mathematics

Robert Tijdeman

Robert Tijdeman 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 Robert Tijdeman rather than just read about it. In short: Robert Tijdeman (born 30 July 1943 in Oostzaan, North Holland) is a Dutch mathematician. Specializing in number theory, he is best known for his Tijdeman's theorem.

Key takeaways

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

Reference excerpt

Robert Tijdeman (born 30 July 1943 in Oostzaan, North Holland) is a Dutch mathematician. Specializing in number theory, he is best known for his Tijdeman's theorem. He is a professor of mathematics at the Leiden University since 1975, and was chairman of the department of mathematics and computer science at Leiden from 1991 to 1993. He was also president of the Royal Dutch Mathematical Society from 1984 to 1986. Tijdeman received his PhD in 1969 from the University of Amsterdam, and received an honorary doctorate from Kossuth Lajos University in 1999. In 1987 he was elected to the Royal Netherlands Academy of Arts and Sciences.

Research In number theory, Tijdeman's theorem states that there are at most a finite number of consecutive powers. Stated another way, the set of solutions in integers x, y, n, m of the exponential diophantine equation

y m = x n + 1 , {\displaystyle y^{m}=x^{n}+1,}

for exponents n and m greater than one, is finite. (This was a significant step towards resolving Catalan’s conjecture, which Preda Mihăilescu accomplished in 2002.) Tijdeman worked closely with T.N. Shorey on various arithmetic problems. He has also worked on algorithms in the area of discrete tomography.

Selected publications Shorey, T. N.; Tijdeman, R. (1990). "On the greatest prime factor of an arithmetical progression". In Baker, A.; Bollobas, B.; Hajnal, A. (eds.). A Tribute to Paul Erdős. Cambridge: Cambridge University Press. pp. 385–390. doi:10.1017/cbo9780511983917.032. ISBN 978-0-511-98391-7. Shorey, T.; Tijdeman, R. (11 August 2010). "On the greatest prime factor of an arithmetical progression. II". Acta Arithmetica. 53 (5): 499–504. doi:10.4064/aa-53-5-499-504. ISSN 0065-1036. Retrieved 27 October 2024. Shorey, T.N.; Tijdeman, R. (1992). "On the greatest prime factor of an arithmetical progression III". In Philippon, Patrice (ed.). Approximations diophantiennes et nombres transcendants: comptes-rendus du colloque tenu au C.I.R.M de Luminy 18-22 juin 1990. Berlin ; New York: W. de Gruyter. ISBN 978-3-11-013486-5. Shorey, T.N.; Tijdeman, R. (1986). Exponential Diophantine Equations. Cambridge, England: Cambridge University Press. ISBN 978-0521268264. OCLC 13010635.

References

External links Tijdeman's web site at Leiden.

Worked examples

Example 1 — a first encounter with Robert Tijdeman

Start with the simplest possible case. Write down what Robert Tijdeman 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 Robert Tijdeman 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 Robert Tijdeman 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 Robert Tijdeman

In research: Robert Tijdeman 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 Robert Tijdeman 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: Robert Tijdeman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1943 births, 20th-century Dutch mathematicians, 21st-century Dutch mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Robert Tijdeman 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 Robert Tijdeman in 20 minutes

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

Frequently asked questions

What is Robert Tijdeman in simple terms?

Robert Tijdeman (born 30 July 1943 in Oostzaan, North Holland) is a Dutch mathematician. Specializing in number theory, he is best known for his Tijdeman's theorem.

Why does Robert Tijdeman 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 Robert Tijdeman?

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 Robert Tijdeman.