Invitation to Algebra

This book presents a compendium style account of a comprehensive mathematical journey from Arithmetic to Algebra. It contains material that is helpful to graduate and advanced undergraduate students in mathematics, university and college professors teaching mathematics, as well as some mathematics teachers teaching in the final year of high school. A successful teacher must know more than what a particular course curriculum asks for. A number of topics that are missing in present-day textbooks, and which may be attractive to students at the graduate or advanced undergraduate level in mathematics, for example, continued fractions, arithmetic progressions of higher order, complex numbers in plane geometry, differential schemes, path semigroups and path algebras, have been carefully presented. This reflects the aim of the book to attract students to mathematics.Contents: IntroductionNatural NumbersIntegers, DivisibilityRational and Real NumbersComplex Numbers and Plane GeometryAlgebraic Structures — An OverviewPolynomialsGroupsRings and FieldsAppendix
Readership: Graduates, advanced undergraduates in mathematics and professors, teachers of mathematics.Algebra;Number Systems;Polynomials;Groups;Rings;Fields;Lattices;Mathematical Abstraction;Mathematical Education;Graphs;Cryptography;Elementary Geometry;Elementary Number Theory0Key Features:This book is unique among books on algebra as it stresses from an algebraic point of view the inter-connectedness of mathematicsIt is a resource for graduate and advanced undergraduate students in mathematics that encourages them to think about mathematicsIt contains a large number of innovative examples and exercises embedded in the textFour topics treated in this book that are not found in other books are: plane geometry of complex numbers; arithmetic of continued fractions; simple approach to polynomials in terms of graphs; differential schemes and arithmetic progressions of higher order