I received my Ph.D. in Mathematics from S.T. Hu in 1962 at UCLA. My specialty is Topology. My interests have broadened to Mathematical Physics and the History of Mathematics in recent years. My conviction that the topological invariants of the degree of a map and index of a vector field must describe basic physical ideas led me to Physics. I turned to the History of Mathematics in order to test my assertion that Mathematics is the study of Well-defined concepts. I also believe that mathematicians are the guardians and exemplars of critical reasoning. Just as English Professors speak out against misuse of language, so should mathematicians speak out against shoddy reasoning. Nowhere in our society is the lack of careful reasoning more prevalent than in the legal profession. Therefore I will include essays on Mathematics and the Law.
Mathematics and the Law
I have written over fifty papers in Mathematics. They range over general topology, combinatorics, homotopy theory, differential manifolds, transfers, evaluation subgroups, Group actions, classical topological invariants, function spaces, fiber bundles, applications of topology to group theory, robotics, and general relativity as well as the history of the Gauss-Bonnet Theorem.
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