دانلود کتاب Portal through Mathematics: Journey to Advanced Thinking (Anneli Lax New Mathematical Library)

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Cover Title Page Contents Foreword Preface for an American Readership Author's Preface Part I 1. Surprising right triangles 2. Surprisingly short solutions of geometric problems 3. A natural assertion with a surprising proof 4. Surprising answers 5. A surprising connection between three sequences Part II Algebra, Calculus, and Geometry: problems 6. Five problems and a function 7. Five solutions of a routine problem 8. Equations of the form f (x, y) = g(x, y) and their generalizations 9. The generalized version of Viete’s formula 10. Multiple roots of polynomials 11. Non-routine applications of the derivative 12. Complex numbers, polynomials, and trigonometry 13. Complex numbers and geometry 14. Areas of triangles and quadrilaterals 15. Constructions in solid geometry 16. Inequalities 17. Diophantine equations 18. Combinatorial tales 19. Integrals Part III. Algebra, Calculus, and Geometry: theory (a little way beyond high school mathematics) 20. Functional equations of elementary functions 21. Sequences given by recurrence relations 22. The “golden ratio” or solving equations of the form f(x) = x 23. Convex functions: inequalities and approximations 24. Taylor’s formula, Euler’s formula, and a combinatorial problem 25. Derivatives of vector-functions 26. Polynomials and trigonometric relations 27. Areas and volumes as functions of co-ordinates 28. Values of trigonometric functions and sequences satisfying a certain recurrence relation 29. Do there exist further “numbers” beyond complex numbers? Solutions of the supplementary problems Index Back Cover