mathematics

Ingo Althöfer

Ingo Althöfer 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 Ingo Althöfer rather than just read about it. In short: Ingo Althöfer (born 1961) is a German mathematician and former professor of operations research at the University of Jena. Althöfer earned his PhD in 1986 at Bielefeld University.

Key takeaways

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

Reference excerpt

Ingo Althöfer (born 1961) is a German mathematician and former professor of operations research at the University of Jena. Althöfer earned his PhD in 1986 at Bielefeld University. His dissertation, Asymptotic Properties of Certain Competition Systems in Artificial Intelligence and Ecology, was supervised by Rudolf Ahlswede.

Contributions Topics in Althöfer's professional research include the realization of finite metric spaces by shortest path metrics in graphs and their approximation by greedy spanners, algorithmic game theory and combinatorial game theory, and heuristic search algorithms for optimization problems. Althöfer is also known for his inventions of games and puzzles, including dice game EinStein würfelt nicht!, for his experiments with self-assembly of Lego building blocks by running them through a washing machine, and for his innovations in computer-human chess playing. In the 1990s he tested his "drei hirn" ["3-brains"] system, in which a human decides between the choices of two computer chess players, against strong human players including grandmaster David Bronstein and woman grandmaster Sofia Polgar. In 2004 he and Timo Klaustermeyer introduced freestyle chess, a style of human chess playing allowing arbitrary consultation with computers or other people.

Books Menzer, Hartmut; Althöfer, Ingo (2014). Zahlentheorie und Zahlenspiele: Sieben ausgewählte Themenstellungen (in German). Berlin/Boston: De Gruyter. ISBN 978-3-486-98963-2. OCLC 898769807. Althöfer, Ingo; Voigt, Roland (2014). Spiele, Rätsel, Zahlen: faszinierendes zu Lasker-Mühle, Sudoku-Varianten, Havannah, EinStein würfelt nicht, Yavalath, 3-Hirn-Schach ... (in German). Heidelberg: Springer Spektrum. ISBN 978-3-642-55301-1. OCLC 894170235. He has also self-published other books through his personal publishing company, 3-Hirn Verlag, and is one of the editors of the multi-volume book series Rudolf Ahlswede's Lectures on Information Theory.

Selected Papers Althöfer, I. (1988). "Nim games with arbitrary periodic moving orders". International Journal of Game Theory. 17 (3). Springer Science and Business Media LLC: 165–175. doi:10.1007/bf01242859. ISSN 0020-7276. S2CID 118788463. Althöfer, Ingo (1991). "Data compression using an intelligent generator: The storage of chess games as an example". Artificial Intelligence. 52 (1). Elsevier BV: 109–113. doi:10.1016/0004-3702(91)90026-g. ISSN 0004-3702. Althöfer, Ingo (2004). "Improved game play by multiple computer hints". Theoretical Computer Science. 313 (3). Elsevier BV: 315–324. doi:10.1016/j.tcs.2003.08.012. ISSN 0304-3975. Althöfer, Ingo (10 November 2020). "Computer Chess and Chess Computers in East Germany". ICGA Journal. 42 (2–3). IOS Press: 152–164. doi:10.3233/icg-200163. ISSN 2468-2438. S2CID 226727158.

Selected Board Games EinStein würfelt nicht! (2005) Galtoni (2012), a mixture of Connect Four and the Galton board San Jego (2015), a variant of Clobber

References

External links

Home page 3-Hirn Verlag, Althöfer's book publishing company

Illustrations

Ingo Althöfer: Althöfer in 2008 — Althöfer in 2008

Worked examples

Example 1 — a first encounter with Ingo Althöfer

Start with the simplest possible case. Write down what Ingo Althöfer 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 Ingo Althöfer 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 Ingo Althöfer 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 Ingo Althöfer

In research: Ingo Althöfer 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 Ingo Althöfer 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: Ingo Althöfer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1961 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ingo Althöfer 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 Ingo Althöfer in 20 minutes

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

Frequently asked questions

What is Ingo Althöfer in simple terms?

Ingo Althöfer (born 1961) is a German mathematician and former professor of operations research at the University of Jena. Althöfer earned his PhD in 1986 at Bielefeld University.

Why does Ingo Althöfer 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 Ingo Althöfer?

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 Ingo Althöfer.