mathematics

Sidney Martin Webster

Sidney Martin Webster 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 Sidney Martin Webster rather than just read about it. In short: Sidney Martin Webster (born 12 November 1945 in Danville, Illinois) is an American mathematician, specializing in multidimensional complex analysis. After military service, Webster attended the University of California, Berkeley as an undergraduate and then as a graduate student, receiving a PhD in 1975 under the supervision of Shiing-Shen Chern with thesis Real hypersurfaces in complex space.

Key takeaways

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

Reference excerpt

Sidney Martin Webster (born 12 November 1945 in Danville, Illinois) is an American mathematician, specializing in multidimensional complex analysis. After military service, Webster attended the University of California, Berkeley as an undergraduate and then as a graduate student, receiving a PhD in 1975 under the supervision of Shiing-Shen Chern with thesis Real hypersurfaces in complex space. Webster was a faculty member at Princeton University from 1975 to 1980 and at the University of Minnesota from 1980 to 1989. In 1989 he became a full professor at the University of Chicago. He has held visiting positions at the University of Wuppertal, Rice University, and ETH Zurich. Webster was a Sloan Fellow for the academic year 1979–1980. In 1994 in Zurich he was an invited speaker of the International Congress of Mathematicians. In 2001 he received, jointly with László Lempert, the Stefan Bergman Prize from the American Mathematical Society. In 2012 Webster was elected a Fellow of the American Mathematical Society. In 1977 he proved a significant theorem on biholomorphic mappings between algebraic real hypersurfaces. Using his expertise on Chern-Moser invariants, he developed a theory that provides a complete set of invariants for nondegenerate real hypersurfaces under volume-preserving biholomorphic transformations. He used the edge-of-the-wedge theorem to prove an extension theorem that generalized a 1974 theorem of Charles Fefferman.

Selected publications Webster, S. M. (1979). "The rigidity of C-R hypersurfaces in a sphere". Indiana University Mathematics Journal. 28 (3): 405–416. doi:10.1512/iumj.1979.28.28027. JSTOR 24892266. Webster, S. M. (1979). "Biholomorphic mappings and the Bergman kernel off the diagonal". Inventiones Mathematicae. 51 (2): 155–169. Bibcode:1979InMat..51..155W. doi:10.1007/BF01390226. S2CID 119485248. with Klas Diederich: Diederich, K.; Webster, S. M. (1980). "A reflection principle for degenerate real hypersurfaces". Duke Math. J. 47 (4): 835–843. doi:10.1215/S0012-7094-80-04749-3. with Jürgen K. Moser: Moser, Jürgen K.; Webster, Sidney M. (1983). "Normal forms for real surfaces in C {\displaystyle \mathbb {C} } 2 near complex tangents and hyperbolic surface transformations". Acta Mathematica. 150: 255–296. doi:10.1007/BF02392973.

References

Worked examples

Example 1 — a first encounter with Sidney Martin Webster

Start with the simplest possible case. Write down what Sidney Martin Webster 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 Sidney Martin Webster 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 Sidney Martin Webster 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 Sidney Martin Webster

In research: Sidney Martin Webster 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 Sidney Martin Webster 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: Sidney Martin Webster is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Sidney Martin Webster 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 Sidney Martin Webster in 20 minutes

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

Frequently asked questions

What is Sidney Martin Webster in simple terms?

Why does Sidney Martin Webster 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 Sidney Martin Webster?

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 Sidney Martin Webster.