mathematics

Philip Hall

Philip Hall 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 Philip Hall rather than just read about it. In short: Philip Hall (11 April 1904 – 30 December 1982) was an English mathematician. His major work was on group theory, notably on finite groups and solvable groups.

Key takeaways

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

Reference excerpt

Philip Hall (11 April 1904 – 30 December 1982) was an English mathematician. His major work was on group theory, notably on finite groups and solvable groups.

Biography He was educated first at Christ's Hospital, where he won the Thompson Gold Medal for mathematics, and later at King's College, Cambridge. He was elected a Fellow of the Royal Society in 1951 and awarded its Sylvester Medal in 1961. He was President of the London Mathematical Society from 1955–1957, and was awarded its Berwick Prize in 1958 and De Morgan Medal in 1965.

Publications Hall, P. (1934). "A Contribution to the Theory of Groups of Prime-Power Order". Proceedings of the London Mathematical Society. s2-36: 29–07. doi:10.1112/plms/s2-36.1.29. Hall, P.; Higman, G. (1956). "On the p-Length of p-Soluble Groups and Reduction Theorems for Burnside's Problem". Proceedings of the London Mathematical Society. s3-6: 1–42. doi:10.1112/plms/s3-6.1.1. Hall, Philip (1988), The collected works of Philip Hall, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853254-5, MR 0986732

See also Abstract clone Commutator collecting process Isoclinism of groups Regular p-group Three subgroups lemma Hall algebra, and Hall polynomials Hall subgroup Hall–Higman theorem Hall–Littlewood polynomial Hall's universal group Hall's marriage theorem Hall word Hall–Witt identity Irwin–Hall distribution Zappa–Szép product

References

Illustrations

Worked examples

Example 1 — a first encounter with Philip Hall

Start with the simplest possible case. Write down what Philip Hall 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 Philip Hall 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 Philip Hall 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 Philip Hall

In research: Philip Hall 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 Philip Hall 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: Philip Hall is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1904 births, 1982 deaths, 20th-century English mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Philip Hall 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 Philip Hall in 20 minutes

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

Frequently asked questions

What is Philip Hall in simple terms?

Philip Hall (11 April 1904 – 30 December 1982) was an English mathematician. His major work was on group theory, notably on finite groups and solvable groups.

Why does Philip Hall 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 Philip Hall?

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 Philip Hall.