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Harley M. Flanders (September 13, 1925 – July 26, 2013) was an American mathematician, known for several textbooks and contributions to his fields: algebra and algebraic number theory, linear algebra, electrical networks, scientific computing.
Flanders received his bachelors (1946), masters (1947) and PhD (1949) at the University of Chicago on the dissertation Unification of class field theory advised by Otto Schilling and André Weil. entry from the Mathematics Genealogy Project He held the Bateman Fellowship at Caltech. He joined the faculty at University of California at Berkeley. In 1955 Flanders heard Charles Loewner speak there on . Notes were taken and the lectures appeared in a limited form with the expectation that Loewner would produce a book on the topic. With his death in 1968 the notes drew the attention of Murray H. Protter and Flanders. They edited Loewner's talks and in 1971 The MIT Press published Charles Loewner: Theory of Continuous Groups. The book was re-issued in 2008.
Teaching posts Flanders held included the faculty at Purdue University (1960-1970), Tel Aviv University (1970–77), visiting professor at Georgia Tech (1977–78), visiting scholar at Florida Atlantic University (1978–85), University of Michigan, Ann Arbor (1985–97, 2000–), University of North Florida (1997–2000), and distinguished mathematician in residence at Jacksonville University (1997–2000). memo from uchicago.edu
Flanders was Editor-in-Chief, American Mathematical Monthly, 1969–1973. He also wrote calculus software MicroCalc, ver 1–7 (1975–). Dr. Flanders is a unique person
In 1991 Flanders was invited to the first SIAM workshop on automatic differentiation, held in Breckenridge, Colorado. Flanders' chapter in the Proceedings is titled "Automatic differentiation of composite functions". He presented an algorithm inputting two n-vectors of (higher) derivatives of F and G at a point, which used the chain rule to construct a linear transformation producing the derivative of the composite F o G. With prompting from editor Griewank, Flanders included application of the algorithm to automatic differentiation of implicit functions.Andreas Griewank & George F. Corliss (editors)(1991) Automatic Differentiation of Algorithms: Theory, Implementation, Application, SIAM , Flanders' paper: Part III, chapter 10, pages 95–9. Recalling his early exposure to the formula of Faa di Bruno, Flanders wrote, "I think Faa's formula is quite inefficient for the practical computation of numerical (not symbolic) derivatives."
Harley Flanders died July 26, 2013, in Ann Arbor, Michigan.
In 1954, Flanders considered the converse of the Poincaré lemma.H. Flanders (1954) An extension theorem for solutions of dω = Ω, Proceedings of the American Mathematical Society 5(3):509, 10
In 1963, Flanders published Differential Forms with Applications to the Physical Sciences which connected applied mathematics and differential forms. A reviewer affirmed that the book forms such a bridge with differential geometry. Republished in 1989 by Dover Books, the book includes a succinct mathematical electromagnetism, where the electric and magnetic components of the field pertain to complementary 2-forms, obtained from exterior derivation of the electromagnetic four-potential.
To support the recruitment of students with capacity to follow these courses, some works on precalculus mathematics were written with J.J. Price: Algebra (1975), Trigonometry (1975), Algebra and Trigonometry (1981), Precalculus Mathematics (1981), and College Algebra (1982).
Flanders continued with Single-Variable Calculus (1981) and another Calculus in 1985
In 1984, Flanders published his textbook on Pascal language: Scientific Pascal (1984) Scientific Pascal via Google Books for which a second edition was published in 1996 by Birkhäuser. That year he also published Calculus: A lab course with MicroCalc (Springer-Verlag).
Differential forms
Flanders is known for advancing an approach to multivariate calculus that is independent of coordinates through treatment of differential forms.
According to Shiing-Shen Chern, "an affine connection on a differentiable manifold gives rise to covariant differentiations of tensor fields. The classical approach makes use of the natural frames relative to local coordinates and works with components of tensor fields, thus giving the impression that this branch of differential geometry is a venture through a maze of indices. The author Flanders gives a mechanism which shows that this is not necessarily so."H. Flanders (1953) "Development of an extended exterior differential calculus", Transactions of the American Mathematical Society 75: 311–26,
Awards
Mathematics education
In 1970, Flanders published the first of several useful for topics commonly taught at college level: with Justin Jesse Price and Robert R. Korfhage a text on Calculus was distributed by Academic Press. With J. J. Price, Flanders also wrote Elementary Functions and Analytic Geometry (1973) and Introductory College Mathematics: with Linear Algebra and Finite Mathematics (1974). With both J.J. Price and R.R. Korfhage, Flanders wrote First Course in Calculus with Analytic Geometry (1974) and Second Course in Calculus (1974).
Selected papers
Categories: 20th-century American Mathematicians, 21st-century American Mathematicians, University Of Chicago Alumni, University Of California, Berkeley Faculty, Purdue University Faculty, Academic Staff Of Tel Aviv University, 2013 Deaths, 1925 Births, Jacksonville University Faculty, University Of Michigan Staff, American Textbook Writers, The American Mathematical Monthly Editors
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