The main goal of this text is to introduce the reader to the field of auto-validating algorithms by providing a theoretical foundation supplemented with illuminating examples. The target audience is undergraduate or graduate students new to the field. Some knowledge of programming is useful, but not strictly necessary. The restriction to the one-dimensional setting is a conscious one. It allows us to focus exclusively on simple, but yet interesting problems, without too much mathematical framework. The computer exercises are intended to "force" the reader into actually discovering how simple it is to implement the methods, and to solve numerical problems with rigour.