mathematics

Richard M. Pollack

Richard M. Pollack 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 Richard M. Pollack rather than just read about it. In short: Richard M. Pollack (January 25, 1935 – September 18, 2018) was an American geometer who spent most of his career at the Courant Institute of Mathematical Sciences at New York University, where he was Professor Emeritus until his death.

Key takeaways

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

Reference excerpt

Richard M. Pollack (January 25, 1935 – September 18, 2018) was an American geometer who spent most of his career at the Courant Institute of Mathematical Sciences at New York University, where he was Professor Emeritus until his death.

Contributions In combinatorics, Pollack published several papers with Paul Erdős and János Pach. Pollack also published papers in discrete geometry. His work with Jacob E. Goodman includes the first nontrivial bounds on the number of order types and polytopes, and a generalization of the Hadwiger transversal theorem to higher dimensions. He and Goodman were the founding editors of the journal Discrete & Computational Geometry. In real algebraic geometry, Pollack wrote a series of papers with Saugata Basu and Marie-Françoise Roy, as well as a book.

Awards and honors In 2003, a collection of original research papers in discrete and computational geometry entitled Discrete and Computational Geometry: The Goodman–Pollack Festschrift was published as a tribute to Jacob E. Goodman and Richard Pollack on the occasion of their 2/3 × 100 birthdays. In 2012, he became a fellow of the American Mathematical Society. A special memorial 556-page issue of Discrete & Computational Geometry for Pollack was published in October 2020.

References

Pollack, Richard (1962), Some Tauberian theorems in elementary prime number theory (Ph.D. Thesis), New York University. Goodman, Jacob E.; Pach, János; Pollack, Richard, eds. (2008), Surveys on Discrete and Computational Geometry: Twenty Years Later, Contemporary Mathematics, vol. 453, American Mathematical Society.

Illustrations

Worked examples

Example 1 — a first encounter with Richard M. Pollack

Start with the simplest possible case. Write down what Richard M. Pollack 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 Richard M. Pollack 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 Richard M. Pollack 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 Richard M. Pollack

In research: Richard M. Pollack 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 Richard M. Pollack 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: Richard M. Pollack is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1935 births, 2018 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Richard M. Pollack 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 Richard M. Pollack in 20 minutes

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

Frequently asked questions

What is Richard M. Pollack in simple terms?

Why does Richard M. Pollack 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 Richard M. Pollack?

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 Richard M. Pollack.