A Concrete Introduction to Higher Algebra
This book is an introduction to higher algebra for students with a background of a year of calculus. The ?rst edition of this book emerged from a set of notes written in the 1970’s for a sophomore-juniorlevel undergraduatecourse at the University at Albany entitled “Classical Algebra”. The objective of the course, and the book, is to offer students a highly motivated introduction to the basic concepts of abstract algebra—rings and ?elds, groups, homomorphisms—by developing the algebraic theory of the familiar examples of integers and polynomials, and introducing the abstract concepts as needed to help illuminate the theory. By building the algebra out of numbers and polynomials, the booktakesmaximaladvantageof the student’spriorexperiencein algebraandari- metic from secondary school and calculus. The new concepts of abstract algebra arise in a familiar context. An ultimate goal of the presentation is to reach a substantial result in abstract algebra, namely, the classi?cation of ?nite ?elds. But while heading generally - wardsthat goal, motivationis maintainedbymanyapplicationsof the new concepts. The student can see throughout that the concepts of abstract algebra help illuminate more concrete mathematics, as well as lead to substantial theoretical results. Thus a student who asks, “Why am I learning this?” will ?nd answers usually within a chapter or two.
Informal and readable introduction to higher algebra New sections on Luhn's formula, Cosets and equations, and detaching coefficientsSuccessful undergraduate text for more than 20 years