mathematics

Jacob Wolfowitz

Jacob Wolfowitz 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 Jacob Wolfowitz rather than just read about it. In short: Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American Jewish statistician and Shannon Award-winning information theorist. He was the father of former United States Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz.

Key takeaways

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

Reference excerpt

Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American Jewish statistician and Shannon Award-winning information theorist. He was the father of former United States Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz.

Early life and education Wolfowitz was born in 1910 in Warsaw, Poland, the son of Helen (Pearlman) and Samuel Wolfowitz. He emigrated with his parents to the United States in 1920. He received a bachelor of science in 1931 from the City College of New York.

Career In the mid-1930s, Wolfowitz began his career as a high school mathematics teacher and continued teaching until 1942 when he received his Ph.D. degree in mathematics from New York University. While a part-time graduate student, Wolfowitz met Abraham Wald, with whom he collaborated in numerous joint papers in the field of mathematical statistics. This collaboration continued until Wald's death in an airplane crash in 1950. In 1951, Wolfowitz became a professor of mathematics at Cornell University, where he stayed until 1970. From 1970 to 1978 he was at the University of Illinois Urbana-Champaign. He died of a heart attack in Tampa, Florida, where he had become a professor at the University of South Florida after retiring from Illinois. Wolfowitz's main contributions were in the fields of statistical decision theory, non-parametric statistics, sequential analysis, and information theory. One of his results is the strong converse to Claude Shannon's coding theorem. While Shannon could prove only that the block error probability can not become arbitrarily small if the transmission rate is above the channel capacity, Wolfowitz proved that the block error rate actually converges to one. As a consequence, Shannon's original result is today termed "the weak theorem" (sometimes also Shannon's "conjecture" by some authors).

Further reading Kiefer, J., ed. Jacob Wolfowitz Selected Papers. New York: Springer-Verlag, 1980. ISBN 0-387-90463-8. Wolfowitz, Jacob, Coding Theorems of Information Theory. New York: Springer-Verlag, 1978. ISBN 0-387-08548-3.

References

External links Jacob Wolfowitz at the Mathematics Genealogy Project. O'Connor, John J.; Robertson, Edmund F., "Jacob Wolfowitz", MacTutor History of Mathematics Archive, University of St Andrews Zacks, Shelemyahu. "Biographical Memories: Jacob Wolfowitz (March 19, 1910–July 16, 1981)". National Academy of Sciences, n.d. Accessed May 3, 2007.

Illustrations

Worked examples

Example 1 — a first encounter with Jacob Wolfowitz

Start with the simplest possible case. Write down what Jacob Wolfowitz 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 Jacob Wolfowitz 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 Jacob Wolfowitz 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 Jacob Wolfowitz

In research: Jacob Wolfowitz 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 Jacob Wolfowitz 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: Jacob Wolfowitz is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1910 births, 1981 deaths, 20th-century American Jews, so understanding it makes those chapters shorter.
In everyday life: Look for Jacob Wolfowitz 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 Jacob Wolfowitz in 20 minutes

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

Frequently asked questions

What is Jacob Wolfowitz in simple terms?

Why does Jacob Wolfowitz 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 Jacob Wolfowitz?

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 Jacob Wolfowitz.