astronomy

William Frederick Eberlein

William Frederick Eberlein is a astronomy 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 William Frederick Eberlein rather than just read about it. In short: William Frederick Eberlein (June 25, 1917, Shawano, Wisconsin – 1986, Rochester, New York) was an American mathematician, specializing in mathematical analysis and mathematical physics. Life Eberlein studied from 1936 to 1942 at the University of Wisconsin and at Harvard University, where he received in 1942 a PhD for the thesis Closure, Convexity, and Linearity in Banach Spaces under the direction of Marshall Stone.

Key takeaways

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

Reference excerpt

William Frederick Eberlein (June 25, 1917, Shawano, Wisconsin – 1986, Rochester, New York) was an American mathematician, specializing in mathematical analysis and mathematical physics.

Life Eberlein studied from 1936 to 1942 at the University of Wisconsin and at Harvard University, where he received in 1942 a PhD for the thesis Closure, Convexity, and Linearity in Banach Spaces under the direction of Marshall Stone. He was married twice—to Mary Bernarda Barry and Patricia Ramsay James. He had four children with Mary Barry, including Patrick Barry Eberlein, another renowned mathematician. Patricia Ramsay James was a mathematician who moved into computer science as the field opened up; their one child is Kristen James Eberlein, the chair of the OASIS Darwin Information Typing Architecture Technical Committee.

Work Eberlein had academic positions at the Institute for Advanced Study (1947–1948), at the University of Wisconsin (1948–1955), at Wayne State University (1955–1956), and from 1957 at the University of Rochester, where he remained for the rest of his career. His doctoral students include William F. Donoghue, Jr. and A. Wayne Wymore.

Contributions He worked on functional analysis, harmonic analysis, ergodic theory, mean value theorems, and numerical integration. Eberlein also worked on spacetime models, internal symmetries in gauge theory, and spinors. His name is attached to the Eberlein–Šmulian theorem in functional analysis, the Eberlein compacta in topology, and the Eberlein mean ergodic theorem.

References

Worked examples

Example 1 — a first encounter with William Frederick Eberlein

Start with the simplest possible case. Write down what William Frederick Eberlein claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 William Frederick Eberlein 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 William Frederick Eberlein 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 William Frederick Eberlein

In research: William Frederick Eberlein appears in astronomy 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 William Frederick Eberlein 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: William Frederick Eberlein is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1917 births, 1986 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for William Frederick Eberlein 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 William Frederick Eberlein in 20 minutes

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

Frequently asked questions

What is William Frederick Eberlein in simple terms?

William Frederick Eberlein (June 25, 1917, Shawano, Wisconsin – 1986, Rochester, New York) was an American mathematician, specializing in mathematical analysis and mathematical physics. Life Eberlein studied from 1936 to 1942 at the University of Wisconsin and at Harvard University, where he receiv…

Why does William Frederick Eberlein matter?

Because it connects several astronomy 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 William Frederick Eberlein?

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 William Frederick Eberlein.