mathematics

Urs Stammbach

Urs Stammbach 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 Urs Stammbach rather than just read about it. In short: Urs Stammbach (born 26 October 1939) is a Swiss mathematician, specializing in homological algebra. Stammbach studied at ETH Zurich, where he obtained his Diplom in 1964 and received his doctorate in 1966 under the supervision of Beno Eckmann (and Heinz Hopf) with dissertation Anwendungen der Homologietheorie der Gruppen auf Zentralreihen und auf Invarianten von Präsentierungen (Applications of homology theory of gr…

Key takeaways

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

Reference excerpt

Urs Stammbach (born 26 October 1939) is a Swiss mathematician, specializing in homological algebra. Stammbach studied at ETH Zurich, where he obtained his Diplom in 1964 and received his doctorate in 1966 under the supervision of Beno Eckmann (and Heinz Hopf) with dissertation Anwendungen der Homologietheorie der Gruppen auf Zentralreihen und auf Invarianten von Präsentierungen (Applications of homology theory of groups to central series and to invariants of presentations). As a postdoc Stammbach was from 1966 to 1967 at ETH Zurich and from 1967 to 1969 at Cornell University. At ETH Zurich, he was from 1969 to 1972 an assistant professor, from 1972 to 1979 an associate professor, and from 1979 to 2005 a full professor, retiring as professor emeritus in 2005. Stammbach's research deals with homological algebra, specifically with its applications to group theory (homology and cohomology of groups). He also does research on the history of mathematics, especially pertaining to Switzerland. In 1990–1991 he was president of the Swiss Mathematical Society.

Selected publications Homology in group theory, Springer 1971 with Peter Hilton: On the differentials in the Lyndon-Hochschild-Serre spectral sequence, Bull. Amer. Math. Soc., Vol. 79, 1973, pp. 796–799 doi:10.1090/S0002-9904-1973-13321-X (See Lyndon–Hochschild–Serre spectral sequence.) Homologie dans les variétés des groupes. Groupes à dualité homologique, Université Laval, Quebec, Collect. Math., No. 19, 1976 Geschichte der Mathematik an der ETH Zürich 1855–1932, Jahrbuch Überblicke Mathematik, Vieweg 1994, pp. 194–216 with Günther Frei: Die Mathematiker an den Zürcher Hochschulen, Birkhäuser 1994 with Günther Frei: Hermann Weyl und die Mathematik an der ETH Zürich 1913–1930, Birkhäuser 1992 with Günther Frei: Heinz Hopf, in Ioan James: History of Topology, Elsevier 1999 with Peter Hilton: A course in homological algebra, 1st edition 1971, 2nd edition, Springer 1997, ISBN 3-540-90032-2 2nd corrected printing. 2013. Lineare Algebra, Teubner Verlag 1980, 4th edition 1994

References

Illustrations

Worked examples

Example 1 — a first encounter with Urs Stammbach

Start with the simplest possible case. Write down what Urs Stammbach 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 Urs Stammbach 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 Urs Stammbach 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 Urs Stammbach

In research: Urs Stammbach 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 Urs Stammbach 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: Urs Stammbach is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1939 births, 20th-century Swiss mathematicians, Academic staff of ETH Zurich, so understanding it makes those chapters shorter.
In everyday life: Look for Urs Stammbach 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 Urs Stammbach in 20 minutes

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

Frequently asked questions

What is Urs Stammbach in simple terms?

Why does Urs Stammbach 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 Urs Stammbach?

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 Urs Stammbach.