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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Mathematical induction,other 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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Graphs,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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Counting, 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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Logic and proofs, 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

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Elementary number theory, 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