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Geometry of Numbers
Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VIII: Geometry of Numbers focuses on bodies and lattices in the n-dimensional euclidean space. The text first discusses convex bodies and lattice points and the covering constant and inhomogeneous determinant of a set. Topics include the inhomogeneous determinant of a set, covering constant of a set, theorem of Minkowski-Hlawka, packing of convex bodies, successive minima and determinant of a set, successive minima of a convex body, extremal bodies, and polar reciprocal convex bodies. The publication ponders on star bodies, as well as points of critical lattices on the boundary, reducible, and irreducible...
Algorithms and Data Structures
The papers in this volume were presented at the Third Workshop on Algorithmsand Data Structures (WADS '93), held in Montreal, Canada, August 1993. The volume opens with five invited presentations: "Computing the all-pairs longest chains in the plane" by M.J. Atallah and D.Z. Chen, "Towards a better understanding of pure packet routing" by A. Borodin, "Tolerating faults in meshes and other networks" (abstract) by R. Cole, "A generalization of binary search" by R.M. Karp, and "Groups and algebraic complexity" (abstract) by A.C. Yao. The volume continues with 52 regular presentations selected from 165 submissions, each of which was evaluated by at least three program committee members, many of whom called upon additional reviewers.
Geometrical Aspects of Functional Analysis
These are the proceedings of the Israel Seminar on the Geometric Aspects of Functional Analysis (GAFA) which was held between October 1985 and June 1986. The main emphasis of the seminar was on the study of the geometry of Banach spaces and in particular the study of convex sets in and infinite-dimensional spaces. The greater part of the volume is made up of original research papers; a few of the papers are expository in nature. Together, they reflect the wide scope of the problems studied at present in the framework of the geometry of Banach spaces.
Mathematical Constants
Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
New Developments in Differential Equations
New Developments in Differential Equations
Using the Mathematics Literature
This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
Geometric Combinatorics
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.
Combinatorial Methods and Models
The fourth volume of Rudolf Ahlswede’s lectures on Information Theory is focused on Combinatorics. Ahlswede was originally motivated to study combinatorial aspects of Information Theory via zero-error codes: in this case the structure of the coding problems usually drastically changes from probabilistic to combinatorial. The best example is Shannon’s zero error capacity, where independent sets in graphs have to be examined. The extension to multiple access channels leads to the Zarankiewicz problem. A code can be regarded combinatorially as a hypergraph; and many coding theorems can be obtained by appropriate colourings or coverings of the underlying hypergraphs. Several such colouring a...
