mathematics

Wilhelm Magnus

Wilhelm Magnus 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 Wilhelm Magnus rather than just read about it. In short: Hans Heinrich Wilhelm Magnus, known as Wilhelm Magnus (5 February 1907 in Berlin, Germany – 15 October 1990 in New Rochelle, New York), was a German-American mathematician. He made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.

Key takeaways

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

Reference excerpt

Hans Heinrich Wilhelm Magnus, known as Wilhelm Magnus (5 February 1907 in Berlin, Germany – 15 October 1990 in New Rochelle, New York), was a German-American mathematician. He made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.

Biography In 1931, Magnus received his PhD from the University of Frankfurt in Germany. His thesis, written under the direction of Max Dehn, was entitled Über unendlich diskontinuierliche Gruppen von einer definierenden Relation (der Freiheitssatz). Magnus was a faculty member in Frankfurt from 1933 until 1938. He refused to join the Nazi Party and, as a consequence, was not allowed to hold an academic post during World War II. In 1947, he became a professor at the University of Göttingen. In 1948, he emigrated to the United States to collaborate on the Bateman Manuscript Project as a co-editor while a visiting professor at the California Institute of Technology. In 1950, he was appointed professor at the Courant Institute of Mathematical Sciences in New York University. He stayed there until 1973, when he moved to the Polytechnic Institute of New York, before retiring in 1978. His doctoral students include Joan Birman, Martin Greendlinger, Edna Grossman, Herbert Keller, Seymour Lipschutz, and Kathryn F. Kuiken.

See also Magnus expansion Magnus–Moldavansky method Commutator collecting process Free Lie algebra Hall word

Selected works with Gilbert Baumslag and Bruce Chandler, eds.: Wilhelm Magnus, Collected Papers. Springer-Verlag, 1984. Noneuclidean tessellations and their groups. Academic Press, 1974. with Bruce Chandler: The History of Combinatorial Group Theory. A Case Study in the History of Ideas. Springer, 1982. Wilhelm Magnus, Abraham Karrass, Donald Solitar, Combinatorial Group Theory. Presentations of Groups in Terms of Generators and Relations, reprint of the 1976 second edition, Dover Publications, Mineola, NY, 2004. ISBN 0-486-43830-9 Wilhelm Magnus, Stanley Winkler, Hill's Equation, reprint of the 1979 second edition, Dover Publications, Mineola, NY, 2004. ISBN 0-486-49565-5. with Israel Grossman: Groups and Their Graphs. Random House (New Mathematical Library 14), 1965. Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz [in German]; Tricomi, Francesco G. (1955), Higher Transcendental Functions. Vols. I-III, McGraw-Hill (The Bateman Manuscript Project: scan) Wilhelm Magnus, Fritz Oberhettinger, and Raz Pal Soni, Formulas and Theorems for the Special Functions of Mathematical Physics. Springer-Verlag New York, New York, 1966. with Fritz Oberhettinger: Formeln und Sätze für die speziellen Funktionen der mathematischen Physik. Springer 1943; 2nd edition, 1948; 3rd edition in English, Formulas and Theorems for the Functions of Mathematical Physics, Chelsea, 1966. with Fritz Oberhettinger: Anwendungen der elliptischen Funktionen in Physik und Technik. Springer 1949.

References

Further reading The Mathematical Legacy of Wilhelm Magnus: Groups, Geometry, and Special Functions. Conference on the Legacy of Wilhelm Magnus May 1–3, 1992 .

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

Worked examples

Example 1 — a first encounter with Wilhelm Magnus

Start with the simplest possible case. Write down what Wilhelm Magnus 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 Wilhelm Magnus 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 Wilhelm Magnus 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 Wilhelm Magnus

In research: Wilhelm Magnus 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 Wilhelm Magnus 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: Wilhelm Magnus is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1907 births, 1990 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Wilhelm Magnus 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 Wilhelm Magnus in 20 minutes

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

Frequently asked questions

What is Wilhelm Magnus in simple terms?

Why does Wilhelm Magnus 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 Wilhelm Magnus?

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 Wilhelm Magnus.