mathematics

Stefan Burr

Stefan Burr 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 Stefan Burr rather than just read about it. In short: Stefan Andrus Burr (born 1940) is a mathematician and computer scientist, specializing in graph theory and number theory, particularly Ramsey theory. He is a retired professor of Computer Science at The City College of New York.

Key takeaways

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

Reference excerpt

Stefan Andrus Burr (born 1940) is a mathematician and computer scientist, specializing in graph theory and number theory, particularly Ramsey theory. He is a retired professor of Computer Science at The City College of New York.

Career He did his undergraduate studies at University of California, Berkeley, graduating with a Bachelor of Arts in Mathematics with Highest Honors in 1961 June. He was a member of their team for the William Lowell Putnam Mathematical Competition on 1958 November 22, where the team received an honorable mention; 1959 November 21, where he individually received an honorable mention; and 1960 December 3, where the team won first prize and he additionally received an honorable mention. As a member of the class of 1961, he received the Dorothea Klumpke Roberts Prize in Mathematics in 1960. As a student there, he joined the Mathematical Association of America in 1960 April/May. He graduated from Princeton University with a Master of Arts in 1963 and a PhD in 1968, both in Mathematics. His PhD thesis, An Elementary Solution of the Waring-Goldbach Problem (1968 or 1969) was advised by Bernard Morris Dwork. While working on his PhD at Princeton, he had a job as a Scientific Programmer for Lockheed MSC (c. 1965). Afterwards, starting c. 1966, he had a job as a member of the technical staff at Bell Telephone Laboratories, then moved to American Telephone & Telegraph (AT&T) Long Lines c. 1975, where he worked as a Staff Supervisor until c. 1978. Afterwards, c. 1979, he became a member of the faculty of City College, part of the City University of New York (CUNY) system, in the Department of Computer Science (and perhaps briefly in the Department of Mathematics). In 1982, he spent 3 months from May to August visiting the University of Coimbra in Portugal as a Fulbright Scholar, where he lectured and researched computer science. He may have spent some time at Lehman College c. 1996 – c. 1998. He retired after teaching in the Fall 2006 semester. He became Mathematics Vice-Chair of the New York Academy of Sciences in January 1988, became Mathematics Chair in 1990, and retired from the position in June 1992. He became a managing editor of the Journal of Graph Theory in 1991, and retired from the position c. 1997. Many of his publications involve problems from the field of Ramsey theory. He has published 27 papers with Paul Erdős. The Burr–Erdős conjecture, published as a conjecture by Burr and Erdős in 1975, solved only in 2015, states that sparse graphs have linearly growing Ramsey numbers.

Selected publications Burr, Stefan A. (1973). "On uniform elementary estimates of arithmetic sums". Proceedings of the American Mathematical Society. 39 (3): 497–502. doi:10.1090/s0002-9939-1973-0314784-8. eISSN 1088-6826. ISSN 0002-9939. JSTOR 2039582. MR 0314784. EBSCOhost 21907347. Burr, S. A.; Erdős, P.; Spencer, J. H. (August 1975). "Ramsey theorems for multiple copies of graphs". Transactions of the American Mathematical Society. 209: 87–99. doi:10.1090/s0002-9947-1975-0409255-0. eISSN 1088-6850. ISSN 0002-9947. JSTOR 1997371. MR 0409255. Burr, S. A.; Erdős, P.; Faudree, R. J.; Rousseau, C. C.; Schelp, R. H. (February 1982). "Ramsey numbers for the pair sparse graph-path or cycle". Transactions of the American Mathematical Society. 269 (2): 501–512. doi:10.1090/s0002-9947-1982-0637704-5. eISSN 1088-6850. ISSN 0002-9947. JSTOR 1998461. MR 0637704.

References

Illustrations

Worked examples

Example 1 — a first encounter with Stefan Burr

Start with the simplest possible case. Write down what Stefan Burr 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 Stefan Burr 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 Stefan Burr 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 Stefan Burr

In research: Stefan Burr 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 Stefan Burr 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: Stefan Burr is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1940 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Stefan Burr 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 Stefan Burr in 20 minutes

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

Frequently asked questions

What is Stefan Burr in simple terms?

Why does Stefan Burr 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 Stefan Burr?

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 Stefan Burr.