mathematics

Roger Godement

Roger Godement 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 Roger Godement rather than just read about it. In short: Roger Godement (French: [ɡɔdmɑ̃]; 1 October 1921 – 21 July 2016) was a French mathematician, known for his work in functional analysis as well as his expository books. Biography Godement started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan.

Key takeaways

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

Reference excerpt

Roger Godement (French: [ɡɔdmɑ̃]; 1 October 1921 – 21 July 2016) was a French mathematician, known for his work in functional analysis as well as his expository books.

Biography Godement started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. His book Topologie Algébrique et Théorie des Faisceaux from 1958 was, as he said, a very unoriginal idea for the time (that is, to write an exposition of sheaf theory); as a non-specialist, he managed to write an enduring classic. It introduced the technical method of flasque resolutions, nowadays called Godement resolutions. It has also been credited as the place in which a comonad can first be discerned. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.

Selected publications Godement, Roger (1952). "A theory of spherical functions. I". Transactions of the American Mathematical Society. 73 (3): 496–556. doi:10.2307/1990805. JSTOR 1990805. MR 0052444. Topologie algébrique et théorie des faisceaux. Hermann 1958, 1960. Cours d´algèbre. Hermann 1963, 1966. Algebra. Hermann 1968. Godement, R. (1970), Notes on Jacquet–Langlands' theory, Institute for Advanced Study Godement, Roger; Jacquet, Hervé (1972). Zeta functions of simple algebras. Lecture Notes in Mathematics. Vol. 260. Berlin-New York: Springer-Verlag. MR 0342495. Analyse mathématique. 4 vols., Springer-Verlag 1998–2001.

See also Commutation theorem for traces Plancherel theorem for spherical functions Standard L-function

References

External links Roger Godement at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Roger Godement", MacTutor History of Mathematics Archive, University of St Andrews

Illustrations

Worked examples

Example 1 — a first encounter with Roger Godement

Start with the simplest possible case. Write down what Roger Godement 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 Roger Godement 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 Roger Godement 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 Roger Godement

In research: Roger Godement 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 Roger Godement 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: Roger Godement is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1921 births, 2016 deaths, Academic staff of Paris Diderot University, so understanding it makes those chapters shorter.
In everyday life: Look for Roger Godement 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 Roger Godement in 20 minutes

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

Frequently asked questions

What is Roger Godement in simple terms?

Roger Godement (French: [ɡɔdmɑ̃]; 1 October 1921 – 21 July 2016) was a French mathematician, known for his work in functional analysis as well as his expository books. Biography Godement started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan.

Why does Roger Godement 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 Roger Godement?

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 Roger Godement.