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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Hermeneutic Modes, Ancient and Modern,mathematics. They bear no relation to formulas or equations, nor to geometry. But thinking about them leads to a lot of interesting mathematics, and you will discover some of that mathematics in this chapter. You will use mathematical induction in a new context and learn some new techniques for prob

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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

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A. F. V. van Engelen,J. Buisman,F. Ijnsenll help me to recall how I solved a similar problem. If I want to reach a goal then I can think about which steps I should do first in order to get there (working forward); or I can think about what could be the last step, reaching the goal (working backward), and what interim goals I could set for

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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 si

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The Second Phase of ,: the Year 1987,tremes etc.) show how deeply ingrained the idea of the extreme is in us. Moreover, the scientific view of the world reveals extremes everywhere: the soap bubble tries to minimise its surface area and is therefore spherical, chemical reactions strive towards a state of minimal energy, and so on. Look

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