astronomy

Ib Madsen

Ib Madsen is a astronomy 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 Ib Madsen rather than just read about it. In short: Ib Henning Madsen (born 12 April 1942, in Copenhagen) is a Danish mathematician, a professor of mathematics at the University of Copenhagen. He is known for (with Michael Weiss) proving the Mumford conjecture on the cohomology of the stable mapping class group, and for developing topological cyclic homology theory.

Key takeaways

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

Reference excerpt

Ib Henning Madsen (born 12 April 1942, in Copenhagen) is a Danish mathematician, a professor of mathematics at the University of Copenhagen. He is known for (with Michael Weiss) proving the Mumford conjecture on the cohomology of the stable mapping class group, and for developing topological cyclic homology theory.

Professional career Madsen earned a candidate degree from the University of Copenhagen in 1965, and a Ph.D. from the University of Chicago in 1970 under the supervision of J. Peter May. In 1971 he took a faculty position at Aarhus University, and he remained there until 2008, when he moved to Copenhagen. His doctoral students have included Søren Galatius and Lars Hesselholt.

Awards and honors Madsen was elected as a member of the Royal Danish Academy of Science and Letters in 1978, as a foreign member of the Royal Swedish Academy of Sciences in 1998, and as a foreign member of the Royal Norwegian Society of Sciences and Letters in 2000. In 2012 he became a fellow of the American Mathematical Society. In 1992, he was awarded the Humboldt Prize. In 2011, he won the Ostrowski Prize for outstanding achievement in pure mathematics, shared with Kannan Soundararajan and David Preiss.

Publications Madsen, Ib; Weiss, Michael (2007). "The stable moduli space of Riemann surfaces: Mumford's conjecture". Annals of Mathematics. (2). 165 (3): 843–941. arXiv:math/0212321. doi:10.4007/annals.2007.165.843. MR 2335797. Galatius, Søren; Tillmann, Ulrike; Madsen, Ib; Weiss, Michael (2009). "The homotopy type of the cobordism category". Acta Mathematica. 202 (2): 195–239. arXiv:math/0605249. doi:10.1007/s11511-009-0036-9. MR 2506750.

References

Illustrations

Worked examples

Example 1 — a first encounter with Ib Madsen

Start with the simplest possible case. Write down what Ib Madsen claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Ib Madsen 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 Ib Madsen 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 Ib Madsen

In research: Ib Madsen appears in astronomy 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 Ib Madsen 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: Ib Madsen is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1942 births, Academic staff of Aarhus University, Academic staff of the University of Copenhagen, so understanding it makes those chapters shorter.
In everyday life: Look for Ib Madsen 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 Ib Madsen in 20 minutes

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

Frequently asked questions

What is Ib Madsen in simple terms?

Why does Ib Madsen matter?

Because it connects several astronomy 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 Ib Madsen?

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 Ib Madsen.