mathematics

William J. Ellison

William J. Ellison 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 William J. Ellison rather than just read about it. In short: William John Ellison (1943 - 16 March 2022) was a British mathematician who worked on number theory. Ellison studied at the University of Cambridge, where he earned his bachelor's degree and then, after spending the academic year 1969/70 at the University of Michigan, his PhD in 1970 under John Cassels with thesis Waring's and Hilbert's 17th Problems.

Key takeaways

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

Reference excerpt

William John Ellison (1943 - 16 March 2022) was a British mathematician who worked on number theory. Ellison studied at the University of Cambridge, where he earned his bachelor's degree and then, after spending the academic year 1969/70 at the University of Michigan, his PhD in 1970 under John Cassels with thesis Waring's and Hilbert's 17th Problems. Subsequently, he became a postdoc at the University of Bordeaux. In 1972 he received the Leroy P. Steele Prize and a Lester Randolph Ford Award for his article "Waring's Problem“, an exposition of Waring's problem

Selected works with Fern Ellison: Prime Numbers (Les nombres premiers, 1975). Wiley, New York 1985, ISBN 0-471-8265-3-7 with Fern Ellison: Zahlentheorie In: Jean Dieudonné (ed.): Geschichte der Mathematik 1700 bis 1900 (Abrege d'histoire des mathematiques 1700–1900, 1978). Vieweg, Braunschweig 1985, online at archive.org, pp. 171–358, ISBN 3-528-08443-X

References

Illustrations

Worked examples

Example 1 — a first encounter with William J. Ellison

Start with the simplest possible case. Write down what William J. Ellison 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 William J. Ellison 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 J. Ellison 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 J. Ellison

In research: William J. Ellison 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 William J. Ellison 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 J. Ellison is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1943 births, 20th-century British mathematicians, 21st-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for William J. Ellison 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 J. Ellison in 20 minutes

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

Frequently asked questions

What is William J. Ellison in simple terms?

Why does William J. Ellison 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 William J. Ellison?

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 J. Ellison.