Background
Alling, Norman Larrabee was born on February 8, 1930 in Rochester, New York, United States. Son of Harold Lattimore and Merle (Kolb) Alling.
(In this volume, a tower of surreal number fields is defin...)
In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given. Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand.
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Alling, Norman Larrabee was born on February 8, 1930 in Rochester, New York, United States. Son of Harold Lattimore and Merle (Kolb) Alling.
Bachelor, Bard College, 1952. Master of Arts, Columbia University, 1954. Doctor of Philosophy, Columbia University, 1958.
Lecturer mathematics, Columbia University, 1955-1957;
assistant professor mathematics, Purdue University, 1957-1962;
associate professor, Purdue University, 1962-1965;
associate professor mathematics, U. Rochester, 1965-1970;
professor, U. Rochester, 1970-1993;
professor emeritus, U. Rochester, since 1993. Lecturer mathematics Massachusetts Institute of Technology, Cambridge, 1962-1964. Visiting professor U. Wüzburg, Federal Republic Germany, 1971.
Research on ordered groups and fields, surreal numbers, valuation theory, extensions of meromorphic function fields, Banach algebras of analytic functions and real algebraic curves.
(In this volume, a tower of surreal number fields is defin...)
Member American Mathematics Society.
Married Katharine McPherson Page, August 20, 1957. Children: Elizabeth Larrabee, Margaret Tilden.