1. Prehistory.- 2 Quadratic Number Fields.- 3 The Modularity Theorem.- 4 Divisibility in Integral Domains.- 5 Arithmetic in some Quadratic Number Fields.- 6 Ideals in Quadratic Number Fields.- 7 The Pell Equation.- 8 Catalan''s Equation.- 9 Ambiguous Ideal Classes and Quadratic Reciprocity.- 10 Quadratic Gauss Sums.- A Computing with Pari and Sage.- B Solutions.- Bibliography.- Name Index.- Subject Index.
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<P>Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important...
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This textbook offers theoretical, algorithmic and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems. It provides an overview of recent advances in control and systems theory, numerical line algebra,...
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