mathematics

Johann Makowsky

Johann Makowsky 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 Johann Makowsky rather than just read about it. In short: Johann (János) A. Makowsky (born March 12, 1948) is a Hungarian-born naturalised Swiss mathematician who works in mathematical logic and the logical foundations of computer science and combinatorics.

Key takeaways

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

Reference excerpt

Johann (János) A. Makowsky (born March 12, 1948) is a Hungarian-born naturalised Swiss mathematician who works in mathematical logic and the logical foundations of computer science and combinatorics. He studied at ETH Zurich from 1967–73. He was a student in Zürich of Ernst Specker and Hans Läuchli in mathematical logic, (Diploma in Mathematics and Physics 1971, Dr. math.sc. in 1974), of Beno Eckmann (Topology and Geometry) and Volker Strassen (Algorithmics), and in Warsaw of Andrzej Mostowski and Witek Marek, where he spent 1972 as an exchange student. Makowsky held visiting positions at the Banach Center in Warsaw (Poland), Stanford University (USA), Simon Fraser University (Canada), University of Florence (Italy), MIT (USA), Lausanne University and ETH Zurich (Switzerland). He held regular positions at the Free University of Berlin and the Technion – Israel Institute of Technology (Haifa, Israel) where he was a full professor. Among his various contributions are:

In model theory, the solution of two open problems in categoricity theory and his study of logics with various interpolation and compactness properties (partially with Saharon Shelah and Jonathan Stavi). In database theory, the first undecidability result of the consequence problem for database dependencies (with Ashok Chandra and Harry Lewis), his work unifying the entity–relationship model and the relational model of databases (with Victor Markowitz), and his work on Boyce–Codd normal form (with E.V. Ravve). In logic programming, his fundamental studies of Horn formulas and their complexity (partially with B. Mahr and A. Itai) In graph algorithms, his unifying approach to tree-width and clique-width via model theory, leading to a general theory of graph polynomials and their definability in various logical formalisms (partially with I. Averbouch, Bruno Courcelle, B. Godlin, T. Kotek, U. Rotics and Boris Zilber). Makowsky was a founding member of the European Association of Computer Science Logic in 1992, its vice-president (2002–2004) and president (2004–2009), and was a member of EACSL's executive council till 2014. During his presidency he established the EACSL Ackermann Award for outstanding PhD theses in computer science logic. In 2008, an event dedicated to Makowsky on his 60th birthday was co-located with the annual meeting of the EACSL. Since 2016, he is a Professor Emeritus at the Faculty of Computer Science at the Technion, and continues his research and teaching and supervising graduate students

References

External links Official website Johann A. Makowsky at DBLP Bibliography Server

Illustrations

Worked examples

Example 1 — a first encounter with Johann Makowsky

Start with the simplest possible case. Write down what Johann Makowsky 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 Johann Makowsky 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 Johann Makowsky 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 Johann Makowsky

In research: Johann Makowsky 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 Johann Makowsky 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: Johann Makowsky is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1948 births, Academic staff of Technion – Israel Institute of Technology, ETH Zurich alumni, so understanding it makes those chapters shorter.
In everyday life: Look for Johann Makowsky 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 Johann Makowsky in 20 minutes

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

Frequently asked questions

What is Johann Makowsky in simple terms?

Why does Johann Makowsky 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 Johann Makowsky?

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 Johann Makowsky.