mathematics

James B. Carrell

James B. Carrell 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 James B. Carrell rather than just read about it. In short: James B. Carrell (born 1940) is an American and Canadian mathematician, who is currently an emeritus professor of mathematics at the University of British Columbia, Vancouver, British Columbia, Canada.

Key takeaways

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

Reference excerpt

James B. Carrell (born 1940) is an American and Canadian mathematician, who is currently an emeritus professor of mathematics at the University of British Columbia, Vancouver, British Columbia, Canada. His areas of research are algebraic geometry, Lie theory, transformation groups and differential geometry. He obtained his Ph.D. at the University of Washington (Seattle) under the supervision of Allendoefer. In 1971, together with Jean Dieudonné, he received the Leroy P. Steele Prize for the article Invariant theory, old and new. He proved theorems in Schubert calculus about singularities of Schubert varieties. The Carrell–Liebermann theorem on the zero set of a holomorphic vector field is used in complex algebraic geometry. He is a fellow of the American Mathematical Society.

References

External links Jim Carrell at math.ubc.ca Jim Carrell in ca.linkedin.com

Illustrations

Worked examples

Example 1 — a first encounter with James B. Carrell

Start with the simplest possible case. Write down what James B. Carrell 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 James B. Carrell 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 James B. Carrell 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 James B. Carrell

In research: James B. Carrell 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 James B. Carrell 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: James B. Carrell is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1940 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for James B. Carrell 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 James B. Carrell in 20 minutes

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

Frequently asked questions

What is James B. Carrell in simple terms?

Why does James B. Carrell 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 James B. Carrell?

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 James B. Carrell.