mathematics

Lester Dubins

Lester Dubins 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 Lester Dubins rather than just read about it. In short: Lester Dubins (April 27, 1920 – February 11, 2010) was an American mathematician noted primarily for his research in probability theory. He was a faculty member at the University of California at Berkeley from 1962 through 2004, and in retirement was Professor Emeritus of Mathematics and Statistics.

Key takeaways

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

Reference excerpt

Lester Dubins (April 27, 1920 – February 11, 2010) was an American mathematician noted primarily for his research in probability theory. He was a faculty member at the University of California at Berkeley from 1962 through 2004, and in retirement was Professor Emeritus of Mathematics and Statistics. It has been thought that, since classic red-and-black casino roulette is a game in which the house on average wins more than the gambler, that "bold play", i.e. betting one's whole purse on a single trial, is a uniquely optimal strategy. While a graduate student at the University of Chicago, Dubins surprised his teacher Leonard Jimmie Savage with a mathematical demonstration that this is not true. Dubins and Savage wrote a book that appeared in 1965 titled How to Gamble if You Must (Inequalities for Stochastic Processes) which presented a mathematical theory of gambling processes and optimal behavior in gambling situations, pointing out their relevance to traditional approaches to probability. Under the influence of the work of Bruno de Finetti, Dubins and Savage worked in the context of finitely additive rather than countably additive probability theory, thereby bypassing some technical difficulties. Dubins was the author of nearly a hundred scholarly publications. Besides probability, some of these were on curves of minimal length under constraints on curvature and initial and final tangents (see Dubins path), Tarski's circle squaring problem, convex analysis, and geometry. His doctoral students include Theodore Hill. Together with Gideon E. Schwarz he proved the Dubins–Schwarz theorem.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Lester Dubins

Start with the simplest possible case. Write down what Lester Dubins 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 Lester Dubins 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 Lester Dubins 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 Lester Dubins

In research: Lester Dubins 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 Lester Dubins 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: Lester Dubins is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1920 births, 2010 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Lester Dubins 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 Lester Dubins in 20 minutes

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

Frequently asked questions

What is Lester Dubins in simple terms?

Why does Lester Dubins 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 Lester Dubins?

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 Lester Dubins.