astronomy

Heinz Prüfer

Heinz Prüfer is a astronomy 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 Heinz Prüfer rather than just read about it. In short: Ernst Paul Heinz Prüfer (10 November 1896 – 7 April 1934) was a German mathematician born in Wilhelmshaven. His major contributions were on abelian groups, graph theory, algebraic numbers, knot theory and Sturm–Liouville theory.

Key takeaways

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

Reference excerpt

Ernst Paul Heinz Prüfer (10 November 1896 – 7 April 1934) was a German mathematician born in Wilhelmshaven. His major contributions were on abelian groups, graph theory, algebraic numbers, knot theory and Sturm–Liouville theory. In 1915 he began his university studies in mathematics, physics and chemistry in Berlin. After that he started his doctorate degree with Issai Schur as his advisor at Friedrich Wilhelm University, Berlin. In 1921 he obtained his doctorate degree. His thesis was named Unendliche Abelsche Gruppen von Elementen endlicher Ordnung (Infinite abelian groups of elements of finite order). This thesis set the road for his contributions on abelian groups. In 1922 he worked with mathematician Paul Koebe in the University of Jena, and in 1923 he obtained tenure and was at this university until 1927. In that year he moved to Münster University where he worked until the end of his life. His final work was about projective geometry, but it was posthumously completed by his students Gustav Fleddermann and Gottfried Köthe. Heinz Prüfer was married, but never had children. He died prematurely at 37 years of age in 1934 in Münster, Germany, due to lung cancer.

Mathematical contributions Heinz Prüfer created the following mathematical notions that were later named after him:

Prüfer sequence (also known as a Prüfer code; it has broad applications in graph theory and network theory). Prüfer domain. Also see Bézout domain, which is a Prüfer domain Prüfer rank Prüfer manifold also known as Prüfer surface or Prüfer analytical manifold Prüfer group Prüfer theorems

References Behnke, H.; Köthe, G. (1935), "Heinz Prüfer", Jahresbericht der Deutschen Mathematiker-Vereinigung, XLV: 32–40 Mader, Adolf (1987), "Heinz Prüfer and his papers on abelian groups", in Rüdiger Göbel, Elbert Walker (ed.), Abelian group theory: proceedings of the Third Conference on Abelian Group Theory at Oberwolfach, August 11–17, 1985, Gordon and Breach, pp. 1–8, ISBN 978-2-88124-166-6, MR 1011302 Solomentsev, E.D. (2001) [1994], "Prüfer surface", Encyclopedia of Mathematics, EMS Press Jürgen Elstrodt and Norbert Schmitz: History of Münster University (2013). Chapter 52. page 111, Heinz Prüfer Biographie. Chapter 52. page 111 Prüfer, Heinz; Fleddermann, Gustav; Köthe, Gottfried, Projektive Geometrie. Aus dem Nachlaß herausgegeben von G. und G.. 2. unveränd. Aufl. VII + 314 S Leipzig 1935., Akademische Verlagsgesellschaft Geest u. Portig K. G. Szmielew, Wanda (1955). "Elementary properties of abelian groups". Fundamenta Mathematicae. 41 (2): 203–271. doi:10.4064/fm-41-2-203-271. Halter-Hoch, Franz (2003), Characterization of Pruefer Multiplication Monoids and Domains by Means of Spectral Module Systems; Volume 139,19-31., Springer Jarden, Moshe (1975), "On Ideal Theory in High Prufer Domains", Manuscripta Mathematica, 14 (4), Springer Verlag ISSN 0025-2611: 303–336, doi:10.1007/BF01169264, S2CID 122203091 Fontana, M; Huckaba, I; Papick, J (1996), Prüfer Domains. Pure and Applied Mathematics Books. 329 Pages;, Marcel Dekker Publishing, New York, ISBN 0-8247-9816-3 Kajimoto, H (2003), "An Extension of the Prüfer Code and Assembly of Connected Graphs from Their Blocks", Graphs and Combinatorics, 19 (2): 231–239, doi:10.1007/s00373-002-0499-3, S2CID 22970936

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

Illustrations

Heinz Prüfer: Heinz Prüfer (1930). — Heinz Prüfer (1930).

Worked examples

Example 1 — a first encounter with Heinz Prüfer

Start with the simplest possible case. Write down what Heinz Prüfer claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Heinz Prüfer 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 Heinz Prüfer 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 Heinz Prüfer

In research: Heinz Prüfer appears in astronomy 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 Heinz Prüfer 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: Heinz Prüfer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1896 births, 1934 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Heinz Prüfer 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 Heinz Prüfer in 20 minutes

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

Frequently asked questions

What is Heinz Prüfer in simple terms?

Why does Heinz Prüfer matter?

Because it connects several astronomy 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 Heinz Prüfer?

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 Heinz Prüfer.