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e-mail schultz@maths.uwa.edu.au
Welcome to my home page. I'm Associate Professor of Mathematics at the University of Western Australia.
Not truth, nor certainty. These I forswore
In my novitiate, as young men called
To holy orders must abjure the world.
"If ..., then," this only I assert;
And my successes are but pretty chains
Linking twin doubts, for it is vain to ask
If what I postulate be justified
Or what I prove possess the stamp of fact.
Yet bridges stand, and men no longer crawl
In two dimensions. And such triumphs stem
In no small measure from the power this game,
Played with the thrice attenuated shades
Of things, has over their originals.
How frail the wand, but how profound the spell!
Clarence R. Wylie, Jr., 1948
A mathematician's failures:
"Now a mathematician has a matchless advantage over general
scientists, historians, politicians, and exponents of other
professions: He can be wrong. A fortiori, he can also be right.
A mistake made by a mathematician, even a great one,
is not a "difference of a point of view" or "another
interpretation of the data" or a "dictate of a conflicting
ideology", it is a mistake. The greatest of all mathematicians,
those who have discovered the greatest quantities of mathematical
truths, are also those who have published the greatest numbers of
lacunary proofs, insufficiently qualified assertions, and flat
mistakes. By attempting to make natural philosophy into a part of
mathematics, Newton relinquished the diplomatic immunity granted
to non-mathematical philosophers, chemists, psychologists, etc.,
and entered into the area where an error is an error even if it
is Newton's error; in fact, all the more so because it is Newton's
error.
The mistakes made by a great mathematician are of two kinds:
first, trivial slips that anyone can correct, and, second, titanic
failures reflecting the scale of the struggle which the great
mathematician waged. Failures of this latter kind are often as
important as successes, for they give rise to major discoveries
by other mathematicians. One error of a great mathematician has
often done more for science than a hundred impeccable little
theorems proved by lesser men. Since Newton was as great
mathematician as ever lived, but still a mathematician, we may
approach his work with the level, tactless criticism which
mathematics demands."
C. A. Truesdell
Algebra
especially abelian groups, modules, endomorphism rings and automorphism groups. Combinatorics including graph theory History of mathematics particularly Ancient and Renaissance algebra, 17th Century calculus and Ancient Chinese mathematics.
Groups and Symmetry and their applications to Physics and Chemistry.
Algebra 214
Mathematics 4P5 Ring Theory
Let Deltai be the maximal normal p-subgroup of the automorphism group of an abelian p-group Gi. If Delta1 = Delta2 then G1 = G2 Almost completely decomposable groups with p-power regulating index have unique decompositions up to near isomorphism. Almost completely decomposable crq groups satisfy the Baer-Kaplansky Theorem up to near isomorphism. The ideal lattice of the endomorphism ring of a separable abelian p-group is characterised by cardinal invariants.
Description of the upper annihilating series of the Jacobson radical of the endomorphism ring of a bounded abelian p-group.
Multiplicative and additive Galois Theory of modules.
Description of new classes of pure fully invariant subgroups of an abelain group.
2004 Responsibilities:
Further Information:
times since Dec 10, 1997.
Author: Phill Schultz, schultz@maths.uwa.edu.au
