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Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Mathematics today is approaching a state of cnSIS. As the demands of science and society for mathematical literacy increase, the percentage of American college students intending to major in mathematics plummets and achievement scores of entering college students continue thelt unremit ting decline. As research in core mathematics reaches unprecedented heights of power and sophistication, the growth of diverse applied special ties threatens to fragment mathematics into distinct and frequently hostile mathematical sciences. These crises in mathematics presage difficulties for science and engineer ing, and alarms are beginning to sound in the scientific and even in the political communities. C...
"Math and bio 2010 grew out of 'Meeting the Challenges: Education across the Biological, Mathematical and Computer Sciences,' a joint project of the Mathematical Association of America (MAA), the National Science Foundation Division of Undergraduate Education (NSF DUE), the National Institute of General Medical Sciences (NIGMS), the American Association for the Advancement of Science (AAAS), and the American Society for Microbiology (ASM)."--Foreword, p. vi
What mathematics should be learned by today's young people as well as tomorrow's workforce? On the Shoulders of Giants is a vision of richness of mathematics expressed in essays on change, dimension, quantity, shape, and uncertainty, each of which illustrate fundamental strands for school mathematics. These essays expand on the idea of mathematics as the language and science of patterns, allowing us to realize the importance of providing hands-on experience and the development of a curriculum that will enable students to apply their knowledge to diverse numerical problems.
The objective of the present book of essays is to convey to the intelligent nonmathematician something of the nature, development, and use of mathe matical concepts, particularly those that have found application in current scientific research. The idea of assembling such a volume goes back at least to 1974, when it was discussed by the then-newly-formed Joint Projects Committee for Mathematics (JPCM) of the American Mathematical Soci ety, the Mathematical Association of America, and the Society for Indus trial and Applied Mathematics. Currently, the nine members of the JPCM are Saunders Mac Lane (Chairman) of the University of Chicago, Frederick J. Almgren, Jr. of Princeton University, Rich...
The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.
Mathematics and democracy: the case for quantitative literacy.
This timely volume raises issues concerning the nature of school mathematics and mathematics at work, and the challenges of teaching valuable mathematics in school and providing appropriate training for a variety of careers. It offers lively commentaries on important `hot' topics: transferring knowledge and skill across contexts; ‘authentic mathematics’; comparability of different types of assessment; and analyses of research methods.