mathematics

Helmut Wielandt

Helmut Wielandt 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 Wielandt rather than just read about it. In short: Helmut Wielandt (19 December 1910 – 14 February 2001) was a German mathematician who worked on permutation groups. He was born in Niedereggenen, Lörrach, Germany.

Key takeaways

Helmut Wielandt 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 Wielandt to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Helmut Wielandt from memory before moving on to harder problems.

Reference excerpt

Helmut Wielandt (19 December 1910 – 14 February 2001) was a German mathematician who worked on permutation groups. He was born in Niedereggenen, Lörrach, Germany. He gave a plenary lecture Entwicklungslinien in der Strukturtheorie der endlichen Gruppen (Lines of Development in the Structure Theory of Finite Groups) at the International Congress of Mathematicians (ICM) in 1958 at Edinburgh and was an Invited Speaker with talk Bedingungen für die Konjugiertheit von Untergruppen endlicher Gruppen (Conditions for the Conjugacy of Finite Groups) at the ICM in 1962 in Stockholm. Among his work in Algebra is an elegant proof of the Sylow Theorems (replacing an older cumbersome proof involving double cosets) that is in the standard textbooks on Abstract Algebra, i.e. Group Theory.

See also Collatz–Wielandt formula Wielandt theorem

Publications Wielandt, Helmut (1964), Finite permutation groups, Boston, MA: Academic Press, MR 0183775 (translated by Ronald D. Bercov) Wielandt, Helmut (10 May 2014). 2014 pbk reprint. Academic Press. ISBN 9781483258294. Topics in the analytic theory of matrices: Lecture notes prepared by Robert R. Meyer from a course by Helmut Wielandt, Department of Mathematics, University of Wisconsin at Madison, 1967, ASIN B0007EOBYU; 129 pages, pbk{{citation}}: CS1 maint: postscript (link) Wielandt, Helmut (1994), Huppert, Bertram; Schneider, Hans (eds.), Mathematische Werke/Mathematical works. Vol. 1. Group theory, Berlin: Walter de Gruyter & Co., ISBN 978-3-11-012452-1, MR 1272467 Wielandt, Helmut (1996), Huppert, Bertram; Schneider, Hans (eds.), Mathematische Werke/Mathematical works. Vol. 2. Linear algebra and analysis, Berlin: Walter de Gruyter & Co., ISBN 978-3-11-012453-8, MR 1430098

References

Deutsch, E.; Hadeler, K. P.; Laffey, Thomas J. (1985), "Helmut Wielandt", Linear Algebra and Its Applications, 71: 1–8, doi:10.1016/0024-3795(85)90228-9, ISSN 0024-3795, MR 0813026 Huppert, Bertram (2001), "Nachruf auf Professor Dr. Dr. hc. Helmut Wielandt", Jahresbericht der Deutschen Mathematiker-Vereinigung, 103 (3): 74–78, ISSN 0012-0456 O'Connor, John J.; Robertson, Edmund F., "Helmut Wielandt", MacTutor History of Mathematics Archive, University of St Andrews

External links Curriculum vitae from Mathematische Werke, Bd. 1 Oberwolfach Photo Collection Prof. Dr. Helmut Wielandt Literature by and about Helmut Wielandt in the German National Library catalogue

Illustrations

Helmut Wielandt: Helmut Wielandt — Helmut Wielandt

Worked examples

Example 1 — a first encounter with Helmut Wielandt

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

In research: Helmut Wielandt 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 Wielandt 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 Wielandt is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1910 births, 2001 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Helmut Wielandt 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 Wielandt in 20 minutes

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

Frequently asked questions

What is Helmut Wielandt in simple terms?

Helmut Wielandt (19 December 1910 – 14 February 2001) was a German mathematician who worked on permutation groups. He was born in Niedereggenen, Lörrach, Germany.

Why does Helmut Wielandt 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 Wielandt?

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 Wielandt.