This quantity celebrates the Pc Algebra system Magma. With a design based mostly on the ontology and semantics of algebra, Magma allows customers to quickly formulate and carry out calculations in the extra summary elements of arithmetic. This book introduces the reader to the position Magma performs in superior mathematical analysis by means of 14 case research which, in most instances, describe computations underpinning new theoretical outcomes. The authors have been chosen each for his or her experience in the actual area and for his or her revolutionary use of Magma. Though under no circumstances exhaustive, the subjects vary from quantity concept and algebraic geometry, by way of illustration concept and group principle to some branches of discrete arithmetic and graph principle. A primary introduction to the Magma language is given in an appendix. The book is concurrently an invite to study a brand new programming language in the context of up to date analysis issues, and an exposition of the forms of drawback that may be investigated utilizing computational algebra.