Unknown

Problem Books in Mathematics Edited by l? R. Halmos ...

Problem Books in Mathematics Series Editor: P.R. Halmos Polynomials by EJ. Barbeau Problems in Geometry by Marcel Berger, Pierre ...

E. J. Barbeau Polynomials With 36 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo ...

E.J. Barbeau Department of Mathematics University of Toronto Toronto, Ontario MS 1Al Canada Series Editor P.R. Halmos Department ...

Preface Particularly during the last thirty years, many criticisms have been directed at the school mathematics curriculum. In r ...

... Vlll Preface wish to broaden their mathematical experience and discover possible ma- terial for use with their regular or en ...

Preface ix profile of the students who did well is interesting. They were not always the final-year senior students, who were “b ...

X Preface (b) Explorations: While these are inserted near related material in the exercises, readers should not feel obliged to ...

Preface xi Toronto, for a grant to hire a student to check over the manuscript. Miss Azita Bassiji, a Toronto undergraduate, has ...

Acknowledgment of Problem S ources Virtually all of the problems in this book come from elsewhere. Some of them I have gotten fr ...

xiv Acknowledgment of Problem Sources Chapter 8: 1, 8, 11, 12, 15, 22, 28, 48 Problems from Olympiads and other competitions lis ...

Acknowledgment of Problem Sources xv and other competitions were taken from the journal Crux Mathematicorum. I am grateful to th ...

Contents Preface Acknowledgment of Problem Sources 1 Fundamentals vii ... Xl 1 1.1 The Anatomy of a Polynomial of a Single Varia ...

... XVlU E.8 Polynomials in each variable separately E.9 The range of a polynomial E.10 Diophantine equations 1.6 Basic Number T ...

Contents xix 71 75 78 E.24 Homogeneous polynomials E.25 Cauchy-Riemann conditions E.26 The Legendre equation 2.4 Graphing Polyno ...

xx Contents 4 Equations 4. 4. 4. 4. 4. 4. 4. 4. 4. Simultaneous Equations in Two or Three Unknowns 4.1.2 Two linear homogeneous ...

Contents xxi E.46 Continued fractions: another approach for quadratics 5.2 Tests for Real Zeros 5.2.7 Descartes’ Rule of Signs 5 ...

xxii 7. 7. 7. 7. E.56 Propagation of error E.57 Summing by differences E.58 The absolute value function Approximation on an Inte ...

1 Fundamentals 1.1 The Anatomy of a Polynomial of a Single Variable 3t3 - 7t2 + 4t + 1 and 8t6 - t5 + fit” + &it - 1 are pol ...

2 1. Fundamentals constant polynomial has degree 0, but, by convention, the zero polyno- mial (all coefficients vanishing) has d ...