mathematics

Klaus Matthes

Klaus Matthes 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 Klaus Matthes rather than just read about it. In short: Klaus Matthes (January 20, 1931 – March 9, 1998) was a German mathematician, known as the founder of the theory of marked and infinitely divisible point processes. From 1981 to 1991 he was the director of the GDR Academy of Sciences' Institute of Mathematics in Berlin.

Key takeaways

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

Reference excerpt

Klaus Matthes (January 20, 1931 – March 9, 1998) was a German mathematician, known as the founder of the theory of marked and infinitely divisible point processes. From 1981 to 1991 he was the director of the GDR Academy of Sciences' Institute of Mathematics in Berlin.

Early years Matthes studied from 1948 to 1954 mathematics at Humboldt University of Berlin. He obtained his PhD from his alma mater in 1958, advised by Heinrich Grell and Kurt Schröder. In 1963 he received the habilitation, with Willi Rinow as one of the referees.

Career Matthes was employed from 1956 to 1961 as scientific assistant at Humboldt University. Then he acted as provisional director of the institute of mathematics at Ilmenau University of Technology. From 1964 to 1968 he was then full professor of mathematics at University of Jena. There he was since 1966 the dean of the mathematical-natural-scientific faculty. In 1969 he moved to Berlin, to the Central Institute for Mathematics and Mechanics of the German Academy of Sciences, later Academy of Sciences of the German Democratic Republic (G.D.R.). From 1981 to 1991 he directed the academy institute of mathematics, which in 1985 was named „Karl-Weierstraß-Institut für Mathematik“. Thanks to the high quality of its staff, its applied part survived the big changes of the East German science system and was re-founded after the German reunification as Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS). In 1974 Klaus Matthes was elected corresponding and in 1980 full fellow of the Academy of Sciences of the GDR. He was decorated in 1971 with the National Prize of East Germany and 1983 with the bronze Vaterländischer Verdienstorden.

Scientific work The main field of Klaus Matthes' scientific work was probability theory. He worked in particular on point processes and their application in queueing theory and branching processes. In queueing theory he studied loss systems, e.g. the Erlang and Engset loss systems, and was the first to apply deep methods of the theory of point processes in queueing. Klaus Matthes can be seen as the father of the theory of marked infinitely divisible point processes. He was, together with Johannes Kerstan and Joseph Mecke, the leader of the East German school of point process theory, which later found successful applications in other fields, e.g. in stochastic geometry. In the context of limit theorems for superpositions of point processes he came to the problem of infinite divisibility of point processes (following a suggestion by Boris Vladimirovich Gnedenko). Together with his coworkers he investigated systematically the structure of infinitely divisible distributions, which culminated in the monograph "Infinitely Divisible Point Processes". Closely related are spatial branching processes, which he studied until the end of his life. A central problem here were equilibrium distributions and their structure. Matthes initiated the today prestigious ″Euler lectures″ in Sanssouci near Potsdam.

Personal life Klaus Matthes was married with the stage producer Gisela Matthes, née Weisse, and he was father of two sons.

Bibliography (selection) Stationäre zufällige Punktfolgen, I.. In: Jahresberichte der Deutschen Mathematiker-Vereinigung. Vol. 66. 1963, pp. 66–79, ISSN 0012-0456 Stationäre zufällige Punktfolgen, II.. In: Jahresberichte der Deutschen Mathematiker-Vereinigung. Vol. 66. 1963, pp. 106–118, ISSN 0012-0456 Verallgemeinerungen der Erlangschen und Engsetschen Formeln. Akademie-Verlag Berlin, 1967 (as coauthor) Verallgemeinerungen eines Satzes von Dobruschin I. In: Mathematische Nachrichten. Vol. 47. 1970, pp. 183–244. ISSN 0025-584X (as coauthor) Verallgemeinerungen eines Satzes von Dobruschin III. In: Mathematische Nachrichten. Vol. 50. 1971, pp. 99–139. ISSN 0025-584X (as coauthor) Einführung in die Bedienungstheorie. München 1971 (as coauthor) Unbegrenzt teilbare Punktprozesse. Akademie-Verlag Berlin. 1974. Series: Mathematische Lehrbücher und Monographien; Vol. 27 (as coauthor) Infinitely divisible Point Processes. John Wiley & Sons, Chichester, 1978. Series: Wiley Series in Probability and Mathematical Statistics. (as coauthor) Equilibrium Distributions of Branching Processes. Akademie-Verlag Berlin, und Kluwer Academic Publishers, Dordrecht, Boston, London, 1988. Series: Mathematical Research; 42. ISBN 3-05-500453-1 (as coauthor) Equilibrium Distributions of Age Dependent Galton Watson Processes I. In: Mathematische Nachrichten. Vol. 56. 1992, pp. 233–267. ISSN 0025-584X (as coauthor) Equilibrium distributions of age-dependent Galton Watson processes II. In: Mathematische Nachrichten. Vol. 160. 1993, pp. 313–324. ISSN 0025-584X (as coauthor) Recurrence of ancestral Lines and Offspring Trees in Time stationary branching Populations. Berlin 1994 (as coauthor)

Literature Dietrich Stoyan: Obituary: Klaus Matthes. In: Journal of Applied Probability. 36(4)/1999. Applied Probability Trust, pp. 1255–1257, ISSN 0021-9002 Short biography with photo

References

Illustrations

Klaus Matthes: Klaus Matthes — Klaus Matthes

Worked examples

Example 1 — a first encounter with Klaus Matthes

Start with the simplest possible case. Write down what Klaus Matthes 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 Klaus Matthes 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 Klaus Matthes 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 Klaus Matthes

In research: Klaus Matthes 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 Klaus Matthes 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: Klaus Matthes is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1931 births, 1998 deaths, 20th-century German statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for Klaus Matthes 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 Klaus Matthes in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Klaus Matthes 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.
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Frequently asked questions

What is Klaus Matthes in simple terms?

Why does Klaus Matthes 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 Klaus Matthes?

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 Klaus Matthes.