This book brings the most important aspects of modern topology within reach of a second-year undergraduate student.

Author: Martin D. Crossley

Publisher: Springer Science & Business Media

ISBN: 1852337826

Category: Mathematics

Page: 224

View: 269

This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

15. Croom, F. H., Basic Concepts of Algebraic Topology (Undergraduate Texts in
Mathematics), Springer-Verlag, Berlin-Heidelberg-New York, 1978. 16. Crossley,
M. D., Essential Topology Series: Springer Undergraduate Mathematics Series, ...

Author: John McCleary

Publisher: American Mathematical Soc.

ISBN: 9780821838846

Category: Mathematics

Page: 211

View: 287

How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time. The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.

Crossley, M.D.: Essential Topology. Springer Undergraduate Mathematics Series
. Springer, London (2005) 31. de Berg, M., van Kreveld, M., Overmars, M.,
Schwarzkopf, O.: Computational Geometry, 2nd edn. Springer, Berlin (2000) 32.

Author: Michael Joswig

Publisher: Springer Science & Business Media

ISBN: 9781447148173

Category: Mathematics

Page: 250

View: 742

Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

[3] Martin Crossley, Essential Topology, Springer Undergraduate Mathematics Series, London, 2005. [4] Keith Kendig, Conics, Mathematical Association of
America, Washington, DC, 2005. [5] Keith Kendig, When and Why Do Water
Levels ...

Author: Keith Kendig

Publisher: American Mathematical Soc.

ISBN: 9781614442073

Category: Mathematics

Page: 375

View: 492

A collection of over 250 multiple-choice problems to challenge and delight everyone from school students to professional mathematicians.

This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses.

Author: Michael Field

Publisher: Springer

ISBN: 9783319675466

Category: Mathematics

Page: 450

View: 374

This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.

This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics.

Author: John Lee

Publisher: Springer Science & Business Media

ISBN: 9781441979407

Category: Mathematics

Page: 433

View: 639

This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.

Author: Vladimir Grigorvich·Bolt雐靉nski鎖Publish On: 2001-03-30

This book is well suited for readers who are interested in finding out what topology is all about.

Author: Vladimir Grigorvich·Bolt雐靉nski鎖

Publisher: Springer Science & Business Media

ISBN: 0387951148

Category: Mathematics

Page: 141

View: 493

Topology is a relatively young and very important branch of mathematics, which studies the properties of objects that are preserved through deformations, twistings, and stretchings. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and well-motivated way. This book is well suited for readers who are interested in finding out what topology is all about.

Author: New Zealand Mathematical SocietyPublish On: 2004

Anyone interested in reviewing any of these books should contact Bruce van
Brunt Institute of Fundamental Sciences Massey University ( email : B ... Crossley
, MD , Essential Topology . ( Springer Undergraduate Mathematics Series )
224pp .

V . Series . oscillations ler . 514 Topology CROSSLEY , Martin D . 514 Essential topology / Martin D . Crossley . London : Springer , c2005 . ix , 224 p . : ill . ; 24 cm
. ( Springer undergraduate mathematics series , 1615 - 2085 ) ...

A substantially revised edition of the UTM volume, with a view to making the book far more accessible to undergraduates.

Author: Ioan M. James

Publisher: Springer Science & Business Media

ISBN: 9781447139942

Category: Mathematics

Page: 230

View: 612

A substantially revised edition of the UTM volume, with a view to making the book far more accessible to undergraduates. It contains a larger number of detailed explanations and exercises, together with fully worked solutions to the essential problems and a new chapter on the historical aspects.

At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized.

Author: I.M. Singer

Publisher: Springer

ISBN: 9781461573470

Category: Mathematics

Page: 232

View: 798

At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.

BOOK REVIEWS Essential Topology BY Martin D . CROSSLEY Springer Undergraduate Mathematics Series . Springer - Verlag , London , 2005 , x + 224
pages . reviewed by Ariel Blanco , Department of Pure Mathematics , School of ...

Author: Mahima Ranjan AdhikariPublish On: 2016-09-16

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications.

Author: Mahima Ranjan Adhikari

Publisher: Springer

ISBN: 9788132228431

Category: Mathematics

Page: 615

View: 870

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line.

Author: Mícheál O'Searcoid

Publisher: Springer Science & Business Media

ISBN: 1846286271

Category: Mathematics

Page: 304

View: 982

The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.

Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology.

Author: Satya Deo

Publisher: Springer

ISBN: 9789811087349

Category: Mathematics

Page: 344

View: 283

This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes challenging, for the reader to provoke their curiosity for problem-solving.

In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating.

Author: M.A. Armstrong

Publisher: Springer Science & Business Media

ISBN: 9781475717938

Category: Mathematics

Page: 251

View: 645

In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.

This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics.

Author: John M. Lee

Publisher: Springer Science & Business Media

ISBN: 9780387987590

Category: Mathematics

Page: 385

View: 833

Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

" 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.

Author: L.Christine Kinsey

Publisher: Springer Science & Business Media

ISBN: 0387941029

Category: Mathematics

Page: 281

View: 386

" . . . 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.

This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology.

Author: Benjamin Fine

Publisher: Springer Science & Business Media

ISBN: 9781461219286

Category: Mathematics

Page: 210

View: 462

The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.

In some points, the book treats its material differently than other texts on the subject: * Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem; * Nets are used extensively, in particular for an intuitive proof of Tychonoff's ...

Author: Volker Runde

Publisher: Springer Science & Business Media

ISBN: 038725790X

Category: Mathematics

Page: 182

View: 107

This should be a revelation for mathematics undergraduates. Having evolved from Runde’s notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde’s text treats its material differently to other books on the subject, providing a fresh perspective.