edited by David Tall Science Education Dept., University of Warwick, Coventry, UK Series: MATHEMATICS EDUCATION LIBRARY volume: 11. This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Its three main parts focus on the nature of advanced mathematical thinking, the theory of its cognitive development, and reviews of cognitive research. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. The reviews of recent research concentrate on cognitive development and conceptual difficulties with the notions of functions, limits, infinity, analysis, proof, and the use of the computer. They provide a wide overview and an introduction to current thinking which is highly appropriate for the college professor in mathematics or the general mathematics educator. Kluwer Academic Publishers, Dordrecht. October 1991. 308 pp. Hardbound. Dfl.180.00. BrP.72.25. July 1994. 312 pp. Paperback. ISBN 0-7923-2812-4. Dfl.65.00. BrP.26.00.