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

Silent-Ischemia

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 problems.

倒轉(zhuǎn)

General problem solving strategies: Similar problems, working forward and backward, interim goals,ll 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 myself.

gnarled

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 is true you need a proof.

冷淡周邊

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 simple number-theoretic terms.

碳水化合物

尖牙

exhilaration

嚴峻考驗

First explorations,We begin our journey into mathematics by investigating three problems. The first one is a simple warm-up exercise, but the other two require some serious searching before we find a solution. During this search we will observe ourselves: How do we proceed intuitively when solving a problem?

dialect

Systemic

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.