Description:
This monograph includes the following topics: a basic introduction to the language, basic arithmetic, permutations, matrices, polynomial rings, finite fields, finite and finitely presented groups, small groups, group representations and character theory, and simple groups. Advanced topics include testing several open conjectures and theorems. In addition, each chapter ends with an extensive list of problems. We hope the reader will find some problems challenging and exciting as they are based on outstanding research papers. Selected solutions can be found at the end of the book.