mathematics

Percy John Daniell

Percy John Daniell 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 Percy John Daniell rather than just read about it. In short: Percy John Daniell (9 January 1889 – 25 May 1946) was a pure and applied mathematician. Early life and education Daniell was born in Valparaíso, Chile.

Key takeaways

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

Reference excerpt

Percy John Daniell (9 January 1889 – 25 May 1946) was a pure and applied mathematician.

Early life and education Daniell was born in Valparaíso, Chile. His family returned to England in 1895. Daniell attended King Edward's School, Birmingham and proceeded to Trinity College, Cambridge (where he was the last Senior Wrangler in 1909). At this time Daniell was an applied mathematician/theoretical physicist.

Mathematical career For a year he lectured at the University of Liverpool and then he was appointed to the new Rice Institute in Houston, Texas. The Rice Institute had him spend a year at the University of Göttingen studying with Max Born and David Hilbert. Daniell was at Rice from 1914 to 1923 when he returned to England to a chair at the University of Sheffield. In a series of papers published between 1918 and 1928, he developed and expanded a generalized theory of integration and differentiation, which is today known as the Daniell integral. In the setting of integration, he also worked on results that lead to the Daniell-Kolmogorov extension theorem in the theory of stochastic processes, independently of Andrey Kolmogorov. He was an Invited Speaker of the ICM in 1920 at Strasbourg.

Death During World War II Daniell advised the British Ministry of Supply. The strain of work during the war took a heavy toll on his health. He died on 25 May 1946, after having collapsed at his home a few weeks earlier.

External links Aldrich, J. (2007) "But you have to remember P.J.Daniell of Sheffield" Electronic Journ@l for History of Probability and Statistics December 2007.

References

Stewart, C.A. (1947), "P. J. Daniell", J. London Math. Soc. s1-22: 75–80. Daniell, Percy John (1918), "A general form of integral", Annals of Mathematics 19: 279–94. –––––– (1919a), "Integrals in an infinite number of dimensions", Annals of Mathematics 20: 281–88. –––––– (1919b), "Functions of limited variation in an infinite number of dimensions", Annals of Mathematics 21: 30–38. –––––– (1920), "Further properties of the general integral", Annals of Mathematics 21: 203–20. –––––– (1921), "Integral products and probability", American Journal of Mathematics 43: 143–62. –––––– (1946), "Discussion on the Symposium on Autocorrelation in Time Series", Supplement to the Journal of the Royal Statistical Society 8-1: 88–90. Shilov, G. E., and Gurevich, B. L. (1978), Integral, Measure, and Derivative: A Unified Approach, Richard A. Silverman, trans., Dover Publications. ISBN 0-486-63519-8

Illustrations

Worked examples

Example 1 — a first encounter with Percy John Daniell

Start with the simplest possible case. Write down what Percy John Daniell 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 Percy John Daniell 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 Percy John Daniell 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 Percy John Daniell

In research: Percy John Daniell 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 Percy John Daniell 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: Percy John Daniell is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1889 births, 1946 deaths, 20th-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Percy John Daniell 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 Percy John Daniell in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Percy John Daniell means in your own words.
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Frequently asked questions

What is Percy John Daniell in simple terms?

Percy John Daniell (9 January 1889 – 25 May 1946) was a pure and applied mathematician. Early life and education Daniell was born in Valparaíso, Chile.

Why does Percy John Daniell 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 Percy John Daniell?

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 Percy John Daniell.