mathematics

Heinrich Tietze

Heinrich Tietze 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 Heinrich Tietze rather than just read about it. In short: Heinrich Franz Friedrich Tietze (August 31, 1880 – February 17, 1964) was an Austrian mathematician, famous for the Tietze extension theorem on functions from topological spaces to the real numbers. He also developed the Tietze transformations for group presentations, and was the first to pose the group isomorphism problem.

Key takeaways

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

Reference excerpt

Heinrich Franz Friedrich Tietze (August 31, 1880 – February 17, 1964) was an Austrian mathematician, famous for the Tietze extension theorem on functions from topological spaces to the real numbers. He also developed the Tietze transformations for group presentations, and was the first to pose the group isomorphism problem. Tietze's graph is also named after him; it describes the boundaries of a subdivision of the Möbius strip into six mutually-adjacent regions, found by Tietze as part of an extension of the four color theorem to non-orientable surfaces.

Education and career Tietze was the son of Emil Tietze and the grandson of Franz Ritter von Hauer, both of whom were Austrian geologists. He was born in Schleinz, Austria-Hungary, and studied mathematics at the Technische Hochschule Wien beginning in 1898. After additional studies in Munich, he returned to Vienna, completing his doctorate in 1904 and his habilitation in 1908. From 1910 until 1918, Tietze taught mathematics in Brno, and was promoted to ordinary professor in 1913. He served in the Austrian army during World War I, and then returned to Brno, but in 1919, he took a position at the University of Erlangen, and then in 1925 moved again to the Ludwig-Maximilians-Universität München, where he remained for the rest of his career. One of his doctoral students was Georg Aumann. Tietze retired in 1950, and died in Munich, West Germany.

Awards and honors Tietze was a fellow of the Bavarian Academy of Sciences and a fellow of the Austrian Academy of Sciences.

Publications Tietze, Heinrich (1957), "Über Schachturnier-Tabellen", Mathematische Zeitschrift, 67: 188–202, doi:10.1007/bf01258856, S2CID 123135166{{citation}}: CS1 maint: deprecated archival service (link) Tietze, Heinrich (1910), "Einige Bemerkungen zum Problem des Kartenfärbens auf einseitigen Flächen", DMV Annual Report{{citation}}: CS1 maint: deprecated archival service (link) Tietze, Heinrich (1915), "Über Funktionen, die auf einer abgeschlossenen Menge stetig sind", Journal für die reine und angewandte Mathematik, 145{{citation}}: CS1 maint: deprecated archival service (link) Über die mit Lineal und Zirkel und die mit dem rechten Zeichenwinkel lösbaren Konstruktionsaufgaben, Mathematische Zeitschrift vol.46, 1940 mit Leopold Vietoris Beziehungen zwischen den verschiedenen Zweigen der Topologie, Enzyklopädie der Mathematischen Wissenschaften 1929[link removed] Über die Anzahl der stabilen Ruhelagen eines Würfels, Elemente der Mathematik vol.3, 1948[link removed] Über die topologische Invarianten mehrdimensionaler Mannigfaltigkeiten, Monatshefte für Mathematik und Physik, vol. 19, 1908, p.1-118 Über Simony Knoten und Simony Ketten mit vorgeschriebenen singulären Primzahlen für die Figur und für ihr Spiegelbild, Mathematische Zeitschrift vol.49, 1943, p.351 (Knot theory) Tietze, Heinrich (1965) [1959], Famous problems of mathematics. Solved and unsolved mathematical problems from antiquity to modern times., New York: Graylock Press, MR 0181558

References

External links Heinrich Tietze at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Heinrich Tietze

Start with the simplest possible case. Write down what Heinrich Tietze 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 Heinrich Tietze 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 Heinrich Tietze 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 Heinrich Tietze

In research: Heinrich Tietze 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 Heinrich Tietze 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: Heinrich Tietze is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1880 births, 1964 deaths, Academic staff of LMU Munich, so understanding it makes those chapters shorter.
In everyday life: Look for Heinrich Tietze 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 Heinrich Tietze in 20 minutes

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

Frequently asked questions

What is Heinrich Tietze in simple terms?

Why does Heinrich Tietze 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 Heinrich Tietze?

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 Heinrich Tietze.