mathematics

Richard Lyons (mathematician)

Richard Lyons (mathematician) 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 Richard Lyons (mathematician) rather than just read about it. In short: Richard Neil Lyons (born January 22, 1945, in New York City, New York) is an American mathematician specializing in finite group theory. Lyons received his PhD in 1970 at the University of Chicago under John Griggs Thompson with the thesis Characterizations of Some Finite Simple Groups with Small 2-Rank.

Key takeaways

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

Reference excerpt

Richard Neil Lyons (born January 22, 1945, in New York City, New York) is an American mathematician specializing in finite group theory. Lyons received his PhD in 1970 at the University of Chicago under John Griggs Thompson with the thesis Characterizations of Some Finite Simple Groups with Small 2-Rank. From 1972 to 2017, he was a professor at Rutgers University. With Daniel Gorenstein and Ronald Solomon he wrote, and is continuing to write, now with Inna Capdeboscq, a series on the second-generation proof of the classification program for finite simple groups. Ten volumes of this series have been published so far. He discovered a sporadic group which Charles Sims constructed and called the Lyons group Ly. In 2012, he shared the Leroy P. Steele Prize for Mathematical Exposition, awarded by the American Mathematical Society, with Michael Aschbacher, Stephen D. Smith, and Ronald Solomon. In 2013, he became a fellow of the American Mathematical Society "for contributions to the classification of the finite simple groups, including the discovery of one of the 26 sporadic finite simple groups.".

Works with Gorenstein: The local structure of finite groups of characteristic 2 type, American Mathematical Society, 1983 with Daniel Gorenstein, Ronald Solomon: The classification of the finite simple groups, American Mathematical Society, 10 Vols., 1994–2023 with Michael Aschbacher, Stephen D. Smith, Ronald Solomon: The classification of finite simple groups: Groups of characteristic 2 type, American Mathematical Society, 2011

References

External links Homepage

Worked examples

Example 1 — a first encounter with Richard Lyons (mathematician)

Start with the simplest possible case. Write down what Richard Lyons (mathematician) 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 Richard Lyons (mathematician) 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 Richard Lyons (mathematician) 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 Richard Lyons (mathematician)

In research: Richard Lyons (mathematician) 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 Richard Lyons (mathematician) 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: Richard Lyons (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Richard Lyons (mathematician) 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 Richard Lyons (mathematician) in 20 minutes

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

Frequently asked questions

What is Richard Lyons (mathematician) in simple terms?

Why does Richard Lyons (mathematician) 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 Richard Lyons (mathematician)?

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 Richard Lyons (mathematician).