mathematics

Miklós Simonovits

Miklós Simonovits 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 Miklós Simonovits rather than just read about it. In short: Miklós Simonovits (4 September 1943 in Budapest) is a Hungarian mathematician who currently works at the Rényi Institute of Mathematics in Budapest and is a member of the Hungarian Academy of Sciences. He is on the advisory board of the journal Combinatorica.

Key takeaways

Miklós Simonovits belongs to mathematics; place it in that map before memorising details.
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Reproduce the core statement of Miklós Simonovits from memory before moving on to harder problems.

Reference excerpt

Miklós Simonovits (4 September 1943 in Budapest) is a Hungarian mathematician who currently works at the Rényi Institute of Mathematics in Budapest and is a member of the Hungarian Academy of Sciences. He is on the advisory board of the journal Combinatorica. He is best known for his work in extremal graph theory and was awarded Széchenyi Prize in 2014. Among other things, he discovered the method of progressive induction which he used to describe graphs which do not contain a predetermined graph and the number of edges is close to maximal. With Lovász, he gave a randomized algorithm using O(n7 log2 n) separation calls to approximate the volume of a convex body within a fixed relative error. Simonovits was also one of the most frequent collaborators with Paul Erdős, co-authoring 21 papers with him.

Career He began his university studies at the Mathematics department of Eötvös Loránd University in 1962, after winning a silver and bronze medal at the International Mathematics Olympiad in 1961 and 1962 respectively. He got his diploma in mathematics from the university in 1967 and defended his PhD under Vera T. Sós in 1971. He taught as an assistant professor and then associate professor at Eötvös Loránd, from 1971 to 1979, mainly combinatorics and analysis. He joined Alfréd Rényi Institute of Mathematics in 1979. In the coming years, he was appointed as the professor in Discrete mathematics. He was also a visiting professor at a number of foreign institutions in US and Canada. He was also a visiting researcher at Moscow State University, Charles University, Prague, Warsaw University, Denmark and various institutions in India. He was elected as a corresponding member at the Hungarian Academy of Sciences in 2001 and full membership was awarded in 2008.

Academic work His main research interests are Combinatorics, Extremal Graph Theory, Theoretical Computer Science and Random Graphs. He discovered the method of progressive induction which he used to describe graphs which do not contain a predetermined graph and the number of edges is close to maximal. With Laszlo Lovász, he gave a randomized algorithm using O(n7 log2 n) separation calls to approximate the volume of a convex body within a fixed relative error. He is a long-time collaborator of Endre Szemerédi and worked with him closely. Simonovits was also one of the most frequent collaborators with Paul Erdős, co-authoring 21 papers with him.

Family His father Simonovits István (1907–1985) was a doctor and a hematologist. He was a member of the Hungarian Academy of Sciences. Beke Anna, his mother, was a mathematics and physics teacher, who also worked in a book publishing company.

Awards Tibor Szele-Medal (1989) Academy Award (1993) Széchenyi-Prize (2014)

Key publications A limit theorem in graph theory (with Erdős Pál, 1966) Anti-Ramsey theorems (coauthor, 1973) On the Structure of Edge Graphs-2 (coauthor, 1976) Spanning Retracts of a Partially Ordered Set (coauthor, 1980) Compactness Results in Extremal Graph-Theory (with Erdős Pál, 1982) Supersaturated Graphs and Hypergraphs (with Erdős Pál, 1983) On Restricted Colorings of K_n (with T. Sós Vera, 1984) Szemerédi Partition And Quasi-Randomness (with T. Sós Vera, 1991) Random Walks in a Convex Body and an Improved Volume Algorithm (with Lovász László, 1993) Isoperimetric Problems for Convex Bodies and a Localization Lemma (coauthor, 1995) Szemerédi's Regularity Lemma and its Applications in Graph Theory (with Komlós János, 1996) The Regularity Lemma and its applications in graph theory (coauthor, 2002) Determinisztikus és véletlen struktúrák az extrém gráfelméletben (Deterministic and random structures in extreme graph-theory) (2002) Triple Systems not Containing a Fano Configuration (with Füredi Zoltán, 2005) Stabilitási módszerek alkalmazása a gráfelméletben (Application of stability methods in graph-theory) (2008)

References

External links Miklós Simonovits' home page

Worked examples

Example 1 — a first encounter with Miklós Simonovits

Start with the simplest possible case. Write down what Miklós Simonovits 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 Miklós Simonovits 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 Miklós Simonovits 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 Miklós Simonovits

In research: Miklós Simonovits 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 Miklós Simonovits 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: Miklós Simonovits is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1943 births, 20th-century Hungarian mathematicians, 21st-century Hungarian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Miklós Simonovits 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 Miklós Simonovits in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Miklós Simonovits means in your own words.
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Work through the three examples above with pen and paper.
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Frequently asked questions

What is Miklós Simonovits in simple terms?

Why does Miklós Simonovits 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 Miklós Simonovits?

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 Miklós Simonovits.