Provides a detailed presentation of the foundations of Riemannian geometry
and the theory of isometric flows on Riemannian manifolds
Gives a self-contained general introduction to the theory of homogeneous
Riemannian spaces, with many illustrative examples
Includes numerous results, some very recent, on geodesic orbit Riemannian
spaces and their important subclasses
This book is devoted to Killing vector fields and the one-parameter isometry groups of
Riemannian manifolds generated by them. It also provides a detailed introduction to
homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields,
presenting both classical and modern results, some very recent, many of which are due to the
authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics
and on some of its important subclasses. To keep the exposition self-contained the book also
includes useful general results not only on geodesic orbit manifolds, but also on smooth and
Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and
compact homogeneous Riemannian spaces. The intended audience is graduate students and
researchers whose work involves differential geometry and transformation groups.
Mathematics : Differential Geometry
Hardcover
ISBN 978-3-030-56657-9
Product category : Monograph
Series : Springer Monographs in Mathematics
This is the first book to cover such a wide range of perspectives and topics in
the field, thus representing a genuinely new contribution to this popular and
active area of research
Features well-written contributions from twelve world experts in their
respective fields, describing both old and new advances in Arakelov geometry
Includes applications to arithmetic geometry of Shimura varieties
Bridging the gap between novice and expert, the aim of this book is to present in a selfcontained
way a number of striking examples of current diophantine problems to which
Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link
between algebraic geometry and diophantine geometry. Based on lectures from a summer
school for graduate students, this volume consists of 12 different chapters, each written by a
different author. The first chapters provide some background and introduction to the subject.
These are followed by a presentation of different applications to arithmetic geometry. The final
part describes the recent application of Arakelov geometry to Shimura varieties and the proof
of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental
tools of Arakelov geometry with original material corresponding to current research. This book
will be particularly useful for graduate students and researchers interested in the connections
between algebraic geometry and number theory. The prerequisites are some knowledge of
number theory and algebraic geometry
Mathematics : Number Theory
Due 2021-01-17
1st ed. 2020, X, 490 p. 10 illus.
Softcover
ISBN 978-3-030-57558-8
Product category : Contributed volume
Series : Lecture Notes in Mathematics
https://doi.org/10.1142/11926 |
July 2020
ISBN: 978-981-122-389-1 (hardcover)
ISBN: 978-981-122-484-3 (softcover)
Many students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds.
Introduction
Linear Systems and Finite Precision Arithmetic
Gaussian Elimination
Norms and Error Analysis
The MPP and the Curse of Dimensionality
Iterative Methods
Solving Ax = b by Optimization
The Conjugate Gradient Method
Eigenvalue Problems
Senior undergraduate and first year graduate in areas related to numerical analysis.
https://doi.org/10.1142/11896 | December 2020
Pages: 160
ISBN: 978-981-122-272-6 (hardcover)
This set of notes is an activity-oriented introduction to linear and multilinear algebra. The great majority of the most elementary results in these subjects are straightforward and can be verified by the thoughtful student. Indeed, that is the main point of these notes ? to convince the beginner that the subject is accessible. In the material that follows there are numerous indicators that suggest activity on the part of the reader: words such as "proposition", "example", "theorem", "exercise", and "corollary", if not followed by a proof (and proofs here are very rare) or a reference to a proof, are invitations to verify the assertions made.
These notes are intended to accompany an (academic) year-long course at the advanced undergraduate or beginning graduate level. (With judicious pruning most of the material can be covered in a two-term sequence.) The text is also suitable for a lecture-style class, the instructor proving some of the results while leaving others as exercises for the students.
This book has tried to keep the facts about vector spaces and those about inner product spaces separate. Many beginning linear algebra texts conflate the material on these two vastly different subjects.
Vector Spaces
Linear Transformations
The Language of Categories
The Spectral Theorem for Vector Spaces
The Spectral Theorem for Inner Product Spaces
A Brief Review of Differential Calculus
Multilinear Maps and Determinants
Tensor Algebras
Differential Manifolds
Differential Forms on Manifolds
Homology and Cohomology
Stokes' Theorem
Geometric Algebra
Clifford Algebras
Upper division undergraduates, beginning graduate students, instructors of linear and multilinear algebra.