mathematics

Heiner Zieschang

Heiner Zieschang 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 Heiner Zieschang rather than just read about it. In short: Heiner Zieschang (12 November 1936 in Kiel – 5 April 2004 in Bochum) was a German mathematician. He was a professor at Ruhr University in Bochum from 1968 till 2002.

Key takeaways

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

Reference excerpt

Heiner Zieschang (12 November 1936 in Kiel – 5 April 2004 in Bochum) was a German mathematician. He was a professor at Ruhr University in Bochum from 1968 till 2002. He was a topologist. In 1996 he was an honorary doctor of University of Toulouse and in 1997 he was an honorary professor of Moscow State University.

Literature Heiner Zieschang: Flächen und ebene diskontinuierliche Gruppen. Berlin 1970, ISBN 3-540-04911-8 (in German) Heiner Zieschang: On decompositions of discontinuous groups of the plane. Math. Zeit. 151 (1976), 165-188 Heiner Zieschang; Elmar Vogt; Hans-Dieter Coldewey: Surfaces and planar discontinuous groups, Berlin 1980 ISBN 0-387-10024-5 Heiner Zieschang: Finite groups of mapping classes of surfaces. Berlin 1981, ISBN 3-540-10857-2 Gerhard Burde; Heiner Zieschang: Knots, Berlin [u.a.] 1985 ISBN 3-11-008675-1; Burde, Gerhard; Zieschang, Heiner (2003). 2nd edition, revised and expanded. Walter de Gruyter. ISBN 978-3-11-017005-4. Ralph Stöcker; Heiner Zischang: Algebraische Topologie. Teubner, Stuttgart 1988, ISBN 3-519-02226-5 (in German) Heiner Zieschang: Lineare Algebra und Geometrie. Stuttgart 1997, ISBN 3-519-02230-3 (in German) Boto v. Querenburg: Mengentheoretische Topologie. 3. Auflage. Springer, Berlin 2001, ISBN 3-540-67790-9 (in German)

References

External links Ruhr-Universität trauert um Prof. Heiner Zieschang Archived 2006-08-27 at the Wayback Machine (in German) Heiner Zieschang – his life and work Zieschang Gedenkschrift, G&T Monograph dedicated to Heiner Zieschang Archived 2011-11-23 at the Wayback Machine Heiner Zieschang at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Heiner Zieschang

Start with the simplest possible case. Write down what Heiner Zieschang 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 Heiner Zieschang 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 Heiner Zieschang 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 Heiner Zieschang

In research: Heiner Zieschang 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 Heiner Zieschang 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: Heiner Zieschang is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1936 births, 2004 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Heiner Zieschang 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 Heiner Zieschang in 20 minutes

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

Frequently asked questions

What is Heiner Zieschang in simple terms?

Heiner Zieschang (12 November 1936 in Kiel – 5 April 2004 in Bochum) was a German mathematician. He was a professor at Ruhr University in Bochum from 1968 till 2002.

Why does Heiner Zieschang 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 Heiner Zieschang?

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 Heiner Zieschang.