mathematics

Monika Ludwig

Monika Ludwig 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 Monika Ludwig rather than just read about it. In short: Monika Ludwig (born 1966 in Cologne) is an Austrian mathematician, University Professor of Convex and Discrete Geometry at the Vienna University of Technology. Academic career Ludwig earned a Dipl.-Ing. degree from the Vienna University of Technology in 1990, and a doctorate in 1994 under the supervision of Peter M.

Key takeaways

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

Reference excerpt

Monika Ludwig (born 1966 in Cologne) is an Austrian mathematician, University Professor of Convex and Discrete Geometry at the Vienna University of Technology.

Academic career Ludwig earned a Dipl.-Ing. degree from the Vienna University of Technology in 1990, and a doctorate in 1994 under the supervision of Peter M. Gruber. She remained at the same university as an assistant and associate professor from 1994 until 2007, when she moved to the Polytechnic Institute of New York University. She returned to the Vienna University of Technology as a full professor in 2010.

Awards and honors Ludwig won the Edmund and Rosa Hlawka Prize of the Austrian Academy of Sciences, given to an outstanding Austrian researcher in geometry of numbers or numerical analysis under the age of 30, in 1998. She won the Prize of the Austrian Mathematical Society in 2004. She became a corresponding member of the Austrian Academy of Sciences in 2011, and a fellow of the American Mathematical Society in 2012. She became a full member of the Austrian Academy of Sciences in 2013.

Notable publications Ludwig, Monika; Reitzner, Matthias (15 October 1999), "A characterization of affine surface area", Advances in Mathematics, 147 (1): 138–172, doi:10.1006/aima.1999.1832 Ludwig, Monika (25 December 2002), "Projection bodies and valuations", Advances in Mathematics, 172 (2): 158–168, doi:10.1016/S0001-8708(02)00021-X Ludwig, Monika (15 July 2003), "Ellipsoids and matrix-valued valuations", Duke Mathematical Journal, 119 (1): 159–188, CiteSeerX 10.1.1.207.4952, doi:10.1215/S0012-7094-03-11915-8 {{citation}}: Cite uses deprecated parameter |citeseerx= (help) Ludwig, Monika (2005), "Minkowski valuations", Transactions of the American Mathematical Society, 357 (10): 4191–4213, doi:10.1090/S0002-9947-04-03666-9 Haberl, Christoph; Ludwig, Monika (2006), "A characterization of L p {\displaystyle L_{p}} intersection bodies", International Mathematics Research Notices, 2006 10548, doi:10.1155/IMRN/2006/10548 Ludwig, Monika (2006), "Intersection bodies and valuations", American Journal of Mathematics, 128 (6): 1409–1428, CiteSeerX 10.1.1.60.8035, doi:10.1353/ajm.2006.0046, JSTOR 40068039, S2CID 11303696 {{citation}}: Cite uses deprecated parameter |citeseerx= (help) Ludwig, Monika (20 August 2010), "General affine surface areas", Advances in Mathematics, 224 (6): 2346–2360, arXiv:0908.2191, doi:10.1016/j.aim.2010.02.004 Ludwig, Monika; Reitzner, Matthias (2010), "A classification of S L ( n ) {\displaystyle SL(n)} invariant valuations", Annals of Mathematics, Second series, 172 (2): 1219–1267, doi:10.4007/annals.2010.172.1219, JSTOR 29764637

References

External links Monika Ludwig publications indexed by Google Scholar

Worked examples

Example 1 — a first encounter with Monika Ludwig

Start with the simplest possible case. Write down what Monika Ludwig 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 Monika Ludwig 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 Monika Ludwig 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 Monika Ludwig

In research: Monika Ludwig 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 Monika Ludwig 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: Monika Ludwig is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1966 births, Academic staff of TU Wien, Austrian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Monika Ludwig 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 Monika Ludwig in 20 minutes

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

Frequently asked questions

What is Monika Ludwig in simple terms?

Monika Ludwig (born 1966 in Cologne) is an Austrian mathematician, University Professor of Convex and Discrete Geometry at the Vienna University of Technology. Academic career Ludwig earned a Dipl.-Ing. degree from the Vienna University of Technology in 1990, and a doctorate in 1994 under the super…

Why does Monika Ludwig 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 Monika Ludwig?

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 Monika Ludwig.