A Concrete Introduction to Higher Algebra 
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Posted: 08122008 at 18:39 
Lindsay N. Childs "A Concrete Introduction to Higher Algebra" Springer  20081114  ISBN: 0387745270  604 pages  PDF  3,8 MB This book is an informal and readable introduction to higher algebra at the postcalculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. The new examples and theory are built in a wellmotivated fashion and made relevant by many applicationsto cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix. Download


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