mathematics

James A. Clarkson

James A. Clarkson 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 A. Clarkson rather than just read about it. In short: James Andrew Clarkson (7 February 1906 – 6 June 1970) was an American mathematician and professor of mathematics who specialized in number theory. He is known for proving inequalities in Hölder spaces, and derived from them, the uniform convexity of Lp spaces.

Key takeaways

James A. Clarkson belongs to mathematics; place it in that map before memorising details.
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Reference excerpt

James Andrew Clarkson (7 February 1906 – 6 June 1970) was an American mathematician and professor of mathematics who specialized in number theory. He is known for proving inequalities in Hölder spaces, and derived from them, the uniform convexity of Lp spaces. His proofs are known in mathematics as Clarkson's inequalities. He was an operations' analyst during World War II, and was awarded the Medal of Freedom for his achievements. He wrote First reader on game theory, and many of his academic papers have been published in several scientific journals. He was an invited speaker at the 1932 International Congress of Mathematicians (ICM) in Zürich.

Life Originally from Massachusetts, in 1934 he received the Ph.D. in mathematics from Brown University, with the dissertation entitled On Definitions of Bounded Variation for Functions of Two Variables, On Double Riemann–Stieltjes Integrals under the supervision of advisor Clarence Raymond Adams. In 1943, he was assigned as a bombing analyst at the Bombing Accuracy Subsection of the Operational Research Section (ORS) at the Headquarters Eighth Air Force division of the United States Air Force, alongside other mathematicians like Frank M. Stewart, J. W. T. Youngs, Ray E. Gilman, and W. J. Youden. He later received the Medal of Freedom. From 1940 to 1948 he held a tenured appointment in the Department of Mathematics in the University of Pennsylvania and then from 1949 to 1970 he held a professorship at Tufts University. Most of his academic papers and contributions have been published by the American Mathematical Society, and Duke Mathematical Journal.

Academic papers James A. Clarkson (1948). "Book Review: The theory of functions of real variables". Bulletin of the American Mathematical Society. 54 (5): 487–490. doi:10.1090/S0002-9904-1948-09003-6. J. A. Clarkson (1947). "A property of derivatives". Bulletin of the American Mathematical Society. 53 (2): 124–126. doi:10.1090/S0002-9904-1947-08757-7. J. A. Clarkson; Erdős, P. (1943). "Approximation by polynomials". Duke Mathematical Journal. 10 (1): 5–11. doi:10.1215/S0012-7094-43-01002-6. C. Raymond Adams; James A. Clarkson (1939). "The Type of Certain Borel Sets in Several Banach Spaces". Transactions of the American Mathematical Society. 45 (2): 322. doi:10.2307/1990120. JSTOR 1990120. C. Raymond Adams; James A. Clarkson (1939). "A Correction to "Properties of Functions f(x, y) of Bounded Variation"". Transactions of the American Mathematical Society. 46 (3): 468. doi:10.2307/1989935. JSTOR 1989935. C. Raymond Adams; James A. Clarkson (1939). "The type of certain Borel sets in several Banach spaces". Transactions of the American Mathematical Society. 45 (2): 322. doi:10.1090/S0002-9947-1939-1501994-1. C. R. Adams; J. A. Clarkson (1939). "A correction to "Properties of functions f(x, y) of bounded variation"" (PDF). Transactions of the American Mathematical Society. 46: 468. doi:10.1090/S0002-9947-1939-0000283-4. Retrieved 8 January 2013. James A. Clarkson (1936). "Uniformly Convex Spaces". Transactions of the American Mathematical Society. 40 (3): 396–414. doi:10.2307/1989630. JSTOR 1989630. J. A. Clarkson; W. C. Randels (1936). "Fourier series convergence criteria, as applied to continuous functions". Duke Mathematical Journal. 2 (1): 112–116. doi:10.1215/S0012-7094-36-00210-7. James A. Clarkson (1936). "Uniformly convex spaces". Transactions of the American Mathematical Society. 40 (3): 396–414. doi:10.1090/S0002-9947-1936-1501880-4. C. Raymond Adams; James A. Clarkson (1934). "Properties of Functions f(x, y) of Bounded Variation". Transactions of the American Mathematical Society. 36 (4): 711. doi:10.2307/1989819. JSTOR 1989819. C. R. Adams; J. A. Clarkson (1934). "On convergence in variation". Bulletin of the American Mathematical Society. 40 (6): 413–418. doi:10.1090/S0002-9904-1934-05874-9. C. Raymond Adams; James A. Clarkson (1934). "Properties of functions f(x, y) of bounded variation". Transactions of the American Mathematical Society. 36 (4): 711. doi:10.1090/S0002-9947-1934-1501762-6. James A. Clarkson; C. Raymond Adams (1933). "On Definitions of Bounded Variation for Functions of Two Variables". Transactions of the American Mathematical Society. 35 (4): 824. doi:10.2307/1989593. JSTOR 1989593. J. A. Clarkson (1933). "On double Riemann–Stieltjes integrals". Bulletin of the American Mathematical Society. 39 (12): 929–937. doi:10.1090/S0002-9904-1933-05771-3. J. A. Clarkson (1932). "A sufficient condition for the existence of a double limit". Bulletin of the American Mathematical Society. 38 (6): 391–393. doi:10.1090/S0002-9904-1932-05403-9. Clarkson, J. A. (1937). "The von Neumann–Jordan constant for the Lebesgue spaces". Annals of Mathematics. Second Series. 38 (1): 114–115. doi:10.2307/1968512. MR 1503327.

References

Worked examples

Example 1 — a first encounter with James A. Clarkson

Start with the simplest possible case. Write down what James A. Clarkson 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 A. Clarkson 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 A. Clarkson 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 A. Clarkson

In research: James A. Clarkson 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 A. Clarkson 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 A. Clarkson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1906 births, 1970 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for James A. Clarkson 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 A. Clarkson in 20 minutes

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Close the page and write down what James A. Clarkson means in your own words.
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Frequently asked questions

What is James A. Clarkson in simple terms?

Why does James A. Clarkson 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 A. Clarkson?

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 A. Clarkson.