mathematics

Laurence Chisholm Young

Laurence Chisholm Young 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 Laurence Chisholm Young rather than just read about it. In short: Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a British mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He was the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians.

Key takeaways

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Reference excerpt

Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a British mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He was the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians. He moved to the US in 1949 but never sought American citizenship. The concept of Young measure is named after him: he also introduced the concept of the generalized curve and a concept of generalized surface which later evolved in the concept of varifold. The Young integral also is named after him and has now been generalised in the theory of rough paths.

Life and academic career Laurence Chisholm Young was born in Göttingen, the fifth of the six children of William Henry Young and Grace Chisholm Young. He held positions of Professor at the University of Cape Town, South Africa, and at the University of Wisconsin-Madison. He was also a chess grandmaster.

Selected publications

Books Young, L. C. (1927), The Theory of Integration, Cambridge Tracts in Mathematics and Mathematical Physics, vol. 21, Cambridge: Cambridge University Press, pp. viii + 53, JFM 53.0207.19, available from the Internet archive. Young, L. C. (1969), Lectures on the Calculus of Variations and Optimal Control, Philadelphia–London–Toronto: W. B. Saunders, pp. xi+331, ISBN 9780721696409, MR 0259704, Zbl 0177.37801. Young, Laurence (1981), Mathematicians and their times. History of mathematics and mathematics of history, North-Holland Mathematics Studies, 48 / Notas de Matemática [Mathematical Notes], 76, Amsterdam–New York: North-Holland Publishing Co., pp. x+344, ISBN 978-0-444-86135-1, MR 0629980, Zbl 0446.01028.

Papers Young, L. C. (1936), "An inequality of the Hölder type, connected with Stieltjes integration", Acta Mathematica, 67 (1): 251–282, doi:10.1007/bf02401743, JFM 62.0250.02, Zbl 0016.10404. Young, L. C. (1937), "Generalized curves and the existence of an attained absolute minimum in the Calculus of Variations", Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III, XXX (7–9): 211–234, JFM 63.1064.01, Zbl 0019.21901, memoir presented by Stanisław Saks at the session of 16 December 1937 of the Warsaw Society of Sciences and Letters. The free PDF copy is made available by the RCIN –Digital Repository of the Scientifics Institutes. Young, L. C. (January 1942), "Generalized Surfaces in the Calculus of Variations", Annals of Mathematics, Second Series, 43 (1): 84–103, doi:10.2307/1968882, JFM 68.0227.03, JSTOR 1968882, MR 0006023, Zbl 0063.09081. Young, L. C. (July 1942a), "Generalized Surfaces in the Calculus of Variations. II", Annals of Mathematics, Second Series, 43 (3): 530–544, doi:10.2307/1968809, JSTOR 1968809, MR 0006832, Zbl 0063.08362. Young, L. C. (1951), "Surfaces parametriques generalisees", Bulletin de la Société Mathématique de France, 79: 59–84, doi:10.24033/bsmf.1419, MR 0046421, Zbl 0044.10203. Young, L. C. (1954), "A variational algorithm" (PDF), Rivista di Matematica della Università di Parma, (1), 5: 255–268, MR 0081437, Zbl 0059.09605. Young, L. C. (1959), "Partial area – I" (PDF), Rivista di Matematica della Università di Parma, (1), 10: 103–113, MR 0141760, Zbl 0107.27402. Young, L. C. (1959a), "Partial area. Part. II: Contours on hypersurfaces" (PDF), Rivista di Matematica della Università di Parma, (1), 10: 171–182, MR 0141761, Zbl 0107.27402. Young, L. C. (1959b), "Partial area. Part III: Symmetrization and the isoperimetric and least area problems" (PDF), Rivista di Matematica della Università di Parma, (1), 10: 257–263, MR 0141762, Zbl 0107.27402. Young, Laurence C. (1989), "Remarks and personal reminiscences", in Roxin, Emilio O. (ed.), Modern optimal control: a conference in honor of Solomon Lefschetz and Joseph P. LaSalle, Lecture Notes in Pure and Applied Mathematics, vol. 119, New York: Marcel Dekker, pp. 421–433, ISBN 9780824781682, MR 1013226.

See also Bounded variation Caccioppoli set Measure theory Varifold

Notes

References

External links O'Connor, John J.; Robertson, Edmund F., "Laurence Chisholm Young", MacTutor History of Mathematics Archive, University of St Andrews Obituary on University of Wisconsin web site Archived 27 September 2011 at the Wayback Machine Laurence Chisholm Young at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Laurence Chisholm Young

Start with the simplest possible case. Write down what Laurence Chisholm Young 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 Laurence Chisholm Young 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 Laurence Chisholm Young 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 Laurence Chisholm Young

In research: Laurence Chisholm Young 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 Laurence Chisholm Young 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: Laurence Chisholm Young is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1905 births, 2000 deaths, 20th-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Laurence Chisholm Young 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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Frequently asked questions

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