Titlebook: Exploring Mathematics; Problem-Solving and Daniel Grieser Textbook 2018 Springer Nature Switzerland AG 2018 MSC (2010): 00-01, 00A07, 00A0

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https://doi.org/10.1057/9781137374769 first one. You can open this figure again and find a yet smaller one, and so on. Some mathematical problems can be tackled in a similar way: solve the problem by reducing it to a smaller problem of the same kind. This technique is called recursion.

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History Taking in Clinical Practiceother instance of the idea of recursion: reduce the problem to a smaller problem of the same kind. Mathematical induction implements this idea for proofs, while recurrence relations are used in problems where you want to determine some quantity.

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https://doi.org/10.1057/9781137372406 can find counting problems in everyday life and in calculating probabilities (how likely is it to have two pairs in a poker hand?). You have already seen some counting problems in previous chapters and learned about the recursion technique. In this chapter we will take a systematic look at counting problems.

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https://doi.org/10.1057/9780230353954 Therefore, if you want to argue reliably then you should know well both the basic logical structures and the phrases we use to express them. In the course of a mathematical investigation you make observations, discover patterns, have insights, make conjectures. In order to be sure that a conjecture is true you need a proof.

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https://doi.org/10.1007/978-94-007-5009-8 with since you were a small child. Therefore number theory is very suitable for your exploration of mathematics, and you will find number-theoretic problems in many places in this book. Number theory has many faces: some of the hardest problems of mathematics, still unsolved today, are stated in simple number-theoretic terms.

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,Recursion – a fundamental idea, first one. You can open this figure again and find a yet smaller one, and so on. Some mathematical problems can be tackled in a similar way: solve the problem by reducing it to a smaller problem of the same kind. This technique is called recursion.

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