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Peter Duren

Peter Duren 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 Peter Duren rather than just read about it. In short: Peter Larkin Duren (April 30, 1935 – July 10, 2020) was an American mathematician. He specialized in mathematical analysis and was known for the monographs and textbooks he has written.

Key takeaways

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

Reference excerpt

Peter Larkin Duren (April 30, 1935 – July 10, 2020) was an American mathematician. He specialized in mathematical analysis and was known for the monographs and textbooks he has written.

Academic career Duren received in 1956 his bachelor's degree from Harvard University and in 1960 his Ph.D. from the Massachusetts Institute of Technology (MIT) under Gian-Carlo Rota with thesis Spectral theory of a class of non-self-adjoint infinite matrix operators. As a postdoc he was an instructor at Stanford University. At the University of Michigan, he became in 1962 an assistant professor, in 1966 an associate professor, in 1969 a professor, and in 2010 a professor emeritus. As a professor, Duren served on the thesis committee of Ted Kaczynski. Duren was in 1968/69 at the Institute for Advanced Study, in 1975 a visiting professor at the Technion in Haifa, in 1964/65 a visiting scientist at Imperial College and the University of Paris-Sud in Orsay, in 1982 a visiting professor at the University of Maryland and in 1982/83 at the Mittag-Leffler Institute, the University of Paris-Sud and at the ETH Zürich. In 1989 he was a visiting scientist at Stanford University, in 1993 at the University of Hawaii and in 1996 at the Norwegian Institute of Technology in Trondheim. He has also been a visiting scientist in Halle, at the Max-Planck Institute in Leipzig, at the University of Witwatersrand, in Santiago de Chile, at the Autonomous University of Madrid, at Bar-Ilan University and the Academia Sinica in Beijing. In 1976/77 he was chief editor of the Michigan Mathematical Journal. He was a co-editor of the American Mathematical Monthly and a festschrift for Frederick Gehring. Duren's research and expository writing deals with function theory and functional analysis, including Hardy spaces, schlicht functions, harmonic analysis, geometric function theory, potential theory, and special functions. Duren died on July 10, 2020, at the age of 85.

Awards From 1964 to 1966, Duren was a Sloan Fellow. In 2012, he became a Fellow of the American Mathematical Society.

Selected works 1970: Theory of H p {\displaystyle H^{p}} -Spaces, Academic Press, Dover 2000 1983: Univalent Functions, Grundlehren der mathematischen Wissenschaften, Springer Verlag 1988: (as editor with Richard A. Askey and Uta C. Merzbach) A Century of Mathematics in America, 3 vols., American Mathematical Society (Centenary of the AMS) 2004: Harmonic Maps in the Plane, Cambridge University Press 2004: (with Alexander Schuster) Bergman Spaces, American Mathematical Society 2012: Invitation to Classical Analysis, American Mathematical Society

References

External links Homepage

Worked examples

Example 1 — a first encounter with Peter Duren

Start with the simplest possible case. Write down what Peter Duren 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 Peter Duren 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 Peter Duren 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 Peter Duren

In research
Peter Duren 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 Peter Duren 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
Peter Duren is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1935 births, 2020 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Peter Duren 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 Peter Duren in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Peter Duren 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 Peter Duren out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Peter Duren in simple terms?

Peter Larkin Duren (April 30, 1935 – July 10, 2020) was an American mathematician. He specialized in mathematical analysis and was known for the monographs and textbooks he has written.

Why does Peter Duren 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 Peter Duren?

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 Peter Duren.

Tags

  • 1935 births
  • 2020 deaths
  • 20th-century American mathematicians
  • 21st-century American mathematicians
  • Fellows of the American Mathematical Society
  • Harvard University alumni
  • Massachusetts Institute of Technology alumni
  • Scientists from New Orleans
  • University of Michigan faculty

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