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On the shoulders of giants
Mathematical
Social
Sciences
21 (1991) 193-200
193
North-Holland
BOOK REVIEWS
Lynn Arthur Steen, ed., On the Shoulders Academy Press, 1990, 232 pages, $17.95.
of Giants.
Washington,
D.C.:
National
This book is concerned with new approaches to basic mathematics education which can introduce students to concepts and ways of thought of century mathematics. L. Steen, in a brief introduction on pattern, discusses basic concepts: structures, attributes, e.g. periodic, dichotomies such as algorith;nic versus existential and so on. T. Banchoff, in an article on dimension, shows how students, even in the first grades, can be introduced to geometrical concepts using experiments with physical models and everyday materials and led to theorems about length, area, volume, growth factors, averages, coordinates, perspective combinatorics, n dimensions. J. Fey, in this essay ‘Quantity’, discusses concepts of measurement, including types of scales, functional relationships, algorithms. D. Senechal, on uncertainty, discusses things related to statistics and the need to train intuition to correct reasoning. M. Senechal, on shape, emphasizes symmetry, discussing the Erlanger program, crystals, tilings, maps, in relation to physics, biology, and art. I. Stewart discusses change, emphasizing the theory of dynamical systems, symmetry and symmetry breaking. It is a unique and very interesting book.
F. W. Roush Mathematical Social Sciences Alabama State University Montgomery, AL 36101 U.S.A.
Vilem Novak, Fuzzy Sets and Their Applications, Translated from Czechoslovakian. Bristol and Philadelphia: Adam Hilger, 1989, 248 pages. This small book has two merits. First, it gives an account of research done in Czechoslovakia and some other Eastern Europe countries in the eighties. Second, it proposes a special view of fuzzy sets that directly stems from Goguen’s logic of vague concepts (1968), further developed by Pavelka (1979) at the end of the seventies, and to which the authors has himself recently contributed (Novak, 1990). As a consequence there is a strong emphasis on multiple-valued logic in the book, and this is what makes it worth reading, since it does not completely fit the usual 0165-4896/91/$3.50
0
1991-Elsevier
Science Publishers
B.V. (North-Holland)
Social
Sciences
21 (1991) 193-200
193
North-Holland
BOOK REVIEWS
Lynn Arthur Steen, ed., On the Shoulders Academy Press, 1990, 232 pages, $17.95.
of Giants.
Washington,
D.C.:
National
This book is concerned with new approaches to basic mathematics education which can introduce students to concepts and ways of thought of century mathematics. L. Steen, in a brief introduction on pattern, discusses basic concepts: structures, attributes, e.g. periodic, dichotomies such as algorith;nic versus existential and so on. T. Banchoff, in an article on dimension, shows how students, even in the first grades, can be introduced to geometrical concepts using experiments with physical models and everyday materials and led to theorems about length, area, volume, growth factors, averages, coordinates, perspective combinatorics, n dimensions. J. Fey, in this essay ‘Quantity’, discusses concepts of measurement, including types of scales, functional relationships, algorithms. D. Senechal, on uncertainty, discusses things related to statistics and the need to train intuition to correct reasoning. M. Senechal, on shape, emphasizes symmetry, discussing the Erlanger program, crystals, tilings, maps, in relation to physics, biology, and art. I. Stewart discusses change, emphasizing the theory of dynamical systems, symmetry and symmetry breaking. It is a unique and very interesting book.
F. W. Roush Mathematical Social Sciences Alabama State University Montgomery, AL 36101 U.S.A.
Vilem Novak, Fuzzy Sets and Their Applications, Translated from Czechoslovakian. Bristol and Philadelphia: Adam Hilger, 1989, 248 pages. This small book has two merits. First, it gives an account of research done in Czechoslovakia and some other Eastern Europe countries in the eighties. Second, it proposes a special view of fuzzy sets that directly stems from Goguen’s logic of vague concepts (1968), further developed by Pavelka (1979) at the end of the seventies, and to which the authors has himself recently contributed (Novak, 1990). As a consequence there is a strong emphasis on multiple-valued logic in the book, and this is what makes it worth reading, since it does not completely fit the usual 0165-4896/91/$3.50
0
1991-Elsevier
Science Publishers
B.V. (North-Holland)