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Focusing methodologically on those historical aspects that are
relevant to supporting intuition in axiomatic approaches to
geometry, the book develops systematic and modern approaches to
the three core aspects of axiomatic geometry: Euclidean,
non-Euclidean and projective. Historically, axiomatic geometry
marks the origin of formalized mathematical activity. It is in
this discipline that most historically famous problems can be
found,... more...

This monograph examines in detail certain concepts that are useful
for the modeling of curves and surfaces and emphasizes the
mathematical theory that underlies these ideas. The two principal
themes of the text are the use of piecewise polynomial
representation (this theme appears in one form or another in every
chapter), and iterative refinement, also called subdivision. Here,
simple iterative geometric algorithms produce, in the limit, curves
with... more...

This volume contains the proceedings of the International
Conference on Number Theory and Discrete Mathematics in honour of
Srinivasa Ramanujan, held at the Centre for Advanced Study in
Mathematics, Panjab University, Chandigarh, India, in October 2000,
as a contribution to the International Year of Mathematics. It
collects 29 articles written by some of the leading specialists
worldwide. Most of the papers provide recent trends, problems and
their... more...

This book is intended for a one year course in Riemannian Geometry.
It will serve as a single source, introducing students to the
important techniques and theorems while also containing enough
background on advanced topics to appeal to those students wishing
to specialize in Riemannian Geometry. Instead of variational
techniques, the author uses a unique approach emphasizing distance
functions and special coordinate systems. He also uses standard... more...

The geometry of the hyperbolic plane has been an active and
fascinating field of mathematical inquiry for most of the past two
centuries. This book provides a self-contained introduction to the
subject, taking the approach that hyperbolic geometry consists of
the study of those quantities invariant under the action of a
natural group of transformations. Topics covered include the upper
half-space model of the hyperbolic plane, Möbius transformations,... more...

This introduction to the theory of complex manifolds covers the
most important branches and methods in complex analysis of
several variables while completely avoiding abstract concepts
involving sheaves, coherence, and higher-dimensional cohomology.
Only elementary methods such as power series, holomorphic vector
bundles, and one-dimensional cocycles are used. Each chapter
contains a variety of examples and exercises.

A novel feature of the book is its integrated approach to algebraic
surface theory and the study of vector bundle theory on both curves
and surfaces. While the two subjects remain separate through the
first few chapters, they become much more tightly interconnected as
the book progresses. Thus vector bundles over curves are studied to
understand ruled surfaces, and then reappear in the proof of
Bogomolov's inequality for stable bundles, which is itself... more...

This volume contains the invited contributions from talks
delivered in the Fall 2011 series of the Seminar on Mathematical
Sciences and Applications 2011 at Virginia State University.
Contributors to this volume, who are leading researchers in
their fields, present their work in a way to generate genuine
interdisciplinary interaction. Thus all articles therein are... more...

This book consists of the notes from the seminar Bonn/ Wuppertal
1983/ 84 on Arithmetic Geometry. It contains a proof for the
Mordell conjecture and may be useful as an introduction to
Arakelov's point of view in diophantine geometry. The third edition
includes an appendix in which a detailed survey on the spectacular
recent developments in arithmetic algebraic geometry is given.
These beautiful new results have their roots in the material
covered by... more...

Alexander Grothendieck's concepts turned out to be astoundingly
powerful and productive, truly revolutionizing algebraic geometry.
He sketched his new theories in talks given at the SÃ©minaire
Bourbaki between 1957 and 1962. He then collected these lectures in
a series of articles in Fondements de la gÃ©omÃ©trie algÃ©brique
(commonly known as FGA). Much of FGA is now common knowledge.
However, some of it is less well known, and only a few... more...