mathematics

Tibor Šalát

Tibor Šalát 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 Tibor Šalát rather than just read about it. In short: Tibor Šalát ((1926-05-13)May 13, 1926 – (2005-05-14)May 14, 2005) was a Slovak mathematician, professor of mathematics, and Doctor of Mathematics who specialized in number theory and real analysis. He was the author and co-author of undergraduate and graduate textbooks in mathematics, mostly in Slovak.

Key takeaways

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

Reference excerpt

Tibor Šalát ((1926-05-13)May 13, 1926 – (2005-05-14)May 14, 2005) was a Slovak mathematician, professor of mathematics, and Doctor of Mathematics who specialized in number theory and real analysis. He was the author and co-author of undergraduate and graduate textbooks in mathematics, mostly in Slovak. And most of his scholarly papers have been published in various scientific journals.

Life Originally from Žitava by the southern region of Slovakia, he studied at the Faculty of Natural Sciences of Charles University in Prague, where in 1952 he defended a dissertation entitled Príspevok k teorii súčtov a nekonečných radov s reálnými členami and supervised by Miloš Kössler and Vojtěch Jarník. In 1952 he went to work at the Faculty of Natural Sciences of Comenius University in Bratislava, where he became an assistant professor in 1962. He was appointed to a full professorship position in 1972. And in 1974, he earned a Ph.D. in Mathematics from the same institution. He specialized in Cantor's expansions, uniform distribution, statistical convergence, summation methods and theory of numbers. He wrote several undergraduate and graduate textbooks.

Academic papers Juraj Činčura; Tibor Šalát; Martin Sleziak; Vladimír Toma (2005). "Sets of statistical cluster points and ℐ-cluster points". Real Analysis Exchange. 30 (2): 565–580. doi:10.14321/realanalexch.30.2.0565. MR 2177419. Pavel Kostyrko; Władysław Wilczyński; Tibor Šalát (2001). "I-Convergence". Real Analysis Exchange. 26 (2): 669–686. MR 1844385. Tibor Šalát (1980). "On statistically convergent sequences of real numbers". Mathematica Slovaca. 30 (2): 139–150. MR 0587239. Tibor Šalát; S. James Taylor; János T. Tóth (1998). "Radii of Convergence of Power Series". Real Analysis Exchange. 24 (1): 263–274. doi:10.2307/44152953. JSTOR 44152953. MR 1691750. Ján Borsík; Jaroslav Červeňanský; Tibor Šalát (1995). "Remarks on functions preserving convergence of infinite series". Real Analysis Exchange. 21 (2): 725–731. doi:10.2307/44152683. JSTOR 44152683. MR 1407285. M. Dindoš; T. Šalát; V. Toma (2003). "Statistical Convergence of Infinite Series". Czechoslovak Mathematical Journal. 53 (4): 989–1000. doi:10.1023/B:CMAJ.0000024535.89828.e8. hdl:10338.dmlcz/127854. MR 2018844. S2CID 121987409. Tibor Šalát (2000). "Remarks on Steinhaus' property and ratio sets of sets of positive integers". Czechoslovak Mathematical Journal. 50 (1): 175–183. doi:10.1023/A:1022457724187. hdl:10338.dmlcz/127559. MR 1745470. S2CID 117275867. Tibor Šalát (2000). "On uniform distribution of sequences". Czechoslovak Mathematical Journal. 50 (2): 331–340. doi:10.1023/A:1022422919181. hdl:10338.dmlcz/127572. MR 1761390. S2CID 117677265.

References

P. Kostyrko, O. Strauch: Professor Tibor Šalát (1926-2005), Tatra Mt. Math. Publ. 31 (2005), 1-16 [1]

Worked examples

Example 1 — a first encounter with Tibor Šalát

Start with the simplest possible case. Write down what Tibor Šalát 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 Tibor Šalát 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 Tibor Šalát 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 Tibor Šalát

In research: Tibor Šalát 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 Tibor Šalát 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: Tibor Šalát is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1926 births, 2005 deaths, Academic staff of Comenius University, so understanding it makes those chapters shorter.
In everyday life: Look for Tibor Šalát 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 Tibor Šalát in 20 minutes

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

Frequently asked questions

What is Tibor Šalát in simple terms?

Why does Tibor Šalát 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 Tibor Šalát?

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 Tibor Šalát.