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Kurt Otto Friedrichs

Kurt Otto Friedrichs is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Kurt Otto Friedrichs rather than just read about it. In short: Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a German-American mathematician. He was the co-founder of the Courant Institute at New York University, and a recipient of the National Medal of Science.

Kurt Otto Friedrichs — main illustration
Kurt Otto Friedrichs — illustration

Key takeaways

  • Kurt Otto Friedrichs belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Kurt Otto Friedrichs to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Kurt Otto Friedrichs from memory before moving on to harder problems.

Reference excerpt

Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a German-American mathematician. He was the co-founder of the Courant Institute at New York University, and a recipient of the National Medal of Science.

Biography Friedrichs was born in Kiel, Schleswig-Holstein on September 28, 1901. His family soon moved to Düsseldorf, where he grew up. He attended several different universities in Germany studying the philosophical works of Heidegger and Husserl, but finally decided that mathematics was his real calling. During the 1920s, Friedrichs pursued this field in Göttingen, which had a renowned Mathematical Institute under the direction of Richard Courant. Courant became a close colleague and lifelong friend of Friedrichs. In 1931, Friedrichs became a full professor of mathematics at the Technische Hochschule in Braunschweig. In early February 1933, a few days after Hitler became the Chancellor of Germany, Friedrichs met and immediately fell in love with a young Jewish student, Nellie Bruell. Their relationship became increasingly challenging and difficult because of the antisemitic Nuremberg Laws of Hitler's government. In 1937, both Friedrichs and Nellie Bruell managed to emigrate separately to New York City where they finally married. Their long and very happy marriage produced five children. Courant had left Germany in 1933 and had founded an institute for graduate studies in mathematics at New York University. Friedrichs joined him when he arrived in 1937 and remained there for forty years. He was instrumental in the development of the Courant Institute of Mathematical Sciences, which eventually became one of the most distinguished research institutes for applied mathematics in the world. Friedrichs died in New Rochelle, New York on December 31, 1982. Friedrichs' greatest contribution to applied mathematics was his work on partial differential equations. He also did major research and wrote many books and papers on existence theory, numerical methods, differential operators in Hilbert space, non-linear buckling of plates, flows past wings, solitary waves, shock waves, combustion, magneto-fluid dynamical shock waves, relativistic flows, quantum field theory, perturbation of the continuous spectrum, scattering theory, and symmetric hyperbolic equations. With Cartan, Friedrichs gave a "geometrized" formulation of Newtonian gravitation theory—also known as "Newton–Cartan theory"—and later developed by Dautcourt, Dixon, Dombrowski and Horneffer, Ehlers, Havas, Künzle, Lottermoser, Trautman, and others. A member of the National Academy of Sciences since 1959, Friedrichs received many honorary degrees and awards for his work. There is a student prize named after Friedrichs at NYU. The American Mathematical Society selected him as the Josiah Willards Gibbs lecturer for 1954. In November 1977, Friedrichs received the National Medal of Science from President Jimmy Carter "for bringing the powers of modern mathematics to bear on problems in physics, fluid dynamics, and elasticity."

Selected bibliography Courant, R.; Friedrichs, K. O. (1948), Supersonic Flow and Shock Waves, New York: Interscience R. von Mises and K. O. Friedrichs, Fluid Dynamics, Springer-Verlag (1971). K. O. Friedrichs, Perturbation of Spectra in Hilbert Space, American Mathematical Society (1965). K. O. Friedrichs, Mathematical aspects of the quantum theory of fields, Interscience (1953). K. O. Friedrichs, Spectral Theory of Operators in Hilbert Space, Springer-Verlag (1981). Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S. (ed.), Selecta, Contemporary Mathematicians, Boston–Basel–Stuttgart: Birkhäuser Verlag, ISBN 0-8176-3270-0. A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgang Wasow, Harold Weitzner.

See also Singular perturbation

References

External links Kurt Otto Friedrichs at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Kurt Otto Friedrichs", MacTutor History of Mathematics Archive, University of St Andrews National Academy of Sciences Biographical Memoir Literature by and about Kurt Otto Friedrichs in the German National Library catalogue

Illustrations

Kurt Otto Friedrichs illustration

Worked examples

Example 1 — a first encounter with Kurt Otto Friedrichs

Start with the simplest possible case. Write down what Kurt Otto Friedrichs claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Kurt Otto Friedrichs before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Kurt Otto Friedrichs ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Kurt Otto Friedrichs

In research
Kurt Otto Friedrichs appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Kurt Otto Friedrichs in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Kurt Otto Friedrichs is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1901 births, 1982 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Kurt Otto Friedrichs outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Kurt Otto Friedrichs in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Kurt Otto Friedrichs means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Kurt Otto Friedrichs out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Kurt Otto Friedrichs in simple terms?

Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a German-American mathematician. He was the co-founder of the Courant Institute at New York University, and a recipient of the National Medal of Science.

Why does Kurt Otto Friedrichs matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Kurt Otto Friedrichs?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Kurt Otto Friedrichs.

Tags

  • 1901 births
  • 1982 deaths
  • 20th-century American mathematicians
  • 20th-century German mathematicians
  • Academic staff of TU Braunschweig
  • Courant Institute of Mathematical Sciences faculty
  • Emigrants from Nazi Germany to the United States
  • Mathematicians from New York (state)
  • Members of the United States National Academy of Sciences
  • National Medal of Science laureates
  • Operator theorists
  • Partial differential equation theorists

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