mathematics

Roger Wolcott Richardson

Roger Wolcott Richardson 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 Roger Wolcott Richardson rather than just read about it. In short: Roger Wolcott Richardson (30 May 1930 – 15 June 1993) was a mathematician noted for his work in representation theory and geometry. Life Richardson was born in Baton Rouge, Louisiana, and educated at Louisiana State University, Harvard University and University of Michigan, Ann Arbor where he obtained a Ph.D. in 1958 under the supervision of Hans Samelson.

Key takeaways

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

Reference excerpt

Roger Wolcott Richardson (30 May 1930 – 15 June 1993) was a mathematician noted for his work in representation theory and geometry.

Life Richardson was born in Baton Rouge, Louisiana, and educated at Louisiana State University, Harvard University and University of Michigan, Ann Arbor where he obtained a Ph.D. in 1958 under the supervision of Hans Samelson. After a postdoc appointment at Princeton University, he accepted a faculty position at the University of Washington in Seattle. He emigrated to the United Kingdom in 1970, taking up a chair at Durham University. In 1978 he moved to the Australian National University in Canberra, where he stayed as faculty until his death. Richardson's best known result states that if P is a parabolic subgroup of a reductive group, then P has a dense orbit on its nilradical, i.e., one whose closure is the whole space. This orbit is now universally known as the Richardson orbit. He was elected a Fellow of the Australian Academy of Science in 1990. In 1997 the Cambridge University Press published Algebraic Groups and Lie Groups: A Volume of Papers in Honour of the Late R. W. Richardson, which was organized by a committee of 5 mathematicians selected by the Australian Mathematical Society. The volume's preface has several paragraphs about Richardson's research.

Publications Nijenhuis, Albert; Richardson Jr., Roger W. (1966). "Cohomology and deformations in graded Lie algebras". Bulletin of the American Mathematical Society. 72 (1): 1–29. doi:10.1090/s0002-9904-1966-11401-5. MR 0195995.

Worked examples

Example 1 — a first encounter with Roger Wolcott Richardson

Start with the simplest possible case. Write down what Roger Wolcott Richardson 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 Roger Wolcott Richardson 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 Roger Wolcott Richardson 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 Roger Wolcott Richardson

In research: Roger Wolcott Richardson 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 Roger Wolcott Richardson 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: Roger Wolcott Richardson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1930 births, 1993 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Roger Wolcott Richardson 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 Roger Wolcott Richardson in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Roger Wolcott Richardson 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.
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Frequently asked questions

What is Roger Wolcott Richardson in simple terms?

Roger Wolcott Richardson (30 May 1930 – 15 June 1993) was a mathematician noted for his work in representation theory and geometry. Life Richardson was born in Baton Rouge, Louisiana, and educated at Louisiana State University, Harvard University and University of Michigan, Ann Arbor where he obtai…

Why does Roger Wolcott Richardson 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 Roger Wolcott Richardson?

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 Roger Wolcott Richardson.