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Zusatztext "? emphasizes the computational aspects of modern abstract algebra?author has integrated the software Mathematica into the discussions-especially in the group theory sections-but is careful not to make any logical reliance on this software. For one wishing to see the theory unfold through a highly computational approach! this text has much to recommend ?writing is logical but not excessively formal?I feel that this text was very courageously written?[the] focus is a bit more narrow that that of the typical first-year undergraduate course in abstract algebra. Yet! if one wishes to develop a deep and intuitive rapport with basic group and Galois theory! then this text has much to offer."--David B. Surowski! in Mathematical Reviews! Issue 2001i Informationen zum Autor John Scherk Klappentext Adequate texts that introduce the concepts of abstract algebra are plentiful. None, however, are more suited to those needing a mathematical background for careers in engineering, computer science, the physical sciences, industry, or finance than Algebra: A Computational Introduction. Along with a unique approach and presentation, the author demonstrates how software can be used as a problem-solving tool for algebra. The numerous exercises and examples along with downloads available from the Internet help establish a valuable working knowledge of Mathematica and provide a good reference for complex problems encountered in the field. Zusammenfassung Demonstrates how software can be used as a problem-solving tool for algebra. This work first introduces permutation groups, then linear groups, before finally tackling abstract groups. It motivates Galois theory by introducing Galois groups as symmetry groups. It includes computations, both as examples and as exercises. Inhaltsverzeichnis Congruences. Permutations. Permutation Groups. Linear Groups. Groups. Subgroups. Symmetry Groups. Group Actions. Counting Formulas. Cosets. Sylow Subgroups. Simple Groups. Abelian Groups. Polynomial Rings. Symmetric Polynomials. Roots of Equations. Galois Groups. Quartics. The General Equation of the nth Degree. Solution by Radicals. Ruler-and-Compass Constructions. Appendix: Mathematica Commands....
