mathematics

Paul Kelly (mathematician)

Paul Kelly (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 Paul Kelly (mathematician) rather than just read about it. In short: Paul Joseph Kelly (June 26, 1915 – July 15, 1995) was an American mathematician who worked in geometry and graph theory. Education and career Kelly was born in Riverside, California.

Key takeaways

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Reference excerpt

Paul Joseph Kelly (June 26, 1915 – July 15, 1995) was an American mathematician who worked in geometry and graph theory.

Education and career Kelly was born in Riverside, California. He earned bachelor's and master's degrees from the University of California, Los Angeles before moving to the University of Wisconsin–Madison for doctoral studies; he earned his Ph.D. in 1942 with a dissertation concerning geometric transformations under the supervision of Stanislaw Ulam. He spent the rest of the war years serving in the United States Air Force as a First Lieutenant, before returning to academia with a teaching appointment at the University of Southern California in 1946. He moved to the University of California, Santa Barbara in 1949, and was chair there from 1957 to 1962. At UCSB, his students included Brian Alspach (through whom he has nearly 30 academic descendants) and Phyllis Chinn. He retired in 1982.

Contributions Kelly is known for posing the reconstruction conjecture with his advisor Ulam, which states that every graph is uniquely determined by the ensemble of subgraphs formed by deleting one vertex in each possible way. He also proved a special case of this conjecture, for trees. He is the coauthor of three textbooks: Projective geometry and projective metrics (1953, with Herbert Busemann), Geometry and convexity: A study in mathematical methods (1979, with Max L. Weiss), and The non-Euclidean, hyperbolic plane: Its structure and consistency (1981, with Gordon Matthews).

Selected articles with David Merriell: Kelly, Paul; Merriell, David (1960). "A class of graphs". Trans. Amer. Math. Soc. 96 (3): 488–492. doi:10.1090/s0002-9947-1960-0115932-0. MR 0115932. with E. G. Straus: Kelly, P. J.; Straus, E. G. (1957). "Inversive and conformal convexity". Proc. Amer. Math. Soc. 8 (3): 572–577. doi:10.1090/s0002-9939-1957-0087973-9. MR 0087973. Kelly, Paul J. (1949). "On Minkowski bodies of constant width". Bull. Amer. Math. Soc. 55 (12): 1147–1150. doi:10.1090/s0002-9904-1949-09345-x. MR 0033079. Kelly, Paul J. (1948). "On isometries of product sets". Bull. Amer. Math. Soc. 54 (8): 723–727. doi:10.1090/s0002-9904-1948-09063-2. MR 0026320. Kelly, Paul J. (1945). "On isometries of square sets". Bull. Amer. Math. Soc. 51 (12): 960–963. doi:10.1090/s0002-9904-1945-08482-1. MR 0013898.

References

Worked examples

Example 1 — a first encounter with Paul Kelly (mathematician)

Start with the simplest possible case. Write down what Paul Kelly (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 Paul Kelly (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 Paul Kelly (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 Paul Kelly (mathematician)

In research: Paul Kelly (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 Paul Kelly (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: Paul Kelly (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1915 births, 1995 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paul Kelly (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 Paul Kelly (mathematician) in 20 minutes

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Frequently asked questions

What is Paul Kelly (mathematician) in simple terms?

Paul Joseph Kelly (June 26, 1915 – July 15, 1995) was an American mathematician who worked in geometry and graph theory. Education and career Kelly was born in Riverside, California.

Why does Paul Kelly (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 Paul Kelly (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 Paul Kelly (mathematician).