mathematics

Steven Kerckhoff

Steven Kerckhoff 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 Kerckhoff rather than just read about it. In short: Steven Paul Kerckhoff (born 1952) is a professor of mathematics at Stanford University, who works on hyperbolic 3-manifolds and Teichmüller spaces. He received his Ph.D. in mathematics from Princeton University in 1978, under the direction of William Thurston.

Key takeaways

Steven Kerckhoff 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 Kerckhoff to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Steven Kerckhoff from memory before moving on to harder problems.

Reference excerpt

Steven Paul Kerckhoff (born 1952) is a professor of mathematics at Stanford University, who works on hyperbolic 3-manifolds and Teichmüller spaces. He received his Ph.D. in mathematics from Princeton University in 1978, under the direction of William Thurston. Among his most famous results is his resolution of the Nielsen realization problem, a 1932 conjecture by Jakob Nielsen. Along with William J. Floyd, he wrote large parts of Thurston's influential Princeton lecture notes, and he is well known for his work (some of which is joint with Craig Hodgson) in exploring and clarifying Thurston's hyperbolic Dehn surgery. Kerckhoff is one of four academics from Stanford University, along with Gunnar Carlsson, Ralph Cohen, and R. James Milgram, who were instrumental in developing the controversial California Mathematics Academic Content Standards for the State Board of Education.

Selected publications Kerckhoff, Steven P. (1983). "The Nielsen realization problem". Annals of Mathematics. 2nd series. 117 (2): 235–265. doi:10.2307/2007076. JSTOR 2007076. MR 0690845. Kerckhoff, Steven P.; Thurston, William P., Noncontinuity of the action of the modular group at Bers' boundary of Teichmüller space. Inventiones Mathematicae 100 (1990), no. 1, 25–47. Kerckhoff, Steven; Masur, Howard; Smillie, John, Ergodicity of billiard flows and quadratic differentials. Annals of Mathematics (2) 124 (1986), no. 2, 293–311. Cooper, Daryl; Hodgson, Craig D.; Kerckhoff, Steven P. Three-dimensional orbifolds and cone-manifolds. With a postface by Sadayoshi Kojima. MSJ Memoirs, 5. Mathematical Society of Japan, Tokyo, 2000. x+170 pp. ISBN 4-931469-05-1 Hodgson, Craig D.; Kerckhoff, Steven P., Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery. Journal of Differential Geometry 48 (1998), no. 1, 1–59.

References Big Business, Race, and Gender in Mathematics Reform, by Steven Krantz (ISBN 0-8218-1398-6). Excerpt from this book. Letter from Kerckhoff, Wayne Bishop, Jane Friedman, and Yat-Sun Poon, to California State Curriculum Commission and California State Board of Education, dated November 21, 2000

External links Steven Kerckhoff at the Mathematics Genealogy Project

Illustrations

Steven Kerckhoff: Kerckhoff gives a talk to Stanford freshmen on choosing courses in mathematics. — Kerckhoff gives a talk to Stanford freshmen on choosing courses in mathematics.

Worked examples

Example 1 — a first encounter with Steven Kerckhoff

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

In research: Steven Kerckhoff 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 Kerckhoff 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 Kerckhoff is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1952 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Steven Kerckhoff 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 Kerckhoff in 20 minutes

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

Frequently asked questions

What is Steven Kerckhoff in simple terms?

Why does Steven Kerckhoff 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 Kerckhoff?

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 Kerckhoff.