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Harley Flanders was born on 13 September, 1925 in Chicago, Illinois, US, is an American mathematician (1925–2013). Discover Harley Flanders's Biography, Age, Height, Physical Stats, Dating/Affairs, Family and career updates. Learn How rich is he in this year and how he spends money? Also learn how he earned most of networth at the age of 87 years old?

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Age 87 years old
Zodiac Sign Virgo
Born 13 September, 1925
Birthday 13 September
Birthplace Chicago, Illinois, US
Date of death 26 July, 2013
Died Place Ann Arbor, Michigan, US
Nationality United States

We recommend you to check the complete list of Famous People born on 13 September. He is a member of famous mathematician with the age 87 years old group.

Harley Flanders Height, Weight & Measurements

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Harley Flanders Net Worth

His net worth has been growing significantly in 2023-2024. So, how much is Harley Flanders worth at the age of 87 years old? Harley Flanders’s income source is mostly from being a successful mathematician. He is from United States. We have estimated Harley Flanders's net worth, money, salary, income, and assets.

Net Worth in 2024 $1 Million - $5 Million
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Source of Income mathematician

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Timeline

1925

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 was a sophomore calculus student of Lester R. Ford at the Illinois Institute of Technology and asked for more challenging reading.

Ford recommended A Course in Mathematical Analysis by Edouard Goursat, translated by Earle Hedrick, which included challenging exercises.

1946

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.

He held the Bateman Fellowship at Caltech.

He joined the faculty at University of California at Berkeley.

1954

In 1954, Flanders considered the converse of the Poincaré lemma.

1955

In 1955 Flanders heard Charles Loewner speak there on continuous groups.

Notes were taken and the lectures appeared in a limited form with the expectation that Loewner would produce a book on the topic.

1960

Teaching posts Flanders held included the faculty at Purdue University (1960), 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).

1963

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.

1968

With his death in 1968 the notes drew the attention of Murray H. Protter and Flanders.

1969

Flanders was Editor-in-Chief, American Mathematical Monthly, 1969–1973.

1970

In 1970, Flanders published the first of several useful textbooks for topics commonly taught at college level: with Justin Jesse Price and Robert R. Korfhage a text on Calculus was distributed by Academic Press.

1971

They edited Loewner's talks and in 1971 The MIT Press published Charles Loewner: Theory of Continuous Groups.

1973

With J. J. Price, Flanders also wrote Elementary Functions and Analytic Geometry (1973) and Introductory College Mathematics: with Linear Algebra and Finite Mathematics (1974).

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).

1975

He also wrote calculus software MicroCalc, ver 1–7 (1975–).

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).

1981

Flanders continued with Single-Variable Calculus (1981) and another Calculus in 1985

1984

In 1984, Flanders published his textbook on Pascal language: Scientific Pascal (1984) for which a second edition was published in 1996 by Birkhäuser.

That year he also published Calculus: A lab course with MicroCalc (Springer-Verlag).

1989

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.

1991

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.

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."

2001

Flanders recalled in 2001 that the final exercise required a proof of a formula for the derivatives of a composite function, generalizing the chain rule, in a form now called the Faa di Bruno formula.

2008

The book was re-issued in 2008.

2013

Harley Flanders died July 26, 2013, in Ann Arbor, Michigan.

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."