THIS IS A TEXTBOOK FOR STUDENTS UNDERTAKING, OR ABOUT TO UNDERTAKE, A first course in Abstract Algebra (e. g. second-year Honours students and second-or third-year Ordinary Degree students in Scottish universities; first year students in many English universities). The first edition of the book proved helpful to many such students, and it is hoped that this second edition may be found even more helpful. The main changes made in producing the se co nd edition have been the inclusion of a whole new chapter on the symmetrie group and the expansion of the existing sets of exercises, together with updating and revising of the text. The book is not an advanced treatise on group theory or on any kindred part of mathematics. But, in contrast to many elementary textbooks, it does penetrate far enough into Abstract Algebra to let the student see that the subject has worthwhile insights to offer, and to introduce hirn to some of the distinctive ways of thinking that produce interesting results. For example, in group theory, the material covered includes cyclic groups, Lagrange's theorem, homomorphisms, normal subgroups, quotient groups, and (in the new chapter) the partition of the symmetrie group of degree n into conjugacy classes and an intro duc ti on to the alternating group of degree n. Although there is only one chapter on rings (and fields), it is a lengthy chapter and covers a wide variety of ideas.

Introduction to Abstract Algebra

Science & Math

Thomas A. Whitelaw

Mathematics

Springer

The new edition of this textbook will provide students of varied backgrounds with a comprehensive and accessible introduction to the primary subject matter of linear algebra. The contents include detailed accounts of matrices and determinants (chapters 2 to 4), finite-dimensional vector spaces (chapter 5), linear mappings (chapters 6 and 7), and (spread through chapters 2, 3, 5 and 6) the applications of these ideas to systems of linear equations, while later chapters (8 to 10) discuss eigenvalues, diagonalization of matrices, euclidean spaces, and quadratic forms. In writing the book, my constant aim has been to draw on my considerable experience of teaching this material to produce an account of it that students striving to gain an understanding of linear algebra will find helpful. In particular, therefore, I have provided suitably detailed explanations of points which students often find difficult. The reader will see that little is taken for granted. For example, the accounts of matrices and vector spaces are self-contained and start right at the begin ning. However, a basic knowledge of elementary ideas and notations con cerning sets is assumed, and from chapter 5 onwards the reader must be able to understand simple arguments about sets (such as proving that one set is a subset of another). Then, from chapter 6 onwards, a knowledge of mappings becomes essential, though to help the reader an appendix on mappings pro vides a condensed summary of everything relevant.

An Introduction to Linear Algebra

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Books by Thomas A. Whitelaw

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Introduction to Abstract Algebra

An Introduction to Linear Algebra