Part of MAA Problem Book Series
Publication planned for: August 2016
format: Paperback
isbn: 9780883858394
This challenging problem-solving book on Euclidean geometry requires nothing of the reader other than courage. Readers will encounter cyclic quadrilaterals, power of a point, homothety, and triangle centers, as well as such classical gems as the nine-point circle, the Simson line, and the symmedian. Both a traditional and a computational view of the use of complex numbers and barycentric coordinates is offered, while more advanced topics are covered in the final part. These include inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also how one would invent the solution to begin with. Providing over 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions, this book is especially suitable for students preparing for national or international mathematical Olympiads.
Preface
Preliminaries
Part I. Fundamentals:
1. Angle chasing
2. Circles
3. Lengths and rules
4. Assorted configurations
Part II. Analytic Techniques:
5. Computational geometry
6. Complex numbers
7. Barycentric coordinates
Part III. Farther from Kansas:
8. Inversion
9. Projective geometry
10. Complete quadrilaterals
11. Personal favorites
Part IV. Appendices: Appendix A. An ounce of linear algebra
Appendix B. Hints
Appendix C. Selected solutions
Appendix D. List of contests and abbreviations
Bibliography
Index
About the author.
EMS Series of Lectures in Mathematics
ISBN print 978-3-03719-156-9,
DOI 10.4171/156
May 2016, 154 pages, softcover, 17 x 24 cm.
Generalized manifolds are a most fascinating subject to study. They were introduced in the 1930s, when topologists tried to detect topological manifolds among more general spaces (this is nowadays called the manifold recognition problem). As such, generalized manifolds have served to understand the nature of genuine manifolds. However, it soon became more important to study the category of generalized manifolds itself.
A breakthrough was made in the 1990s, when several topologists discovered a systematic way of constructing higher-dimensional generalized manifolds, based on advanced surgery techniques. In fact, the development of controlled surgery theory and the study of generalized manifolds developed in parallel. In this process, earlier studies of geometric surgery turned out to be very helpful.
Generalized manifolds will continue to be an attractive subject to study, for there remain several unsolved fundamental problems. Moreover, they hold promise for new research, e.g. for finding appropriate structures on these spaces which could bring to light geometric (or even analytic) aspects of higher-dimensional generalized manifolds.
This is the first book to systematically collect the most important material on higher-dimensional generalized manifolds and controlled surgery. It is self-contained and its extensive list of references reflects the historic development. The book is based on our graduate courses and seminars, as well as our talks given at various meetings, and is suitable for advanced graduate students and researchers in algebraic and geometric topology.
Keywords: Homology manifold, Poincare duality, degree 1 normal map, boundedly controlled surgey, surgery spectrum, assembly map, Quinn index, Euclidean neighborhood retract, cell-like resolution, disjoint disks property, manifold recognition problem
IRMA Lectures in Mathematics and Theoretical Physics Vol. 27
ISBN print 978-3-03719-161-3,
DOI 10.4171/161
May 2016, 652 pages, hardcover, 17 x 24 cm.
This volume is the sixth in a series dedicated to Teichmuller theory in a broad sense, including various moduli and deformation spaces, and the study of mapping class groups. It is divided into five parts:
Part A: The metric and the analytic theory.
Part B: The group theory.
Part C: Representation theory and generalized structures.
Part D: The Grothendieck?Teichmuller theory.
Part D: Sources.
The topics surveyed include Grothendieck’s construction of the analytic structure of Teichmuller space, identities on the geodesic length spectrum of hyperbolic surfaces (including Mirzakhani’s application to the computation of Weil?Petersson volumes), moduli spaces of configurations spaces, the Teichmuller tower with the action of the Galois group on dessins d’enfants, and several others actions related to surfaces. The last part contains three papers by Teichmuller, translated into English with mathematical commentaries, and a document that contains H. Grotzsch’s comments on Teichmuller’s famous paper Extremale quasikonforme Abbildungen und quadratische Differentiale.
The handbook is addressed to researchers and to graduate students.
Published: 23 May 2016
Publisher: International Press of Boston, Inc.
(ISBN 9781571463210)
Paperback
244 pages
This volume presents lively and engaging articles from the lecturers and the participants of the 22nd Gokova Geometry-Topology Conference, held on the shores of Gokova Bay, Turkey, in May of 2015.
Topics include high-dimensional geometric, symplectic and contact topology, low-dimensional manifolds, the triangulation theorem, the higher-dimensional contact geometry, and more.
The 22nd Gokova Geometry-Topology Conference was sponsored by the National Science Foundation, by the Turkish Mathematical Society, and by the European Research Council.
Surveys of Modern Mathematics, Volume 10
Textbook
To Be Published: 30 June 2016
Paperback
194 pages
Finite group theory is remarkable for the simplicity of its statements?and
the difficulty of their proofs. It is essential in several branches of
mathematics, notably number theory.
Finite Groups: An Introduction is an elementary textbook on finite group theory. Written by the eminent French mathematician Jean-Pierre Serre (a principal contributor to algebraic geometry, group theory, and number theory), this brand-new textbook is based upon a course given by Serre at l’Ecole Normale Superieure de Jeunes Filles, Paris in 1978?1979.
Each of the ten chapters is followed by a series of exercises.
Handbook of Statistics, Volume 34
Subject Area: Engineering / Electronics - Electronic Projects
ISBN-13: 9780444635709
Pub Date: 04/13/2016
Weight: 700.00 grams
Pages: 544
Product Type: Hardcover
Shelving Classification:
MATHEMATICS / General,
MATHEMATICS / Probability & Statistics / General
Brings together all relevant aspects of randomized response and indirect questioning
Tackles how to gather and analyze data relating to stigmatizing human traits
Gives an encyclopedic coverage of the topic
Covers recent developments and extrapolates to future trends