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Paul Rabinowitz

Paul Rabinowitz 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 Paul Rabinowitz rather than just read about it. In short: Paul H. Rabinowitz (born 1939) is the Edward Burr Van Vleck Professor of Mathematics and a Vilas Research Professor at the University of Wisconsin, Madison.

Paul Rabinowitz — main illustration
Paul Rabinowitz — illustration

Key takeaways

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

Reference excerpt

Paul H. Rabinowitz (born 1939) is the Edward Burr Van Vleck Professor of Mathematics and a Vilas Research Professor at the University of Wisconsin, Madison. He received a Ph.D. from New York University in 1966 under the direction of Jürgen Moser. From 1966 to 1969 he held a position as assistant professor at Stanford University. He has visited many mathematical institutions all over the world (among them universities at Aarhus, Pisa, Paris and ETH in Zurich). In 1978 Paul Rabinowitz became a fellow of the John Simon Guggenheim Memorial Foundation. He works in the fields of partial differential equations and nonlinear analysis. He is best known for his global bifurcation theorem and the mountain pass theorem, the latter done jointly with Antonio Ambrosetti. However also the linking and saddle point theorems, results concerning the existence of periodic solutions to hamiltonian systems, variational methods in the theory of critical points of strongly indefinite functional, in collaboration with Vieri Benci, and under the absence of compactness conditions of the Palais–Smale type. Many other achievements of Paul Rabinowitz have found their place in the history of mathematics. He is the recipient of numerous honors and awards, including the George David Birkhoff Prize in 1998. He was elected as a member of the United States National Academy of Sciences in 1998. In 2012 he became a fellow of the American Mathematical Society. In 2014 Paul Rabinowitz was awarded with the Juliusz Schauder Medal, the prize established by the Juliusz Schauder Center for Nonlinear Studies at the Nicolaus Copernicus University in Toruń, Poland, in recognition of his important contribution in the field of topological methods in nonlinear analysis.

References and notes

External links Paul Rabinowitz at the Mathematics Genealogy Project Announcement of Election to National Academy Juliusz P. Schauder Center for Nonlinear Studies

Illustrations

Paul Rabinowitz illustration

Worked examples

Example 1 — a first encounter with Paul Rabinowitz

Start with the simplest possible case. Write down what Paul Rabinowitz 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 Paul Rabinowitz 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 Paul Rabinowitz 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 Paul Rabinowitz

In research
Paul Rabinowitz 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 Paul Rabinowitz 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
Paul Rabinowitz is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1939 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Paul Rabinowitz 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 Paul Rabinowitz in 20 minutes

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

Frequently asked questions

What is Paul Rabinowitz in simple terms?

Paul H. Rabinowitz (born 1939) is the Edward Burr Van Vleck Professor of Mathematics and a Vilas Research Professor at the University of Wisconsin, Madison.

Why does Paul Rabinowitz 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 Paul Rabinowitz?

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 Paul Rabinowitz.

Tags

  • 1939 births
  • 20th-century American mathematicians
  • 21st-century American mathematicians
  • Fellows of the American Mathematical Society
  • Fellows of the Society for Industrial and Applied Mathematics
  • Foreign members of the Russian Academy of Sciences
  • Living people
  • Members of the United States National Academy of Sciences
  • University of Wisconsin–Madison faculty

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