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Norman Levinson

Norman Levinson 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 Norman Levinson rather than just read about it. In short: Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing.

Key takeaways

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

Reference excerpt

Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society and in 1971 the Chauvenet Prize (after winning in 1970 the Lester R. Ford Award) of the Mathematical Association of America for his paper A Motivated Account of an Elementary Proof of the Prime Number Theorem. In 1974 he published a 54-pages long paper, later simplified by Matthew Young to 7 pages, proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey. He received both his bachelor's degree and his master's degree in electrical engineering from MIT in 1934, where he had studied under Norbert Wiener and took almost all of the graduate-level courses in mathematics. He received the MIT Redfield Proctor Traveling Fellowship to study at the University of Cambridge, with the assurance that MIT would reward him with a PhD upon his return regardless of whatever he produced at Cambridge. Within the first four months in Cambridge, he had already produced two papers. In 1935, MIT awarded him with the PhD in mathematics. His death in 1975 was caused by a brain tumor. He was married since 1938; his widow Zipporah died at age 93 in 2009. He had two daughters and four grandchildren. Norman Levinson's doctoral students include Raymond Redheffer and Harold Shapiro.

See also Levinson recursion Levinson's inequality Levinson's theorem

Publications Levinson, Norman (1940), Gap and density theorems (AMS Colloquium Publications vol. 26), New York: Amer. Math. Soc. ISBN 0-8218-1026-X Coddington, Earl A.; Levinson, Norman (1955), Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, MR 0069338 ISBN 978-0-89874-755-3 Levinson, Norman (1998), Nohel, John A.; Sattinger, David H. (eds.), Selected papers of Norman Levinson. Vol. 1, Contemporary Mathematicians, Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-3862-7, MR 1491093 Levinson, Norman (1998), Nohel, John A.; Sattinger, David H. (eds.), Selected papers of Norman Levinson. Vol. 2, Contemporary Mathematicians, Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-3979-2, MR 1491093

References

External links O'Connor, John J.; Robertson, Edmund F., "Norman Levinson", MacTutor History of Mathematics Archive, University of St Andrews

Worked examples

Example 1 — a first encounter with Norman Levinson

Start with the simplest possible case. Write down what Norman Levinson 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 Norman Levinson 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 Norman Levinson 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 Norman Levinson

In research
Norman Levinson 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 Norman Levinson 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
Norman Levinson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1912 births, 1975 deaths, 20th-century American Jews, so understanding it makes those chapters shorter.
In everyday life
Look for Norman Levinson 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 Norman Levinson in 20 minutes

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

Frequently asked questions

What is Norman Levinson in simple terms?

Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing.

Why does Norman Levinson 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 Norman Levinson?

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 Norman Levinson.

Tags

  • 1912 births
  • 1975 deaths
  • 20th-century American Jews
  • 20th-century American engineers
  • 20th-century American mathematicians
  • American mathematical analysts
  • American number theorists
  • Deaths from brain cancer in the United States
  • Institute for Advanced Study visiting scholars
  • Jewish American scientists
  • MIT School of Engineering alumni
  • Massachusetts Institute of Technology faculty

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