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MATHEMATICSFounding Advisor: Shiing Shen ChernFREE access to featured articles at www.worldscientific.com/ijm
Geometry & Topology
Bestsellers in
Proceedings of the International Congress of Mathematicians (ICM) 2018 5396pp • Mar 2019978-981-3272-87-3 (Set) US$850 £750
View this flyer online at http://tiny.cc/ws-geometry19-2
30Year s
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Ernest Irving Freese’s Geometric Transformations The Man, the Manuscript, the Magnificent Dissections!by Greg N Frederickson (Purdue University, USA)
“This book does not just uncover a mathematical gem. It is also a piece of art and a mind-puzzling set of ingenious dissections done by a master of architectural drawings and amateur mathematician. It is a practical book that shows the beauty of dissection and how we can get from a polygon to another by cutting it to pieces and recollect them in some special way. The book is written in a very elegant style, and nicely presented. Freese’s manuscript was photographed and wasn’t altered in any way — this preserved its beauty. Freese’s drawing shows ingenuity and it shows how meticulous he was. For those people who are interested in geometry or in geometric dissections and for those who admire puzzles and recreational mathematics this book is a must.” Mathematical Association of America
432pp Jan 2018978-981-3220-46-1 US$98 £81978-981-3220-47-8(pbk) US$38 £32
Lectures on Differential Geometryby S S Chern (UC Berkeley), W H Chen(Beijing University) & K S Lam (California State Polytechnic University)
This book is an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern. The present book is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds, and an appendix on the relationship between differential geometry and theoretical physics, this book includes a chapter on Finsler geometry and an appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.
368pp Nov 1999978-981-02-3494-2 US$65 £54978-981-02-4182-7(pbk) US$34 £28
The Geometry of the Octonionsby Tevian Dray & Corinne A Manogue (Oregon State University, USA)
“The book offers an abundance of explicit constructions that are valuable for both beginners and experts, who often tend to underestimate such an approach in the pursuit of abstract ideas … It is an interesting compilation of an approachable introductory level review on division algebras and their connection to Lie groups.” Journal of Geometry and Symmetry in Physics
This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generalization, the Lorentz group, as well as the eigenvalue problem for Hermitian matrices. More sophisticated applications include the exceptional Lie groups, octonionic projective spaces, and applications to particle physics.
Readership: Advanced undergraduates, graduate students and faculty in mathematics and physics.
228pp Jun 2015978-981-4401-81-4 US$114 £95
Classic Text
Bestsellers in GEOMETRY & TOPOLOGY
WORLD SCIENTIFICPrefer Digital? View this flyer online at http://tiny.cc/ws-geometry19-2 2
Undergraduate ConvexityFrom Fourier and Motzkin to Kuhn and Tuckerby Niels Lauritzen (Aarhus University, Denmark)
“Undergraduate Convexity would make an excellent textbook. An instructor might choose to have students present some of the examples while he or she provides commentary, perhaps alternating coaching and lecturing. A course taught from this book could be a good transition into more abstract mathematics, exposing students to general theory then giving them the familiar comfort of more computational exercises. One could also use the book as a warm-up to a more advanced course in optimization.” Mathematical Association of America
Readership: Undergraduates focusing on convexity and optimization.
Textbook300pp Jun 2013978-981-4412-51-3 US$95 £79978-981-4452-76-2(pbk) US$45 £37
Problems & Solutions196pp Nov 2016978-981-3146-21-1 US$68 £56978-981-3143-64-7(pbk) US$38 £32
An Introduction to Differential Manifoldsby Dennis Barden & Charles Thomas (University of Cambridge, UK)
“This book is an excellent introductory text into the theory of differential manifolds with a carefully thought out and tested structure and a sufficient supply of exercises and their solutions. It does not only guide the reader gently into the depths of the theory of differential manifolds but also careful on giving advice how one can place the information in the right context. It is certainly written in the best traditions of great Cambridge mathematics.” Acta Scientiarum Mathematicarum
Readership: Upper level undergraduates, beginning graduate students, and lecturers in geometry and topology.
