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Michael M. Neumann received his Doctor of Science degree in 1974 and the Habilitation in Mathematics in 1979, both from the University of Saarbrucken, Germany. Before joining Mississippi State University in 1989, he was a Heisenberg Fellow of the German Science Foundation in Saarbrucken and Associate Professor of Mathematics at the University of Essen, Germany. Dr. Neumann hold visiting professorships at the University of Osnabruck, Germany, the University of Copenhagen, Denmark, the University of Palermo, Italy, the University of California at Los Angeles, and the California Institute of Technology. He gave more than 120 invited conference and colloquium talks in fourteen countries, including a one-hour address to the Danish Mathematical Society at the Annual Meeting in 1993.

Michael M. Neumann was named Outstanding Honors Faculty Member at Mississippi State University in 1992, and received the MSU Alumni Association Lower Level Teaching Award in 1999. His main research interests include operator theory, functional analysis, and convex analysis with applications to mathematical economics. Dr. Neumann has published more than seventy refereed articles in these areas. In 1997, he organized a Special Session on "Banach Algebras" at the Annual Meeting of the American Mathematical Society in San Diego, while, in 1999, he served on the International Scientific Committee for the organization of the International Congress on "Operator Theory and Banach Algebras" in Rabat, Morocco.

An Introduction to Local Spectral Theory

Neumann, Michael M.
Publisher: London Mathematical Society Monographs Series, Clarendon Press - Oxford University Press
ISBN: 0198523815
Collaborators: Kjeld B. Laursen

This research monograph centers around an area of operator theory where complex analysis, Banach algebras, and harmonic analysis overlap and interact. Modern local spectral theory is built on the classical spectral theorem, and thus dates back to seminal work of van Neumann and the origins of quantum mechanics and functional analysis. The main purpose of this book is to provide an in-depth introduction to the spectral theory of operators on Banach spaces whose pioneers include Dunford, Bishop, and Foias.

The book describes in detail some of the research activities of the Analysis Seminar in the Department of Mathematics and Statistics at Mississippi State University. It includes extensive applications of local spectral theory to the invariant subspace problem for operators on Banach spaces and to the spectral properties of multipliers and convolution operators. It also presents the connections to the theory of automatic continuity.

Mathematica Projects for Vector Calculus

Neumann, Michael M.
Publisher: Kendall/Hunt
second printing 1999,1996
ISBN: 0787228583
Collaborators: T. Len Miller

The book contains about fifty in-depth computer projects for an introductory course in multivariate calculus. It starts with a streamlined introduction to the computer algebra system Mathematica that is tailored to the needs of calculus and arranged as a series of computer exercises. Two sample projects on the motion of projectiles and roller coasters are then discussed in considerable detail. There are three chapters with computer projects for students. First, the emphasis is on the notions of velocity, acceleration, and curvature, together with their graphical representation and animation. The projects in the next chapter center around tangent planes, Taylor polynomials in several variables, least squares approximations, techniques of optimization, change of variables in multiple integrals, and Green's theorem. Finally, cylindrical and spherical coordinates, roller casters, monkey saddles, Mobius strips, Stokes' theorem, and the divergence theorem are addressed.

Through its emphasis on symbolic and numerical computations and graphical representations performed by a computer algebra system, the book marks a new era in the undergraduate mathematics curriculum. It is currently being used in the instruction of several calculus classes at Mississippi State University, as part of the program "Student Research Projects for Multi variate Calculus" in the Department of Mathematics and Statistics. This program has been partially supported by a grant from the Division of Undergraduate Education of the National Science Foundation.

Mathematical Systems in Economics

Neumann, Michael M.
Publisher: Hain Verlag bei Athenäum
Collaborators: Heinz König

The main goal of this book is the presentation of equilibrium analysis in mathematical economics, written for mathematicians. After an introductory chapter on economic models and Leontief systems, two long chapters are devoted to the careful discussion of the relevant background material from convex analysis and fixed-point theory. These mathematical theories are then applied to derive the existence of equilibria in private-ownership economies and in some of their generalizations. The final chapter presents the connections between equilibria and optimality, and studies the core of large economic systems. The book is in the spirit of the Nobel-prize winning work of Debreu, and includes a number of new results related to recent research by Gale and Mas-Colell.

From Mathematical Reviews (87k:90001): "The book covers equilibrium theory with special emphasis on existence, and it contains a large chapter on convex analysis with a wealth of material, much of which cannot be found in other, similar texts. The presentation is at a very high level of perfection, and the topics covered are treated in considerable detail, bringing the reader up to the level of current research. Thus the book belongs to the very best among this kind of textbooks." (reviewed by Hans Keiding, Aarhus, Denmark).