mathematics

Peter M. Gruber

Peter M. Gruber 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 Peter M. Gruber rather than just read about it. In short: Peter Manfred Gruber (28 August 1941, Klagenfurt – 7 March 2017, Vienna) was an Austrian mathematician working in geometric number theory as well as in convex and discrete geometry. Biography Gruber obtained his PhD at the University of Vienna in 1966, under the supervision of Nikolaus Hofreiter.

Key takeaways

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

Reference excerpt

Peter Manfred Gruber (28 August 1941, Klagenfurt – 7 March 2017, Vienna) was an Austrian mathematician working in geometric number theory as well as in convex and discrete geometry.

Biography Gruber obtained his PhD at the University of Vienna in 1966, under the supervision of Nikolaus Hofreiter. From 1971, he was Professor at the University of Linz, and from 1976, at the TU Wien. He was a member of the Austrian Academy of Sciences, a foreign member of the Russian Academy of Sciences, and a corresponding member of the Bavarian Academy of Sciences and Humanities. His past doctoral students include Monika Ludwig.

Selected publications Gruber, P.M. (2007). Convex and Discrete Geometry. Berlin: Springer-Verlag. Gruber, P.M.; Lekkerkerker, C.G. (1987). Geometry of Numbers. Amsterdam: North-Holland.

Decorations and awards 1967: Prize of the Austrian Mathematical Society 1978, 1980 and 1982: Chairman of the Austrian Mathematical Society 1991: Full member of the Austrian Academy of Sciences (Corresponding member since 1988) 1996: Medal of the Union of Czech Mathematicians and Physicists 2001: Austrian Cross of Honour for Science and Art, 1st class 2001: Medal of the mathematical and physical faculty of Charles University in Prague 2003: Foreign member of the Russian Academy of Sciences 2008: Grand Silver Medal for Services to the Republic of Austria 2013: Fellow of the American Mathematical Society, for "contributions to the geometry of numbers and to convex and discrete geometry". Honorary doctorates from the Universities of Siegen, Turin and Salzburg Member of the Academies of Sciences in Messina and Modena Corresponding member of the Bavarian Academy of Sciences

Notes

Illustrations

Worked examples

Example 1 — a first encounter with Peter M. Gruber

Start with the simplest possible case. Write down what Peter M. Gruber 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 Peter M. Gruber 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 Peter M. Gruber 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 Peter M. Gruber

In research: Peter M. Gruber 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 Peter M. Gruber 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: Peter M. Gruber is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1941 births, 2017 deaths, 20th-century Austrian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Peter M. Gruber 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 Peter M. Gruber in 20 minutes

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

Frequently asked questions

What is Peter M. Gruber in simple terms?

Peter Manfred Gruber (28 August 1941, Klagenfurt – 7 March 2017, Vienna) was an Austrian mathematician working in geometric number theory as well as in convex and discrete geometry. Biography Gruber obtained his PhD at the University of Vienna in 1966, under the supervision of Nikolaus Hofreiter.

Why does Peter M. Gruber 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 Peter M. Gruber?

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 Peter M. Gruber.