A paradox is the mathematician's best joke. Like a good joke, the paradox develops easily, in a logical and seemingly plausible manner, until it reaches the punch line, which is an unbelievable, completely surprising error, which gleefully mocks simple logic. Some paradoxes are easily explained because they rely on the incorrect use of a well-known basic rule. Some believe that such mistakes should not be called paradoxes at all, but only erroneous arguments. This book is a collection of paradoxes, fallacies and thinking challenges which are suitable for integration into mathematics studies in high school. Each of the activities in this book will encourage students to see familiar mathematical concepts in a new light and deepen their understanding of these concepts.

This book introduces the basic and fundamental sentences of probability (with full mathematic demonstration) on one hand and gives intuitive ideas that are the background of the probability theory development on the other. Probability is the basis for statistics, but also aids in nature sciences and social sciences as well as philosophy. The Prerequisites for this course are calculus, linear algebra, and set theory.

In Mathematical Logic we study the language of mathematics and its connection to mathematical objects. The language we discuss in this book is formal mathematical language, which contains Latin letters, punctuations and symbols. However, we will also present examples from standard daily language.

This book is based on lectures given by Prof. Nati Liniel at the Hebrew University in the course Discrete Mathematics.