mathematics

Shaul Foguel

Shaul Foguel 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 Shaul Foguel rather than just read about it. In short: Shaul Reuven Foguel (Hebrew: שאול פוגל, December 5, 1931 - December 19, 2020) was an Israeli mathematician. Shaul Foguel was born to one of the founding families of the City of Tel Aviv and his mother Dora Malkin was a direct descendant of Saul Wahl.

Key takeaways

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

Reference excerpt

Shaul Reuven Foguel (Hebrew: שאול פוגל, December 5, 1931 - December 19, 2020) was an Israeli mathematician. Shaul Foguel was born to one of the founding families of the City of Tel Aviv and his mother Dora Malkin was a direct descendant of Saul Wahl. He received his B.S. and M.S. in Mathematics from the Hebrew University of Jerusalem and his PhD in Mathematics from Yale University in 1958. He wrote his dissertation under Nelson Dunford on "Studies in Spectral Operators and the Basis Problem". Shaul Foguel was Professor Emeritus of the Hebrew University of Jerusalem, and a supporter of the Israeli Left. He ran in the 1969 Knesset elections on the Peace List along with Gadi Yatziv, although it failed to win a seat. He spent his retirement in New York City, where his two sons, Professor Tuval Foguel of Adelphi University, and Sy Foguel, the CEO of Berkshire Hathaway GUARD Insurance Companies live.

Publications Shaul R. Foguel "Selected topics in the study of Markov operators" Dept. of Mathematics, University of North Carolina at Chapel Hill, 1980 Shaul R. Foguel "The Ergodic theory of Markov processes" Van Nostrand Reinhold Co., 1969

Selected articles Foguel, Shaul R. (1983). "A generalized 0–2 law". Israel Journal of Mathematics. 45 (2): 219–224. doi:10.1007/BF02774018. Foguel, Shaul R. (1979). "Harris operators". Israel Journal of Mathematics. 33 (3): 281–309. doi:10.1007/BF02762166. Foguel, Shaul R. (1979). "Shlomo Horowitz 1938–1978". Israel Journal of Mathematics. 33 (3): 175–176. doi:10.1007/BF02762158. Foguel, Shaul R. (1976). "More on the "Zero-Two" Law". Proceedings of the American Mathematical Society. 61 (2): 262–264. doi:10.1090/S0002-9939-1976-0428076-2.

References

Illustrations

Worked examples

Example 1 — a first encounter with Shaul Foguel

Start with the simplest possible case. Write down what Shaul Foguel 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 Shaul Foguel 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 Shaul Foguel 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 Shaul Foguel

In research: Shaul Foguel 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 Shaul Foguel 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: Shaul Foguel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1931 births, 2020 deaths, Academic staff of the Hebrew University of Jerusalem, so understanding it makes those chapters shorter.
In everyday life: Look for Shaul Foguel 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 Shaul Foguel in 20 minutes

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

Frequently asked questions

What is Shaul Foguel in simple terms?

Why does Shaul Foguel 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 Shaul Foguel?

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 Shaul Foguel.