mathematics

Mikhail Postnikov

Mikhail Postnikov 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 Mikhail Postnikov rather than just read about it. In short: Mikhail Mikhailovich Postnikov (Russian: Михаи́л Миха́йлович По́стников; 27 October 1927 – 27 May 2004) was a Soviet mathematician, known for his work in algebraic and differential topology. Biography He was born in Shatura, near Moscow.

Key takeaways

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

Reference excerpt

Mikhail Mikhailovich Postnikov (Russian: Михаи́л Миха́йлович По́стников; 27 October 1927 – 27 May 2004) was a Soviet mathematician, known for his work in algebraic and differential topology.

Biography He was born in Shatura, near Moscow. He received his Ph.D. from Moscow State University under the direction of Lev Pontryagin, and then became a professor at this university. He died in Moscow.

Selected publications Fundamentals of Galois theory, 1961; 142 pp. Dover reprint, 2004 The variational theory of geodesics, Translated from the Russian by Scripta Technica, Inc. Edited by Bernard Russell Gelbaum. Saunders, Philadelphia, Pa., 1967; 200 pp. Linear algebra and differential geometry. Translated from the Russian by Vladimir Shokurov. Mir Publishers, 1982; 319 pp. Smooth manifolds, Mir Publishers, 1989; 511 pp. Geometry VI: Riemannian Geometry, Springer, 2001, 504 pp.

French Leçons de géométrie : Semestre I : Géométrie analytique, Éditions Mir, 1981; 279 pp. Leçons de géométrie : Semestre II : Algèbre linéaire et géométrie différentielle, Éditions Mir, 1981; 263 pp. Leçons de géométrie : Semestre III : Variétés différentiables, Éditions Mir, 1990; 431 pp. Leçons de géométrie : Semestre IV : Géométrie différentielle, Éditions Mir, 1990; 439 pp. Leçons de géométrie : Semestre V : Groupes et algèbres de Lie, Éditions Mir, 1985; 374 pp.

See also Postnikov system Postnikov square

References

Bibliography O'Connor, John J.; Robertson, Edmund F., "Mikhail Mikhailovich Postnikov", MacTutor History of Mathematics Archive, University of St Andrews Postnikov, M. M. (1993), "Pages of a mathematical autobiography (1942--1953)", in Zdravkovska, Smilka; Duren, Peter L. (eds.), Golden years of Moscow mathematics, Hist. Math., vol. 6, Providence, R.I.: American Mathematical Society, pp. 155–178, ISBN 978-0-8218-9003-5, MR 1246563 Rudyak, Yuli (2009), "M. M. Postnikov: his life, work and legacy", Algebraic topology---old and new, Banach Center Publications, vol. 85, Polish Acad. Sci. Inst. Math., Warsaw, pp. 15–29, doi:10.4064/bc85-0-1, ISBN 978-83-86806-04-1, MR 2503515

Worked examples

Example 1 — a first encounter with Mikhail Postnikov

Start with the simplest possible case. Write down what Mikhail Postnikov 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 Mikhail Postnikov 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 Mikhail Postnikov 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 Mikhail Postnikov

In research: Mikhail Postnikov 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 Mikhail Postnikov 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: Mikhail Postnikov is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1927 births, 2004 deaths, 20th-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Mikhail Postnikov 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 Mikhail Postnikov in 20 minutes

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

Frequently asked questions

What is Mikhail Postnikov in simple terms?

Why does Mikhail Postnikov 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 Mikhail Postnikov?

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 Mikhail Postnikov.