mathematics

Steven Hurder

Steven Hurder 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 Steven Hurder rather than just read about it. In short: Steven Edmond Hurder is an American mathematician specializing in foliation theory, differential topology, smooth ergodic theory, rigidity of group actions and spectral and index theory of operators. Hurder is a professor emeritus at University of Illinois Chicago.

Key takeaways

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

Reference excerpt

Steven Edmond Hurder is an American mathematician specializing in foliation theory, differential topology, smooth ergodic theory, rigidity of group actions and spectral and index theory of operators. Hurder is a professor emeritus at University of Illinois Chicago. Hurder was named as an inaugural fellow of the American Mathematical Society in 2013.

Education Hurder received his PhD in 1980 at University of Illinois Urbana-Champaign. His advisor was Franz W. Kamber, and the title of his dissertation was Dual Homotopy Invariants of G-Foliations.

Selected publications Hurder, Steven (1981). Dual homotopy invariants of G-foliations, Topology, 20(4):365–387. Hurder, Steven; Katok, Anatoly (1990). Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Inst. Hautes Études Sci. Publ. Math. no. 72, 5–61. Clark, Alex; Hurder, Steven (2013). Homogeneous matchbox manifolds, Trans. Amer. Math. Soc. 365, no. 6, 3151–3191. Hurder, Steven (1992). Rigidity for Anosov actions of higher rank lattices, Ann. of Math. (2) 135, no. 2, 361–410. Hurder, S.; Katok, A (1987). Ergodic theory and Weil measures for foliations, Ann. of Math. (2) 126, no. 2, 221–275. Douglas, Ronald G.; Kaminker, Jerome (1991). Cyclic cocycles, renormalization and eta-invariants, Invent. Math. 103 (1991), no. 1, 101—179.

References

External links Steven Hurder's homepage

Worked examples

Example 1 — a first encounter with Steven Hurder

Start with the simplest possible case. Write down what Steven Hurder 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 Steven Hurder 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 Steven Hurder 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 Steven Hurder

In research: Steven Hurder 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 Steven Hurder 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: Steven Hurder is common in secondary-school and first-year university syllabi. It links to neighbouring topics American mathematician stubs, American mathematicians, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Steven Hurder 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 Steven Hurder in 20 minutes

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

Frequently asked questions

What is Steven Hurder in simple terms?

Why does Steven Hurder 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 Steven Hurder?

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 Steven Hurder.