France
Spectral Methods for Incompressible Viscous Flow
2002. Approx. 450 pp. 61 figs. Hardcover
0-387-95221-7
This well-written book explains the theory of spectral methods and their aplication to incompressible fluid flow in clear and elementary terms. It begins with an introduction to the fundamentals of spectral methods and then moves on to cover, in particular, the Fourier and Chebyshev methods. Examples and exercises are included. Chapters 4 and 5 handle streamfunction-vorticity and velocity-pressure for Navier-Stokes equations. Chapter 6 addresses special topics such as self- adaptive coordinate transform, domain decomposition, treatment of singularities, and free-surface flow. The work will be useful to those teaching in the field at the graduate level, as well as to researchers working in the area.
Contents: Introduction.- Chapter 1: Fundamentals of Spectral Methods.- Chapter 2: Fourier Method.- Chapter 3: Chebyshev Method.- Chapter 4: Navier-Stokes equations: Streamfunction-vorticity.- Chapter 5: Navier-Stokes equations: Velocity-pressure.- Chapter 6: Special Topics.- Self-adaptive coordinate transform.- Domain decomposition.- Treatment of singularities.- Free-surface flow.- Conclusion.- References.
13:40 02/03/22
Series: Applied Mathematical Sciences. VOL. 148
Toth, G., Rutgers University, Camden, NJ, USA
Glimpses of Algebra and Geometry, 2nd ed.
Approx. 485 pp. 205 figs. Hardcover
0-387-95345-0
The purpose of Glimpses of Algebra and Geometry is to fill a gap between undergraduate and graduate mathematics studies. It is one of the few undergraduate texts to explore the subtle and sometimes puzzling connections between Number Theory, Classical Geometry and Modern Algebra in a clear and easily understandable style. Over 160 computer-generated images, accessible to readers via the World Wide Web, facilitate an understanding of mathematical concepts and proofs even further.
Glimpses also sheds light on some of the links between the first recorded intellectual attempts to solve ancient problems of Number Theory and Geometry and twentieth century mathematics. GLIMPSES will appeal to students who wish to learn modern mathematics, but have few prerequisite courses, and to high-school teachers who always had a keen interest in mathematics, but seldom the time to pursue background technicalities. Even postgraduate mathematicians will enjoy being able to browse through a number of mathematical disciplines in one sitting.
This new edition includes invaluable improvements throughout the text, including an in-depth treatment of root formulas, a detailed and complete classification of finite Mobius groups a la Klein, and a quick, direct, and modern approach to Felix Klein "Normalformsatz," the main result of his spectacular theory of icosahedron and his solution of the irreducible quintic in terms of hypergeometric functions.
Gabor Toth is the Chair and Graduate Director of the Department of Mathematical Sciences at Rutgers University, Camden. His previous publications include Finite Mobius Groups, Spherical Minimal Immersions and Moduli (2001), Harmonic Maps and Minimal Immersion Through Representation Theory (1990) and Harmonic and Minimal Maps with Applications in Geometry and Physics (1984). Professor Toth main fields of interest involve the geometry of eigenmaps and spherical minimal immersions and the visualization of mathematics via computers.
Contents: "A Number is a multitude composed of units" (Euclid).-
"..there are no irrational numbers at all" (Kronecker).-
Rationality, Elliptic Curves and Fermat's Last Theorem.- Algebraic or Transcendential?- Complex Arithmetic.- Quadratic, Cubic, and Quartic Equations.- Stereographic Projection.- Proof of the Fundamental Theorem of Algebra.- Symmetries of Regular Polygons.- Discrete Subgroups of Iso(R2).- Mobius Geometry.- Complex Linear Fractional Transformations.- "Out of nothing I have created a new universe" (Bolyai).- Fuchsian Groups.- Riemann Surfaces.- General Surfaces.- The Five Platonic Solids.- Finite Mobius Groups.- Detour in Topology: Euler-Poincare Characteristic.- Detour in Graph Theory: Euler, Hamilton and the Four Color Theorem.- Dimension Leap.- Quaternions.- Back to R3!- Invariants.- The Icosahedron and the Unsolvable Quintic.- The Fourth Dimension.- Appendices.- Solutions for 100 Selected Problems.
Series: Undergraduate Texts in Mathematics.
Fritzsche, K., University of Wuppertal, Germany;
Grauert, H., University of Gottingen, Germany
From Holomorphic Functions to Complex Manifolds
2002. Approx. 420 pp. 28 figs. Hardcover
0-387-95395-7
This book is an introduction to the theory of complex manifolds. The author's intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involving sheaves, coherence, and higher-dimensional cohomology have been completely avoided. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Nevertheless, deep results can be proved, for example the Remmert-Stein theorem for analytic sets, finiteness theorems for spaces of cross sections in holomorphic vector bundles, and the solution of the Levi problem. Each chapter is complemented by a variety of examples and exercises. The only prerequisite needed to read this book is a knowledge of real analysis and some basic facts from algebra, topology, and the theory of one complex variable. The book can be used as a first introduction to several complex variables as well as a reference for the expert.
