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This book is a reference for librarians, mathematicians, and statisticians involved in college and research level mathematics and statistics in the 21st century. We are in a time of transition in scholarly communications in mathematics, practices which have changed little for a hundred years are giving way to new modes of accessing information. Where journals, books, indexes and catalogs were once the physical representation of a good mathematics library, shelves have given way to computers, and users are often accessing information from remote places. Part I is a historical survey of the past 15 years tracking this huge transition in scholarly communications in mathematics. Part II of the book is the bibliography of resources recommended to support the disciplines of mathematics and statistics. These are grouped by type of material. Publication dates range from the 1800's onwards. Hundreds of electronic resources-some online, both dynamic and static, some in fixed media, are listed among the paper resources. Amazingly a majority of listed electronic resources are free.
A Handbook of Integer Sequences contains a main table of 2300 sequences of integers that are collected from all branches of mathematics and science. This handbook describes how to use the main table and provides methods for analyzing and describing unknown and important sequences. This compilation also serves as an index to the literature for locating references on a particular problem and quickly finds numbers such as 712, number of partitions of 30, 18th Catalan number, or expansion of ? to 60 decimal places. Other topics include the method of differences, self-generating sequences, polyominoes, permutations, and puzzle sequences. This publication is a good source for students and researchers who are confronted with strange and important sequences.
For anyone interested in the history and effects of the introduction of so-called “Modern Mathematics” (or “Mathématique Moderne,” or “New Mathematics,” etc.) this book, by Dirk De Bock and Geert Vanpaemel, is essential reading. The two authors are experienced and highly qualified Belgian scholars and the book looks carefully at events relating to school mathematics for the period from the end of World War II to 2010. Initially the book focuses on events which helped to define the modern mathematics revolution in Belgium before and during the 1960s. The book does much more than that, however, for it traces the influence of these events on national and international debates during the early phases of the reform. By providing readers with translations into English of relevant sections of key Continental documents outlining the major ideas of leading Continental scholars who contributed to the “Mathématique Moderne” movement, this book makes available to a wide readership, the theoretical, social, and political backdrops of Continental new mathematics reforms. In particular, the book focuses on the contributions made by Belgians such as Paul Libois, Willy Servais, Frédérique Lenger, and Georges Papy. The influence of modern mathematics fell away rapidly in the 1970s, however, and the authors trace the rise and fall, from that time into the 21st century, of a number of other approaches to school mathematics—in Belgium, in other Western European nations, and in North America. In summary, this is an outstanding, landmark publication displaying the fruits of deep scholarship and careful research based on extensive analyses of primary sources.
L. E. J. Brouwer Collected Works, Volume 2: Geometry, Analysis, Topology, and Mechanics focuses on the contributions and principles of Brouwer on geometry, topology, analysis, and mechanics, including non-Euclidean spaces, integrals, and surfaces. The publication first ponders on non-Euclidean spaces and integral theorems, lie groups, and plane transition theorem. Discussions focus on remarks on multiple integrals, force field of the non-Euclidean spaces with negative curvature, difference quotients and differential quotients, characterization of the Euclidean and non-Euclidean motion groups, and continuous one-one transformations of surfaces in themselves. The book also takes a look at vector fields on surfaces and new methods in topology, including continuous vector distributions on surfaces and orthogonal trajectories of the orbits of a one parameter plane projective group. The book then ponders on mechanics and topology of surfaces, as well as the motion of a particle on the bottom of a rotating vessel under the influence of gravitational force. The publication is a valuable reference for researchers interested in geometry, topology, analysis, and mechanics.
The international New Math developments between about 1950 through 1980, are regarded by many mathematics educators and education historians as the most historically important development in curricula of the twentieth century. It attracted the attention of local and international politicians, of teachers, and of parents, and influenced the teaching and learning of mathematics at all levels—kindergarten to college graduate—in many nations. After garnering much initial support it began to attract criticism. But, as Bill Jacob and the late Jerry Becker show in Chapter 17, some of the effects became entrenched. This volume, edited by Professor Dirk De Bock, of Belgium, provides an outstanding overview of the New Math/modern mathematics movement. Chapter authors provide exceptionally high-quality analyses of the rise of the movement, and of subsequent developments, within a range of nations. The first few chapters show how the initial leadership came from mathematicians in European nations and in the United States of America. The background leaders in Europe were Caleb Gattegno and members of a mysterious group of mainly French pure mathematicians, who since the 1930s had published under the name of (a fictitious) “Nicolas Bourbaki.” In the United States, there emerged, during the 1950s various attempts to improve U.S. mathematics curricula and teaching, especially in secondary schools and colleges. This side of the story climaxed in 1957 when the Soviet Union succeeded in launching “Sputnik,” the first satellite. Undoubtedly, this is a landmark publication in education. The foreword was written by Professor Bob Moon, one of a few other scholars to have written on the New Math from an international perspective. The final “epilogue” chapter, by Professor Geert Vanpaemel, a historian, draws together the overall thrust of the volume, and makes links with the general history of curriculum development, especially in science education, including recent globalization trends.
This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included.The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn's Lemma, is also expected.