astronomy

Harald Bergström

Harald Bergström is a astronomy 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 Harald Bergström rather than just read about it. In short: Harald Bergström (1 April 1908 – 23 May 2001) was a Swedish mathematician, specializing in probability theory. Education and career Harald Bergström studied mathematics, physics and chemistry at the Uppsala University and received in 1931 his master's degree.

Key takeaways

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

Reference excerpt

Harald Bergström (1 April 1908 – 23 May 2001) was a Swedish mathematician, specializing in probability theory.

Education and career Harald Bergström studied mathematics, physics and chemistry at the Uppsala University and received in 1931 his master's degree. From 1932 to 1934 he taught at secondary schools and then worked as a research assistant at the Uppsala University. There he received his Ph.D. in 1938 and taught until 1945. In 1946 he moved to Chalmers University of Technology in Göteborg, where in 1949 he was appointed a professor of applied mathematics. In 1960 he was also appointed a professor for numerical analysis and mathematical statistics. In 1974 he retired as professor emeritus. At the University of Uppsala, Harald Bergström did research mainly on algebraic number fields and related topics. After his move to Chalmers University of Technology, he focused on probability theory and statistics. He was supervisor to Peter Jagers. He made important contributions to central limit theorems and the theory of alpha stable distributions. The widely used Bergström's inequality is named, amongst others, after him. He was an invited speaker at the International Congress of Mathematicians in 1936 at Oslo and in 1950 at Cambridge, Massachusetts. In 1973 Chalmers University of Technology published a book of essays in honour of his sixty-fifth birthday.

Selected publications

Books Limit Theorems for Convolutions. Almqvist och Wicksell, Stockholm, und Wiley, New York 1963. Weak Convergence of Measures. Academic Press, New York 1982.

Articles Zur Theorie der biquadratischen Zahlkörper. Die Arithmetik auf klassenkörpertheoretischer Grundlage. Dissertation. In: Nova Acta Regiae Societatis Scientiarum Upsaliensis. Series 4, Volume 10, No. 8. Almqvist & Wiksell, Uppsala 1937. Über die Methode von Woronoj zur Berechnung einer Basis eines kubischen Zahlkörpers. In: Arkiv för matematik, astronomi och fysik. Volume 25B, No. 26. Almqvist & Wiksell, Stockholm 1937. Vereinfachter Beweis des Hauptidealsatzes der Klassenkörpertheorie. In: Arkiv för matematik, astronomi och fysik. Volume 29B, No. 6. Almqvist & Wiksell, Stockholm 1943. Struktur der Erweiterungen abelscher Gruppen. In: Arkiv för matematik, astronomi och fysik. Volume 30, No. 4. Almqvist & Wiksell, Stockholm 1944. On the central limit theorem. Scandinavian Actuarial Journal Vol. 27, 1944. doi:10.1080/03461238.1944.10404925 On the central limit theorem in the space Rk, k > 1 Scandinavian Actuarial Journal Vol. 28, 1945, pp. 106–127. doi:10.1080/03461238.1945.10404921 On the central limit theorem in the case of not equally distributed random variables. Scandinavian Actuarial Journal Vol. 32, 1949, pp. 37–62. doi:10.1080/03461238.1949.10419757 On some Expansions of stable distribution functions. In: Arkiv för matematik. Vol. 2, No. 18. Almqvist & Wiksell, Stockholm 1952, pp. 375–378. Eine Theorie der stabilen Verteilungsfunktionen. In: Archiv der Mathematik. Volume 2, 1953, pp. 380–391. On the limit theorem for convolutions of distribution functions. In: Journal für die Reine und Angewandte Mathematik.Part 1: 1957 Vol. 198, pp. 121–142.Part 2: 1958 Vol. 199, pp. 1–22. Bergström, H. (1970). "A comparison method for distribution functions of sums of independent and dependent random variables". Theory of Probability & Its Applications. 15 (3): 430–457. doi:10.1137/1115048.

References

External links Literature by and about Harald Bergström in the German National Library catalogue

Illustrations

Worked examples

Example 1 — a first encounter with Harald Bergström

Start with the simplest possible case. Write down what Harald Bergström claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Harald Bergström 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 Harald Bergström 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 Harald Bergström

In research: Harald Bergström appears in astronomy 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 Harald Bergström 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: Harald Bergström is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1908 births, 2001 deaths, 20th-century Swedish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Harald Bergström 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 Harald Bergström in 20 minutes

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

Frequently asked questions

What is Harald Bergström in simple terms?

Harald Bergström (1 April 1908 – 23 May 2001) was a Swedish mathematician, specializing in probability theory. Education and career Harald Bergström studied mathematics, physics and chemistry at the Uppsala University and received in 1931 his master's degree.

Why does Harald Bergström matter?

Because it connects several astronomy 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 Harald Bergström?

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 Harald Bergström.