Klaus Fritzsche received his PhD from the University of Gottingen in 1975, under the direction of Professor Hans Grauert. Since 1984, he has been Professor of Mathematics at the University of Wuppertal, where he has been investigating convexity problems on complex spaces and teaching undergraduate and graduate courses on Real and Complex Analysis. Hans Grauert studied physics and mathematics in Mainz, Munster and Zurich. He received his PhD in mathematics from the University of Munster and in 1959 he became a full professor at the University of Gottingen. Professor Grauert is responsible for many important developments in mathematics in the Twentieth Century. Along with Reinhold Remmert, Karl Stein and Henri Cartan, he founded the theory of Several Complex Variables in its modern form. He also proved various important theorems, including Levi's Problem and the coherence of higher direct image sheaves. Professor Grauert is the author of 10 books and his Selected Papers was published by Springer in 1994.
Keywords: Complex Manifolds, Holomorphic Functions, Several Complex Variables, Complex Function Theory
Contents: Holomorphic Functions.- Domains of Holomorphy.- Analytic Sets.- Complex Manifolds.- Stein Theory.- Kaehler Manifolds.- Boundary Behavior.
Series: Graduate Texts in Mathematics. VOL. 213
Takesaki, M., University of California, Los Angeles, CA, USA
Theory of Operator Algebras II
2002. Approx. 450 pp. Hardcover
3-540-42914-X
Together with "Theory of Operator Algebras I, III" (EMS 124 and 127), this book, written by one of the most prominent researchers in the field of operator algebras, summarises the scientific work of the author focusing on von Neumann algebras and non-commutative integration.
The book is part of the recently developed part of the "Encyclopaedia of Mathematical Sciences" on operator algebras and non-commutative geometry (see http://www.springer.de/math/ems/index.html#operatoralgebra). The book provides essential and comprehensive information to graduate students and researchers in mathematics and mathematical physics.
Keywords: Operator algebra, ergodic transformation groups, von Neumann algebra, C * -algebra
Contents: Preface.- Chapter VI. Left Hilbert Algebras.- Chapter VII. Weights.- Chapter VIII. Modular Automorphism Groups.- Chapter IX. Non-Commutative Integration.- Chapter X. Crossed Products and Duality.- Chapter XI. Abelian Automorphism Groups.- Chapter XII. Structure of a von Neumann Algebra of Type III.- Appendix.- Bibliography.- Index.
Series: Encyclopaedia of Mathematical Sciences. VOL. 125
Takesaki, M., University of California, Los Angeles, CA, USA
Theory of Operator Algebras III
2002. Approx. 550 pp. Hardcover
3-540-42913-1
Together with "Theory of Operator Algebras I, II" (EMS 124 and 125), this book, written by one of the most prominent researchers in the field of operator algebras, summarises the scientific work of the author focusing on von Neumann algebras and non-commutative integration.
The book is part of the recently developed part of the "Encyclopaedia of Mathematical Sciences" on operator algebras and non-commutative geometry (see http://www.springer.de/math/ems/index.html#operatoralgebra). The book provides essential and comprehensive information to graduate students and researchers in mathematics and mathematical physics.
Keywords: Operator algebra, ergodic transformation groups, von Neumann algebra, C * -algebra
Contents: Preface.- Chapter XIII. Ergodic Transformaton Groups and the Associated von Neumann Algebras.- Chapter XIV. Approximately Finite Dimensional von Neumann Algebras.- Chapter XV. Nuclear C*-Algebras.- Chapter XVI. Injective von Neumann Algebras.- Chapter XVII. Non-Commutative Ergodic Theory.- Chapter XVIII. Structure of Approximately Finite Dimensional Factors.- Chapter XIX. Subfactors of a Factor of Tape II1.- Appendix.- Bibliography.- Index.
Series: Encyclopaedia of Mathematical Sciences. VOL. 127
Menger, K.
Selecta Mathematica , Band 1 / Volume 1
Schweizer, B., University of Massachusetts, Amherst, MA, USA; Sigmund, K., Universitat Wien; Schmetterer, L., Universitat Wien; Gruber, P., Universitat Wien; Hlawka, E., Technische Universitat Wien; Reich, L., Universitat Graz (Hrsg.)
2002. X, 606 S. 4 Abb. Geb.
3-211-83734-5
Karl Menger, one of the founders of dimension theory, belongs to the most original mathematicians and thinkers of the twentieth century. He was a member of the Vienna Circle and the founder of its mathematical equivalent, the Viennese Mathematical Colloquium. Both during his early years in Vienna and, after his emigration, in the United States, Karl Menger made significant contributions to a wide variety of mathematical fields, and greatly influenced some of his colleagues. The Selecta Mathematica contain Menger's major mathematical papers, based on his own selection from his extensive writings. They deal with topics as diverse as topology, geometry, analysis and algebra, as well as writings on economics, sociology, logic, philosophy and mathematical results. The two volumes are a monument to the diversity and originality of Menger's ideas.
Contents: Schweizer, B., Sklar A.: Introduction.- Sigmund, K.: Karl Menger and Vienna's Golden Autumn.- Johnson, M. D.: Introduction to Menger's Work on Dimension Theory.- Selected Papers on Dimension Theory.- Crilly, T., Moran, A.: Introduction to Menger's Work on Curve Theory and Topology.- Selected Papers on Curve Theory and Topology.- Plauman, P., Strambach, K.: Introduction to Menger's "Untersuchungen uber allgemeine Metrik".- Untersuchungen uber allgemeine Metrik.- Sagan, H.: Introduction to Menger's Work on the Calculus of Variations.- Selected Papers on Calculus of Variations.- Benz, W.: Introduction to Menger's Work on the Algebra of Geometry.- Selected Papers on Algebra of Geometry.- Benz, W.: Introduction to Menger's Expository Papers on Geometry.- Selected Expository Papers on Geometry.- List of Publications - Karl Menger.