mathematics

Mechthild Stoer

Mechthild Stoer 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 Mechthild Stoer rather than just read about it. In short: Mechthild Maria Stoer is a German applied mathematician and operations researcher known for her work on the minimum cut problem and in network design. She is one of the namesakes of the Stoer–Wagner algorithm for minimum cuts, which she published with Frank Wagner in 1994.

Key takeaways

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

Reference excerpt

Mechthild Maria Stoer is a German applied mathematician and operations researcher known for her work on the minimum cut problem and in network design. She is one of the namesakes of the Stoer–Wagner algorithm for minimum cuts, which she published with Frank Wagner in 1994.

Education and career Stoer was a master's student of Martin Grötschel at the University of Augsburg in Germany, receiving a diploma in 1987 with the thesis Dekompositionstechniken beim Travelling Salesman Problem. She continued working with Grötschel in Augsburg for a Ph.D.; her 1992 dissertation, Design of Survivable Networks, was also published by Springer-Verlag in the series Lecture Notes in Mathematics (vol. 1531, 1992). After completing her doctorate she worked for Telenor in Norway, focusing on the applications of combinatorial optimization in telecommunication.

Recognition Stoer's work on minimum cuts received the inaugural European Symposium on Algorithms Test-of-Time Award in 2015. The award citation states that "The algorithm continues to be taught because of its elegance and used because of its efficiency and ease of implementation."

Selected publications Stoer, Mechthild (1992), Design of Survivable Networks, Lecture Notes in Mathematics, vol. 1531, Berlin: Springer-Verlag, doi:10.1007/BFb0088963, ISBN 3-540-56271-0, MR 1223549 Grötschel, Martin; Monma, Clyde L.; Stoer, Mechthild (1992), "Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints", Operations Research, 40 (2): 309–330, doi:10.1287/opre.40.2.309, MR 1162949 Grötschel, Martin; Monma, Clyde L.; Stoer, Mechthild (1992), "Facets for polyhedra arising in the design of communication networks with low-connectivity constraints", SIAM Journal on Optimization, 2 (3): 474–504, doi:10.1137/0802024, MR 1172502 Stoer, Mechthild; Dahl, Geir (1994), "A polyhedral approach to multicommodity survivable network design", Numerische Mathematik, 68 (1): 149–167, doi:10.1007/s002110050054, MR 1278454 Stoer, Mechthild; Wagner, Frank (1997), "A simple min-cut algorithm", Journal of the ACM, 44 (4): 585–591, doi:10.1145/263867.263872, MR 1481316; previously announced in 1994 at the European Symposium on Algorithms, doi:10.1007/BFb0049404

References

Worked examples

Example 1 — a first encounter with Mechthild Stoer

Start with the simplest possible case. Write down what Mechthild Stoer 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 Mechthild Stoer 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 Mechthild Stoer 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 Mechthild Stoer

In research: Mechthild Stoer 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 Mechthild Stoer 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: Mechthild Stoer is common in secondary-school and first-year university syllabi. It links to neighbouring topics German applied mathematicians, German women mathematicians, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Mechthild Stoer 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 Mechthild Stoer in 20 minutes

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

Frequently asked questions

What is Mechthild Stoer in simple terms?

Why does Mechthild Stoer 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 Mechthild Stoer?

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 Mechthild Stoer.