232pp Mar 2003978-1-86094-354-6 US$74 £61978-1-86094-355-3(pbk) US$45 £37
How Surfaces Intersect in Space (2nd Edition)An Introduction to Topologyby J Scott Carter (Univ. South Alabama)
“In this excellent book the author teaches us to see a bit more than it meets our eyes. Without hurry he introduces us to the world of topological images. Step by step the reader learns the beauty of topological vision. Surfaces and their intersections, curves and knots, three-dimensional manifolds, surfaces in dimension 4 etc., all these material are presented in an informal easy way, making the exposition available to undergraduate students. As to the pictures, they are really delightful. I especially enjoyed the movies of surfaces and movie moves. On the whole the book is a successful attempt of an introduction to topology focusing on its spirit and skipping its technical side.” Vladimir Turaev (Directeur de Recherche au CNRS)
Readership: Undergraduates, graduates and mathematicians.
338pp May 1995978-981-02-2082-2 US$76 £63978-981-02-2066-2(pbk) US$36 £30
Morse TheorySmooth and Discreteby Kevin P Knudson (University of Florida, USA)
"The book fills a gap existing in the literature. His book covers both theories in an introductory way. It is self-contained. In addition, many detailed and motivational examples are included, so even the non-specialist reader will find the text clear and user-friendly. This book could be a nice text for a course on Morse theory in a wide sense. Researchers interested specifically in an introduction to discrete Morse theory can now avoid looking for various papers or sections of several books." Mathematical Reviews Clippings
Readership: Graduate students in geometry and topology.
196pp Aug 2015978-981-4630-96-2 US$65 £54
Lectures on the Geometry of Manifolds (2nd Edition)by Liviu I Nicolaescu (Univ. of Notre Dame, USA)
“... advanced graduate students will find the present book a fine text and reference. Virtually everything is created from scratch and presented in a thoughtful manner ... the chapter on cohomology is really a tour-de-force, involving geometry, topology and analysis in a fashion that every graduate student should see ... All-in-all, this is an excellent book for the right audience ... this book has everything for a full year-long course introducing students to the modern workings of global analysis.” Zentralblatt MATH
Readership: Mathematicians.
608pp Oct 2007978-981-270-853-3 US$180 £149978-981-277-862-8(pbk) US$99 £82
Modern Differential Geometry for Physicists (2nd Edition)by Chris J Isham (Imperial College)
“This book is carefully written, and attention is paid to rigor and relevant details … The key notions are discussed with great care and from many points of view, which attenuates the shock of the formalism.” Mathematical Reviews
“The mathematical notions are sprinkled with many remarks and hints of physical flavour; therefore, the text may be extremely valuable for those mathematics students interested in applications of differential geometry to other areas.” Mathematics Abstracts
304pp Mar 1999978-981-02-3555-0 US$82 £68978-981-02-3562-8(pbk) US$43 £36
Journal of Knot Theory and
Its RamificationsFREE access to featured articles at www.worldscientific.com/jktr
Bestsellers in GEOMETRY & TOPOLOGY
WORLD SCIENTIFIC Prefer Digital? View this flyer online at http://tiny.cc/ws-geometry19-2 3
Journal of Topology and
AnalysisFREE access to featured articles at www.worldscientific.com/jta
Hyperbolic Manifolds and Holomorphic Mappings (2nd Edition)An Introductionby Shoshichi Kobayashi (University of California,Berkeley, USA)
The first edition, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.
Readership: Researchers and students.
160pp Nov 2005978-981-256-496-2 US$55 £46978-981-256-589-1(pbk) US$33 £27 Symmetries of Islamic
Geometrical Patternsby Syed Jan Abas & Amer Shaker Salman (University of Wales, UK)
“Symmetry is one of the most important and pervasive principles in Mathematics, particularly in its Geometrical form. Here, mathematics combines with art and exhibits clearly its aesthetic appeal. Islamic patterns provide a marvellous illustration of symmetry and Drs. Abas and Salman perform a useful service by taking this as their theme and blending it with ideas on computer graphics.” Foreword by Michael Atiyah
Readership: General.
440pp Dec 1994978-981-02-1704-4 US$72 £60
Riemannian Geometry in an Orthogonal Frameby É Cartan (from lectures delivered by É Cartan at the Sorbonne in 1926 – 27) and translated by V V Goldberg (New Jersey Institute of Technology, USA)
“... on behalf of advanced students and of overall geometers now and in the future the reviewer expresses his hearty appreciation to Professors S P Finikov and V V Goldberg for their utmost endeavor of translating É Cartan’s ever valuable lectures ... ” Zentralblatt MATH
Readership: Senior undergraduates, graduate students and researchers in geometry and topology.
