Shape of Algebra in the Mirrors of Mathematics, The: A Visual, Computer-Aided Exploration of Elementary Algebra and Beyond
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ISBN-13:
9789814313599
Veröffentl:
2011
Erscheinungsdatum:
30.10.2011
Seiten:
632
Autor:
Gabriel Katz
Gewicht:
1045 g
Format:
241x164x41 mm
Sprache:
Englisch
Beschreibung:
The Shape of Algebra is the authors' attempt to share their mathematical experiences with readers who have more than a passing interest in mathematics, but have only a traditional exposure to elementary algebra. Secondary school and college teachers and students who want to expand their horizons in the field will find a fresh presentation of familiar concepts and some unexpected results.
Introduction - Maps upon Maps; Maps, Models, and the Coordinate Plane; The Universe of Quadratic Polynomials; The Complex Numbers; The Geometry of Complex Linear Polynomial Maps; Complex Polynomial Maps, Closed Plane Curves and their Invariants; Experimenting with the Geometry of Complex Polynomial Maps of Degrees Two and Three; The Old Art of Solving Cubic Equations and the New Science; Complex Polynomial Maps of Higher Degrees and the Fundamental Theorem of Algebra; Local and Global Geometry of Complex Polynomial Maps; The Fundamental Theorem and the Complex Viete Map; Appendices: Estimating Polynomial Expressions; More about the Taylor Formula for Polynomials; The Geometry of Discriminants; Line Integrals and an Analytical Proof of the Loop Theorem; Deformations of Complex Polynomials and the Braids.
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