This book the first of two volumes contains over 250 selected exercises in Algebra which have
featured as exam questions for the Arithmetic course taught by the authors at the University of
Pisa. Each exercise is presented together with one or more solutions carefully written with
consistent language and notation. A distinguishing feature of this book is the fact that each
exercise is unique and requires some creative thinking in order to be solved. The themes
covered in this volume are: mathematical induction combinatorics modular arithmetic Abelian
groups commutative rings polynomials field extensions finite fields. The book includes a
detailed section recalling relevant theory which can be used as a reference for study and
revision. A list of preliminary exercises introduces the main techniques to be applied in
solving the proposed exam questions. This volume is aimed at first year students in Mathematics
and Computer Science.