280pp Dec 2001978-981-02-4746-1 US$95 £79978-981-02-4747-8(pbk) US$49 £41
Differential Geometry of Warped Product Manifolds and Submanifoldsby Bang-Yen Chen (Michigan State University, USA)
The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson – Walker's and Schwarzschild's. The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
Readership: Graduate students and researchers interested in warped product manifolds and submanifolds in geometry, mathematical physics and general relativity.
516pp Jul 2017978-981-3208-92-6 US$158 £131
Differential Geometry of Curves and Surfacesby Masaaki Umehara & Kotaro Yamada (Tokyo Institute of Technology, Japan)
Key Features:• Avoiding a dictionary-like presentation,
the text reads as one clear, naturally flowing story
• Many important topics, such as the fundamental theorems of both curves and surfaces, geodesics, the Gauss–Bonnet theorem, etc, are all explained succinctly
• Unlike other textbooks, mathematically rich and special topics are presented, such as properties of spirals, classification of regular homotopy type of plane curves, the existence of isothermal coordinates and curvature line coordinates, and criteria for singularities
Readership: Undergraduate and graduate students, and researchers.
328pp Jul 2017978-981-4740-23-4 US$88 £73978-981-4740-24-1(pbk) US$48 £42
In the Search for Beauty Unravelling Non-Euclidean Geometryby Voldemar Smilga
“Smilga not only offers a thorough account of the historical development of geometry from Euclid to Einstein, but does this in a very entertaining and enjoyable way. In his characteristic witty and engaged style, he describes the struggle of many outstanding mathematicians in Europe and in the Orient to grasp the significance of Euclid’s fifth postulate. It is amazing to follow the ensuing intellectual fights. The zeal with which Lobachevsky”s resolution of the problem was rejected by some of his contemporaries, for instance, shows that it was not easy to distinguish facts from beliefs even before the invention of the internet ... I highly recommend the book — it is a real pleasure to read.” Heinrich Leutwyler (Albert Einstein Center for Fundamental Physics, Universität Bern)
Readership: All students, historians and researchers interested in mathematical physics.
248pp Dec 2018978-981-3274-35-8 US$78 £70978-981-120-830-0(pbk) US$38 £35
Bestsellers in GEOMETRY & TOPOLOGY
Lecture Notes on Chern – Simons – Witten Theoryby Sen Hu (University of Science & Technology of China)
212pp | 978-981-02-3909-1(pbk) | US$48 £40
Supermanifolds: Theory and Applicationsby Alice Rogers (King’s College London)
Complete exposition of the basics of supermanifold theory and its main applications.
264pp | 978-981-3203-21-1(pbk) | US$58 £48
Geometric Modular Forms and Elliptic Curves (2nd Edition)by Haruzo Hida (University of California, Los Angeles, USA)
Comprehensive account of the theory of moduli spaces of elliptic curves and its application to modular forms.
468pp | 978-981-4368-64-3 | US$140 £124
Geometry of Möbius Transformations: Elliptic, Parabolic and Hyperbolic Actions of SL2(R) (With DVD-ROM)by Vladimir V Kisil (University of Leeds, UK)
Exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane.
208pp | 978-1-84816-858-9 | US$98 £81
Lectures on Chern-Weil Theory and Witten Deformationsby Weiping Zhang (Nankai Institute of Mathematics, Tianjin, P R China)
132pp | 978-981-02-4686-0(pbk) | US$28 £23
Riemann-Finsler Geometryby Shiing-Shen Chern (Nankai Institute of Mathematics, P R China) & Zhongmin Shen (Indiana University Purdue University Indianapolis, USA)
204pp | 978-981-238-358-7(pbk) | US$21 £17
Spectral Geometry of the Laplacian: SpectralAnalysis and Differential Geometry of the Laplacianby Hajime Urakawa (Tohoku University, Japan)
First book on the spectrum of the Laplacian
312pp | 978-981-3109-08-7 | US$118 £98
Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity and Applicationsby Willi-Hans Steeb (University of Johannesburg, South Africa)
Plenty of stimulating material and is very suitable for deepening many concepts of differential geometry and relativity in a hands-on manner.
296pp | 978-981-3232-96-9(pbk) | US$48 £42
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