mathematics

Nikolai Andreevich Lebedev

Nikolai Andreevich Lebedev 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 Nikolai Andreevich Lebedev rather than just read about it. In short: Nikolai Andreevich Lebedev (Russian: Никола́й Андре́евич Ле́бедев; August 8, 1919 – January 8, 1982) was a Soviet mathematician who worked on complex function theory and geometric function theory. Jointly with Isaak Milin, he proved the Lebedev–Milin inequalities that were used in the proof of the Bieberbach conjecture.

Key takeaways

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

Reference excerpt

Nikolai Andreevich Lebedev (Russian: Никола́й Андре́евич Ле́бедев; August 8, 1919 – January 8, 1982) was a Soviet mathematician who worked on complex function theory and geometric function theory. Jointly with Isaak Milin, he proved the Lebedev–Milin inequalities that were used in the proof of the Bieberbach conjecture.

See also Conformal map Power series

Biographical references Aleksandrov, I. A.; Bazilevich, I. E.; Kuz'min, G. V.; Lozinskii, S. M.; Tamrazov, P. M.; Shirokov, N. A. (1983), "Николай Андреевич Лебедев (некролог)", Uspekhi Matematicheskikh Nauk, 38 (2(230)): 195–199, MR 0695474, Zbl 0515.01018, translated in English as "Nikolai Andreevich Lebedev (obituary)", Russian Mathematical Surveys, 38 (2): 177–182, 1983, Bibcode:1983RuMaS..38..177A, doi:10.1070/RM1983v038n02ABEH003472, MR 0695474, Zbl 0528.01020. Goluzina, E. G.; Zhuk, V. V.; Kuzmina, G. V.; Shirokov, N. A. (2001), "Николай Андреевич Лебедев и Ленинградская школа теории функций (50–70 гг.)", Zapiski Nauchnykh Seminarov POMI, 276: 5–19, MR 1850360, Zbl 1077.01525, translated in English as "Nikolai Andreevich Lebedev and the Leningrad School of Function Theory in the 50s–70s", Journal of Mathematical Sciences, 118 (1): 4733–4739, 2003, doi:10.1023/A:1025562313596, MR 1850360, S2CID 117992735, Zbl 1077.01525.

References Grinshpan, Arcadii Z. (2002), "Logarithmic Geometry, Exponentiation, and Coefficient Bounds in the Theory of Univalent Functions and Nonoverlapping Domains", in Kuhnau, Reiner (ed.), Geometric Function Theory, Handbook of Complex Analysis, vol. 1, Amsterdam: North-Holland, pp. 273–332, ISBN 978-0-444-82845-3, MR 1966197, Zbl 1083.30017. Hayman, W. K. (1994) [1958], Multivalent functions, Cambridge Tracts on Mathematics, vol. 110 (Second ed.), Cambridge: Cambridge University Press, pp. xii+263, ISBN 978-0-521-46026-2, MR 1310776, Zbl 0904.30001. Kuhnau, Reiner, ed. (2002), Geometric Function Theory, Handbook of Complex Analysis, vol. 1, Amsterdam: North-Holland, pp. xii+536, ISBN 978-0-444-82845-3, MR 1966187, Zbl 1057.30001. Milin, I. M. (1977) [1971], Univalent functions and orthonormal systems, Translations of Mathematical Monographs, vol. 49, Providence, R.I.: American Mathematical Society, pp. iv+202, ISBN 978-0-8218-1599-1, MR 0369684, Zbl 0342.30006 (Translation of the 1971 Russian edition, edited by P. L. Duren).

Worked examples

Example 1 — a first encounter with Nikolai Andreevich Lebedev

Start with the simplest possible case. Write down what Nikolai Andreevich Lebedev 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 Nikolai Andreevich Lebedev 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 Nikolai Andreevich Lebedev 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 Nikolai Andreevich Lebedev

In research: Nikolai Andreevich Lebedev 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 Nikolai Andreevich Lebedev 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: Nikolai Andreevich Lebedev is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1919 births, 1982 deaths, Complex analysts, so understanding it makes those chapters shorter.
In everyday life: Look for Nikolai Andreevich Lebedev 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Nikolai Andreevich Lebedev” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Nikolai Andreevich Lebedev in 20 minutes

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

Frequently asked questions

What is Nikolai Andreevich Lebedev in simple terms?

Why does Nikolai Andreevich Lebedev 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 Nikolai Andreevich Lebedev?

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 Nikolai Andreevich Lebedev.