mathematics

Lajos Takács

Lajos Takács 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 Lajos Takács rather than just read about it. In short: Lajos Takács (August 21, 1924 (Maglód) – December 4, 2015) was a Hungarian mathematician, known for his contributions to probability theory and, in particular, queueing theory. He wrote over two hundred scientific papers and six books.

Key takeaways

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

Reference excerpt

Lajos Takács (August 21, 1924 (Maglód) – December 4, 2015) was a Hungarian mathematician, known for his contributions to probability theory and, in particular, queueing theory. He wrote over two hundred scientific papers and six books. He studied at the Technical University of Budapest (1943-1948), taking courses with Charles Jordan and received an M.S. for his dissertation On a Probability-theoretical Investigation of Brownian Motion (1948). From 1945-48 he was a student assistant to Professor Zoltán Bay and participated in his famous experiment of receiving microwave echoes from the Moon (1946). In 1957 he received the Academic Doctor's Degree in Mathematics for his thesis Stochastic processes arising in the theory of particle counters (1957). He worked as a mathematician at the Tungsram Research Laboratory (1948–55), the Research Institute for Mathematics of the Hungarian Academy of Sciences (1950–58) and was an associate professor in the Department of Mathematics of the L. Eötvös University (1953–58). He was the first to introduce semi-Markov processes in queueing theory. He took a lecturing appointment at Imperial College in London and London School of Economics (1958), before moving to Columbia University in New York City (1959–66) and Case Western Reserve University in Cleveland (1966–87), advising over twenty Ph.D. theses. He also held visiting appointments at Bell Labs and IBM Research, had sabbaticals at Stanford University (1966). He was a Professor of Statistics and Probability at Case Western Reserve University from 1966 until he retired as Professor Emeritus in 1987. Takács was married to Dalma Takács, an author and professor of English Literature at Notre Dame College of Ohio. He had two daughters, the contemporary figurative realist artist Judy Takács and Susan, a legal assistant.

Publications The following is a partial list of publications

Some Investigations Concerning Recurrent Stochastic Processes of a Certain Kind, Magyar Tud. Akad. Alk. Mat.Int. Kozl. vol.3, pp. 115–128, 1954. Investigations of Waiting Time Problems by Reduction to Markov Processes, Acta Math. Acad. Sci. Hung. vol.6, pp. 101–129, 1955. Sojourn times for the Brownian motion, Journal of Applied Mathematics and Stochastic Analysis, vol. 11, no. 3, pp. 231–246, 1998 In memoriam: Pál Erdős (1913-1996), Journal of Applied Mathematics and Stochastic Analysis, vol. 9, no. 4, pp. 563–564, 1996 Sojourn times, Journal of Applied Mathematics and Stochastic Analysis, vol. 9, no. 4, pp. 415–426, 1996 Brownian local times, Journal of Applied Mathematics and Stochastic Analysis, vol. 8, no. 3, pp. 209–232, 1995 Limit distributions for queues and random rooted trees, Journal of Applied Mathematics and Stochastic Analysis, vol. 6, no. 3, pp. 189–216, 1993 On a probability problem connected with railway traffic, Journal of Applied Mathematics and Stochastic Analysis, vol. 4, no. 1, pp. 1–27, 1991 Conditional limit theorems for branching processes, Journal of Applied Mathematics and Stochastic Analysis, vol. 4, no. 4, pp. 263–292, 1991 On the distribution of the number of vertices in layers of random trees, Journal of Applied Mathematics and Stochastic Analysis, vol. 4, no. 3, pp. 175–186, 1991 Queues, random graphs and branching processes, Journal of Applied Mathematics and Stochastic Analysis, vol. 1, no. 3, pp. 223–243, 1988 On the distribution of the supremum for stochastic processes, Annales de l'institut Henri Poincaré (B) Probabilités et Statistiques, 6(3):237-247, 1970 On the Total Heights of Random Rooted Binary Trees, J. Comb. Theory, Ser. B 61(2): 155-166 (1994) Counting forests, Discrete Mathematics 84(3): 323-326 (1990) On Cayley's formula for counting forests, J. Comb. Theory, Ser. A 53(2): 321-323 (1990) A generalization of an inequality of Stepanov, J. Comb. Theory, Ser. B 48(2): 289-293 (1990) On the Number of Distinct Forests, SIAM Journal on Discrete Mathematics 3(4): 574-581 (1990) On the "problème des ménages", Discrete Mathematics 36(3): 289-297 (1981) On a Combinatorial Theorem Related to a Theorem of G. Szegö, J. Comb. Theory, Ser. A 30(3): 345-348 (1981) An Identity for Ordered Partial Sums, J. Comb. Theory, Ser. A 23(3): 364-365 (1977)

Books Stochastic Processes. Problems and Solutions (Methuen, 1960) Introduction to the Theory of Queues, (Oxford University Press, 1962) Combinatorial Methods in the Theory of Stochastic Processes, (John Wiley, 1967)

Awards 1993 Foreign Membership Magyar Tud. Akad. 1994 John von Neumann Theory Prize 2002 Fellows Award. Inst. for Operations Research and Management Sciences

Literature Jewgeni H. Dshalalow and Ryszard Syski, Lajos Takács and his work, in Jrn. of Applied Math. and Stochastic Analysis, 7(3):215-237, 1994. Studies in Applied Probability, Papers in Honour of Lajos Takacs. by J. Galambos, J. Gani, The Journal of the Operational Research Society, 46(11):1397-98, 1995

References

External links Biography of Lajos Takács from the Institute for Operations Research and the Management Sciences

Worked examples

Example 1 — a first encounter with Lajos Takács

Start with the simplest possible case. Write down what Lajos Takács 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 Lajos Takács 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 Lajos Takács 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 Lajos Takács

In research: Lajos Takács 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 Lajos Takács 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: Lajos Takács is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1924 births, 2015 deaths, Case Western Reserve University faculty, so understanding it makes those chapters shorter.
In everyday life: Look for Lajos Takács 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 Lajos Takács in 20 minutes

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

Frequently asked questions

What is Lajos Takács in simple terms?

Why does Lajos Takács 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 Lajos Takács?

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 Lajos Takács.