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Beskrivelse
The theory of polynomial equations is more than the Factor, the Remainder and the Rational Roots theorems. The interplay of complex numbers with the minimal polynomial for nth roots of unity adds zest to an otherwise pedestrian treatment. The use of a little linear algebra facilitates the tedious work that often accompanies symmetric functions. You will experience unexpected connections between the average of the roots of p(x) = 0, the average of the roots of its derivative, the foci of an ellipse, reciprocal polynomials and a famous Euler result!
Many of the topics were inspired by Conkwright (1941), Uspensky (1948) and Hillman and Alexanderson (1966). Notes and preliminary versions have been successfully used in MA courses for secondary teachers at the University of Northern Colorado for over a decade now.
Who could benefit from this book?Preservice teachersIn-service secondary teachersWell prepared HS seniorsStudents preparing for mathematical competitionsAmateur mathematiciansPrimary FeaturesEasy and pleasant to readPlenty of accessible and challenging problems (try to factor x5 + x + 1)Sicherman diceReciprocal polynomialsDiscriminant of xn - 1 = 0Four sample classroom exams with solutions
