mathematics

Grigorii Fikhtengol'ts

Grigorii Fikhtengol'ts 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 Grigorii Fikhtengol'ts rather than just read about it. In short: Grigorii Mikhailovich Fikhtengol'ts (Russian: Григо́рий Миха́йлович Фихтенго́льц, Ukrainian: Григорій Михайлович Фіхтенгольц, romanized: Hryhorii Mykhailovych Fikhtenholts; 8 June 1888 – 26 June 1959) was a Soviet mathematician working on real analysis and functional analysis. Fikhtengol'ts was one of the founders of the Leningrad school of real analysis.

Key takeaways

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

Reference excerpt

Grigorii Mikhailovich Fikhtengol'ts (Russian: Григо́рий Миха́йлович Фихтенго́льц, Ukrainian: Григорій Михайлович Фіхтенгольц, romanized: Hryhorii Mykhailovych Fikhtenholts; 8 June 1888 – 26 June 1959) was a Soviet mathematician working on real analysis and functional analysis. Fikhtengol'ts was one of the founders of the Leningrad school of real analysis. He was born in Odessa, Russian Empire in 1888, and graduated from the Imperial Novorossiia University in 1911. He authored a three-volume textbook titled "A Course of Differential and Integral Calculus" (Курс дифференциального и интегрального исчисления). The textbook covers mathematical analysis of functions of one real variable, functions of many real variables, and complex functions. Due to the depth and precision of the material's presentation, the book holds a classical position in the mathematical literature. It has been translated into several languages, including German, Ukrainian, Polish, Chinese, and Persian. However, no English translation has been completed yet. He also authored a two-volume textbook titled "The fundamentals of mathematical analysis", originally known as "Основы математического анализа". The textbook had been translated to Vietnamese and English. In Vietnam, the text is known as "Cơ sở giải tích toán học - G.M Fichtengôn". Fikhtengol'ts's books on analysis are widely used in Middle and Eastern European, as well as Chinese universities, due to their exceptionally detailed and well-organized presentation of material on mathematical analysis. For unknown reasons, these books have not gained the same level of fame in universities in other parts of the world. He was an Invited Speaker of the ICM in 1924 in Toronto. Leonid Kantorovich and Isidor Natanson were among his students.

Books

Grigorii Mikhailovich Fikhtengol'ts (1965). The Fundamentals of Mathematical Analysis. Vol. 1. Pergamon Press. ISBN 9781483139074.

Grigorii Mikhailovich Fikhtengol'ts (1965). The Fundamentals of Mathematical Analysis. Vol. 2. Pergamon Press. ISBN 9781483154138.

References

Kantorovič, L. V.; Natanson, I. P. (1958). "Grigoriĭ Mihaĭlovič Fihtengolʹc (on his seventieth birthday)". Vestnik Leningrad. Univ. (in Russian). 13 (7): 5–13. MR 0099901. Kantorovič, L. V.; Natanson, I. P. (1959). "Grigoriĭ Mihaĭlovič Fihtengolʹc. Necrologue". Uspekhi Mat. Nauk (in Russian). 14 (5 (89)): 123–128. MR 0110626. Bogachev, V. I. (2005). "On the works of G. M. Fikhtengolʹts on the theory of the integral". Istor.-Mat. Issled. (2) (in Russian). 9 (44). MR 2365093.

External links

Grigorii Mikhailovich Fichtenholz Grigorii Fikhtengol'ts at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Grigorii Fikhtengol'ts

Start with the simplest possible case. Write down what Grigorii Fikhtengol'ts 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 Grigorii Fikhtengol'ts 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 Grigorii Fikhtengol'ts 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 Grigorii Fikhtengol'ts

In research: Grigorii Fikhtengol'ts 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 Grigorii Fikhtengol'ts 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: Grigorii Fikhtengol'ts is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1888 births, 1959 deaths, Burials at Serafimovskoe Cemetery, so understanding it makes those chapters shorter.
In everyday life: Look for Grigorii Fikhtengol'ts 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 Grigorii Fikhtengol'ts in 20 minutes

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

Frequently asked questions

What is Grigorii Fikhtengol'ts in simple terms?

Why does Grigorii Fikhtengol'ts 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 Grigorii Fikhtengol'ts?

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 Grigorii Fikhtengol'ts.