mathematics

Otomar Hájek

Otomar Hájek 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 Otomar Hájek rather than just read about it. In short: Otomar Hájek (December 31, 1930 – December 18, 2016) was a Czech-American mathematician, known for his contributions to dynamical systems, game theory and control theory. He was born in Belgrade in Serbia, moving with his family to Prague in 1935, to the Netherlands in 1939 and via Algeria and southern France to London in 1940 where they lived until 1945 when they returned to Prague.

Key takeaways

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

Reference excerpt

Otomar Hájek (December 31, 1930 – December 18, 2016) was a Czech-American mathematician, known for his contributions to dynamical systems, game theory and control theory. He was born in Belgrade in Serbia, moving with his family to Prague in 1935, to the Netherlands in 1939 and via Algeria and southern France to London in 1940 where they lived until 1945 when they returned to Prague. After high school in 1949 he studied mathematics at Charles University in Prague, resulting in a Ph.D. in 1963 with his thesis Dynamical Systems in the Plane. At the same place he joined the mathematics and physics faculty in 1965, before moving in 1968 to Cleveland and Case Western Reserve University, where he worked until 1995 as a professor, becoming an emeritus in 1996. In the mid-1970s, Hájek also received von Humboldt award at TH Darmstadt, Fachbereich Mathematik.

Books Hájek, Otomar (1968), Dynamical systems in the plane, Boston, MA: Academic Press, MR 0240418 Hájek, Otomar (2008) [1975], Pursuit Games: An Introduction to the Theory and Applications of Differential Games of Pursuit and Evasion, New York: Dover Publications, ISBN 978-0-486-46283-7, MR 0456557 Hájek, Otomar (2008) [1991], Hájek, Otamar (ed.), Control theory in the plane, Lecture Notes in Control and Information Sciences, vol. 153, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0042035, ISBN 978-3-540-85254-4, MR 1109709

References

Worked examples

Example 1 — a first encounter with Otomar Hájek

Start with the simplest possible case. Write down what Otomar Hájek 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 Otomar Hájek 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 Otomar Hájek 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 Otomar Hájek

In research: Otomar Hájek 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 Otomar Hájek 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: Otomar Hájek is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1930 births, 2016 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Otomar Hájek 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 Otomar Hájek in 20 minutes

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

Frequently asked questions

What is Otomar Hájek in simple terms?

Why does Otomar Hájek 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 Otomar Hájek?

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 Otomar Hájek.