Todd Feil – författare

Originally published in the New Mathematical Library almost half a century ago, this charming book explains how to solve cryptograms based on elementary mathematical principles, starting with the Caesar cipher and building up to progressively more sophisticated substitution methods. Todd Feil has updated the book for the technological age by adding two new chapters covering RSA public-key cryptography, one-time pads, and pseudo-random-number generators.

Like its popular predecessors, this text develops ring theory first by drawing on students'' familiarity with integers and polynomials. This unique approach motivates students in studying abstract algebra and helps them understand the power of abstraction. This edition makes it easier to teach unique factorization as an optional topic and reorganizes the core material on rings, integral domains, and fields. Along with new exercises on Galois theory, it also includes a more detailed treatment of permutations as well as new chapters on Sylow theorems.

Like its popular predecessors, A First Course in Abstract Algebra: Rings, Groups, and Fields, Third Edition develops ring theory first by drawing on students’ familiarity with integers and polynomials. This unique approach motivates students in the study of abstract algebra and helps them understand the power of abstraction. The authors introduce groups later on using examples of symmetries of figures in the plane and space as well as permutations.New to the Third EditionMakes it easier to teach unique factorization as an optional topic Reorganizes the core material on rings, integral domains, and fieldsIncludes a more detailed treatment of permutationsIntroduces more topics in group theory, including new chapters on Sylow theoremsProvides many new exercises on Galois theoryThe text includes straightforward exercises within each chapter for students to quickly verify facts, warm-up exercises following the chapter that test fundamental comprehension, and regular exercises concluding the chapter that consist of computational and supply-the-proof problems. Historical remarks discuss the history of algebra to underscore certain pedagogical points. Each section also provides a synopsis that presents important definitions and theorems, allowing students to verify the major topics from the section.