| المراجعة التحريرية | Algebraic curves have regained a prominent position in mathematics. In light of their importance, the goal of this book is to provide a reasonable understanding of algebraic curves and their use. Beginning with standard curves (polynomial, parametric, conic, and user defined), kendig expands the study by first shrinking the plane to a disk by adjoining points at infinity, and then shifting the domain from real to complex numbers to establish bezout's theorem. Given this context, the study shifts further to determining the topological properties of algebraic curves, relating genus to a polynomial's degree, investigating singularities, and using compact riemann surfaces. Throughout, the author emphasizes the geometry and intuitive aspects of algebraic curves, without delving into a tedious chain of proofs. He briefly considers applications of algebraic curves, ranging from andrew wiles's special use of elliptic curves in his proof of fermat's last theorem to their use in cryptography, dynamical systems, and robotics. Readers should be familiar with basic ideas from geometric topology, complex analysis, and abstract algebra. Since kendig developed the content as a guide rather than a textbook, no problem sets are included, but the author does suggest appropriate textbooks in a bibliography."" - j. Johnson, choice magazine |
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