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.

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