by Pavel Pech (University of South Bohemia, Czech Republic)

SELECTED TOPICS IN GEOMETRY WITH CLASSICAL VS. COMPUTER PROVING

This textbook presents various techniques of elimination based on Grobner bases to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects ? which cannot easily be done with a ruler and compass.
Each problem is firstly solved by the method of automatic theorem proving. Secondly, problems are solved classically ? without using computer where possible ? so that readers can compare the strengths and weaknesses of both approaches.

Contents:

Automatic Theorem Proving
Generalization of the Formula of Heron
Simson?Wallace Theorem
Transversals in a Polygon
Petr?Douglas?Neumann's Theorem
Geometric Inequalities
Regular Polygons

Readership: Undergraduate and graduate students in mathematics.

250pp (approx.) Pub. date: Scheduled Winter 2007
ISBN 978-981-270-942-4
981-270-942-8

edited by Philippe G Ciarlet (City University of Hong Kong, Hong Kong)
& Ta-Tsien Li (Fudan University, China)

DIFFERENTIAL GEOMETRY: THEORY AND APPLICATIONS

This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a self-contained and accessible manner. Although the field is often considered a “classical” one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role.
The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and mesh generation in finite element methods.

This volume will be very useful to graduate students and researchers in pure and applied mathematics.

Contents:

An Introduction to Differential Geometry (P G Ciarlet)
An Introduction to Shell Theory (P G Ciarlet & C Mardare)
Some New Results and Current Challenges in the Finite Element Analysis of Shells (D Chapelle)
A Differential Geometry Approach to Mesh Generation (P Frey)

Readership: Graduate students and researchers in pure mathematics, applied mathematics and applied sciences including mechanics.

300pp (approx.) Pub. date: Scheduled Spring 2008
ISBN 978-981-277-146-9
981-277-146-8

edited by Say Song Goh (National University of Singapore, Singapore), Amos Ron (University of Wisconsin-Madison, USA) & Zuowei Shen (National University of Singapore, Singapore)

MATHEMATICS AND COMPUTATION IN IMAGING SCIENCE AND INFORMATION PROCESSING

The explosion of data arising from rapid advances in communication, sensing and computational power has concentrated research effort on more advanced techniques for the representation, processing, analysis and interpretation of data sets. In view of these exciting developments, the program “Mathematics and Computation in Imaging Science and Information Processing” was held at the Institute for Mathematical Sciences, National University of Singapore, from July to December 2003 and in August 2004 to promote and facilitate multidisciplinary research in the area. As part of the program, a series of tutorial lectures were conducted by international experts on a wide variety of topics in mathematical image, signal and information processing.
This compiled volume contains survey articles by the tutorial speakers, all specialists in their respective areas. They collectively provide graduate students and researchers new to the field a unique and valuable introduction to a range of important topics at the frontiers of current research.

Contents:

Subdivision on Arbitrary Meshes: Algorithms and Theory (D Zorin)
High Order Numerical Methods for Time Dependent Hamilton?Jacobi Equations (C-W Shu)
Theory and Computation of Variational Image Deblurring (T F Chan & J Shen)
Data Hiding ? Theory and Algorithms (P Moulin & R Koetter)
Image Steganography and Steganalysis: Concepts and Practice (M Kharrazi et al.)
The Apriori Algorithm ? A Tutorial (M Hegland)

Readership: Graduate students and researchers in mathematical image, signal and information processing.

276pp Pub. date: Oct 2007
ISBN 978-981-270-905-9
981-270-905-3

edited by Jian-Shu Li (Hong Kong University of Science & Technology, Hong Kong), Eng-Chye Tan (National University of Singapore, Singapore), Nolan Wallach (University of California, San Diego, USA) & Chen-Bo Zhu (National University of Singapore, Singapore)

HARMONIC ANALYSIS, GROUP REPRESENTATIONS, AUTOMORPHIC FORMS AND INVARIANT THEORY In Honor of Roger E. Howe

This volume carries the same title as that of an international conference held at the National University of Singapore, 9?11 January 2006 on the occasion of Roger E. Howe’s 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe’s mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications.

Contents:

The Theta Correspondence over R
The Heisenberg Group, SL(3,R), and Rigidity
Pfaffians and Strategies for Integer Choice Games
When Is an L-Function Non-Vanishing in Part of the Critical Strip?
Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L-Functions
The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group
On the Classification of Discrete Series of Some Classical p-Adic Groups
Some Algebras of Essentially Compact Distributions of a Reductive p-Adic Group
Annihilators of Generalized Verma Modules of the Scalar Type for Classical Lie Algebras
Branching to a Maximal Compact Subgroup
Small Semisimple Subalgebras of Semisimple Lie Algebras

Readership: Graduate students and research mathematicians in harmonic analysis, group representations, automorphic forms and invariant theory.

380pp (approx.) Pub. date: Scheduled Winter 2007
ISBN 978-981-277-078-3
981-277-078-X

by Jurgen Eichhorn (Universitat Greifswald, Germany)

INDEX THEORY, DETERMINANTS AND TORSION FOR OPEN MANIFOLDS

For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis.

Contents:

Absolute Invariants for Open Manifolds and Bundles:
Absolute Characteristic Numbers
Index Theorems for Open Manifolds
Non-linear Sobolev Structures
Generalized Dirac Operators:
Generalized Dirac Operators, Their Heat Kernel and Spectral Properties
Duhamels Principle, Trace Class Conditions and Scattering Theory
Trace Class Properties
Relative Index Theory:
Relative Index Theorems
The Spectral Shift Function and the Scattering Index
Relative Zeta Functions, Eta Functions, Determinants, Partition Functions of QFT and Torsion

Readership: Graduate students, mathematicians and physicists interested in global analysis.

250pp (approx.) Pub. date: Scheduled Summer 2008
ISBN 978-981-277-144-5
981-277-144-1