mathematics

Helmut Ulm

Helmut Ulm 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 Helmut Ulm rather than just read about it. In short: Helmut Ulm (born 21 June 1908 in Gelsenkirchen; died 13 June 1975) was a German mathematician who established the classification of countable periodic abelian groups by means of their Ulm invariants. Career Helmut Ulm's father was an elementary school teacher in Elberfeld.

Key takeaways

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

Reference excerpt

Helmut Ulm (born 21 June 1908 in Gelsenkirchen; died 13 June 1975) was a German mathematician who established the classification of countable periodic abelian groups by means of their Ulm invariants.

Career Helmut Ulm's father was an elementary school teacher in Elberfeld. After finishing high school in Wuppertal in 1926, he attended the universities of Göttingen (1926–1927), Jena (1927) and Bonn (1927–1930), where he studied mathematics and physics, attending the lectures of Richard Courant, Erich Bessel-Hagen, Felix Hausdorff, and the joint Hausdorff–Otto Toeplitz seminar. He graduated summa cum laude in 1930 with a thesis about countable periodic abelian groups (1933). In 1933–1935 he was an assistant in Göttingen and worked with Wilhelm Magnus and Olga Taussky-Todd editing David Hilbert's Collected Works. His Habilitationsschrift developed a generalization of the elementary divisor theory to infinite matrices, continuing ideas of Ulm's teacher Toeplitz. It was submitted in Münster in 1936 and refereed by Heinrich Behnke, Gottfried Köthe, F. K. Schmidt, and B. L. van der Waerden. Ulm's promotion was delayed, apparently, due to his anti-Nazi views. From 1935 until his retirement in 1974 Ulm worked at the University of Münster, as an assistant, docent, and eventually professor (1968). Besides his three important papers on the classification of infinite abelian groups, Ulm published only a few notes in the proceedings of the Münster mathematical seminar, one of which dealt with solution of systems of linear equations by a computer. He suffered from poor health. During the World War II, Ulm worked as a cryptographer at Pers Z S starting in August 1941 on a part-time basis from Thursday through to Saturday and on Monday through Wednesday at Münster. After the war he mostly taught courses in applied mathematics and supervised several Ph.D. theses; those of G. Tillmann (1952) and G. Roth (1961) were close to his old work on infinite-dimensional linear algebra and infinite groups.

Bibliography Helmut Ulm, Zur Theorie der abzählbar-unendlichen Abelschen Gruppen. Math. Ann. 107, 774–803 (1933) JFM 59.0143.03 Zbl 0006.15003 Helmut Ulm, Zur Theorie der nicht-abzählbaren primären abelschen Gruppen. Math. Z. 40, 205–207 (1935) Zbl 0011.39307 Helmut Ulm, Elementarteilertheorie unendlicher Matrizen. Math. Ann. 114, 493–505 (1937) Zbl 0017.09901

References

Göbel, R., Helmut Ulm: his work and its impact on recent mathematics. Abelian group theory (Perth, 1987), 1–10, Contemp. Math., 87, Amer. Math. Soc., Providence, RI, 1989 MR 0995259 Sanford Segal, Mathematicians under the Nazis. Princeton University Press, 2003 ISBN 0-691-00451-X

External links Helmut Ulm at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Helmut Ulm

Start with the simplest possible case. Write down what Helmut Ulm 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 Helmut Ulm 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 Helmut Ulm 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 Helmut Ulm

In research: Helmut Ulm 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 Helmut Ulm 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: Helmut Ulm is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1908 births, 1975 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Helmut Ulm 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 Helmut Ulm in 20 minutes

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

Frequently asked questions

What is Helmut Ulm in simple terms?

Helmut Ulm (born 21 June 1908 in Gelsenkirchen; died 13 June 1975) was a German mathematician who established the classification of countable periodic abelian groups by means of their Ulm invariants. Career Helmut Ulm's father was an elementary school teacher in Elberfeld.

Why does Helmut Ulm 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 Helmut Ulm?

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 Helmut Ulm.