Blending the theoretical with the practical in the instruction of modern algebra, iModern Algebra with Applications, Second Edition/i provides interesting and important applications of this subject—effectively holding your interest and creating a more seamless method of instruction. Filled with in-depth insights and over six hundred exercises of varying difficulty, this invaluable text can help anyone appreciate and understand this subject.Preface to the First Edition.pPreface to the Second Edition.pList of Symbols.p1. Introduction.p2. Boolean Algebras.p3. Groups.p4. Quotient Groups.p5. Symmetry Groups in Three Dimensions.p6. Pólya–Burnside Method of Enumeration.p7. Monoids and Machines.p8. Rings and Fields.p9. Polynomial and Euclidean Rings.p10.Quotient Rings.p11. Field Extensions.p12. Latin Squares.p13. Geometrical Constructions.p14. Error-Correcting Codes.pAppendix 1: Proofs.pAppendix 2: Integers.pBibliography and References.pAnswers to the Odd-Numbered Exercises.pIndex.“…an ideal starter into algebra for all kinds of students, and a very useful addition to existing textbooks…” (iZentralblatt Math/i, Vol.1050, 2005)bWILLIAM J. GILBERT, DPHil/b, is a professor in the Department of Pure Mathematics at the University of Waterloo, Ontario, Canada. He received his DPhil in mathematics from Oxford University in 1968.pbW. KEITH NICHOLSON, PHD/b, is a professor in the Department of Mathematics and Statistics at the University of Calgary, Alberta, Canada. He received his PhD in pure mathematics from the University of California at Santa Barbara in 1970.Praise for the first editionP”This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addit@Mýp£× ¾Û€