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Author: Richard Evan Schwartz
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 330
ISBN-13: 0821853686
DOWNLOAD EBOOKThe goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Author: David W. Farmer
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 111
ISBN-13: 0821804510
DOWNLOAD EBOOKIn most mathematics textbooks, the most exciting part of mathematics - the process of invention and discovery - is completely hidden from the student. The aim of Knots and Surfaces is to change all that. Knots and Surfaces guides the reader through Euler's formula, one and two-sided surfaces, and knot theory using games and examples. By means of a series of carefully selected tasks, this book leads the reader on to discover some real mathematics. There are no formulas to memorize; no procedures to follow. This book is a guide to the mathematics - it starts you in the right direction and brings you back if you stray too far. Discovery is left to you. This book is aimed at undergraduates and those with little background knowledge of mathematics.
Author: Tobias Holck Colding
Publisher: American Mathematical Society
Published: 2024-01-18
Total Pages: 330
ISBN-13: 1470476401
DOWNLOAD EBOOKMinimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.
Author: Sebastián Montiel
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 395
ISBN-13: 0821847635
DOWNLOAD EBOOKOffers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.
Author: L.Christine Kinsey
Publisher: Springer Science & Business Media
Published: 1997-09-26
Total Pages: 304
ISBN-13: 9780387941028
DOWNLOAD EBOOK" . . . that famous pedagogical method whereby one begins with the general and proceeds to the particular only after the student is too confused to understand even that anymore. " Michael Spivak This text was written as an antidote to topology courses such as Spivak It is meant to provide the student with an experience in geomet describes. ric topology. Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition or geometric sense. I have tried in this text to provide the undergraduate with a pragmatic introduction to the field, including a sampling from point-set, geometric, and algebraic topology, and trying not to include anything that the student cannot immediately experience. The exercises are to be considered as an in tegral part of the text and, ideally, should be addressed when they are met, rather than at the end of a block of material. Many of them are quite easy and are intended to give the student practice working with the definitions and digesting the current topic before proceeding. The appendix provides a brief survey of the group theory needed.
Author: John Stillwell
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 225
ISBN-13: 1461209293
DOWNLOAD EBOOKThe geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.
Author: A. B. Katok
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 307
ISBN-13: 0821846795
DOWNLOAD EBOOKSurfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle.
Author: Herbert Busemann
Publisher: Courier Corporation
Published: 2013-11-07
Total Pages: 210
ISBN-13: 0486154998
DOWNLOAD EBOOKThis exploration of convex surfaces focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. It also examines intrinsic geometry and the realization of intrinsic metrics. 1958 edition.
Author: Lars-Erik Andersson
Publisher: SIAM
Published: 2010-01-01
Total Pages: 373
ISBN-13: 0898717612
DOWNLOAD EBOOKThis is an introduction to the mathematical theory which underlies subdivision surfaces, as it is used in computer graphics and animation. Subdivision surfaces enable a designer to specify the approximate form of a surface that defines an object and then to refine it to get a more useful or attractive version. A considerable amount of mathematical theory is needed to understand the characteristics of the resulting surfaces, and this book explains the material carefully and rigorously. The text is highly accessible, organising subdivision methods in a unique and unambiguous hierarchy which builds insight and understanding. The material is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points, but gives a broad discussion of the various methods. It is therefore an excellent preparation for more advanced texts that delve more deeply into special questions of regularity.
Author: Scott Carter
Publisher: Springer Science & Business Media
Published: 2004-04-05
Total Pages: 234
ISBN-13: 9783540210405
DOWNLOAD EBOOKThis book discusses knotted surfaces in 4-dimensional space and surveys many of the known results, including knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory.
