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Full Description
The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990s. As early as the 1960s, I.M. Gelfand and his colleagues in the USSR thought hard about this same question and developed a style for presenting basic mathematics in a clear and simple form that engaged the curiosity and intellectual interest of thousands of school and college students. These same ideas, this development, are available in the present books to any student who is willing to read, to be stimulated, and to learn. Algebra is an elementary algebra text from one of the leading mathematicians of the world - a major contribution to the teaching of the very first high school level course in a centuries old topic - refreshed by the author's inimitable pedagogical style and deep understanding of mathematics and how it is taught and learned.
Contents
1. Introduction. 2. Exchange of Terms in Addition. 3. Exchange of Terms in Multiplication. 4. Addition in the Positional Number System. 5. The Multiplication Table and the Multiplication Method. 6. The Division Algorithm. 7. The Binary System. 8. The Commutative Law. 9. The Associative Law. 10. The Use of Parentheses. 11. The Distributive Law. 12. Letters in Algebra. 13. The Addition of Negative Numbers. 14. The Multiplication of Negative Numbers. 15. Dealing with Fractions. 16. Powers. 17. Big Numbers Around Us. 18. Negative Powers. 19. Small Numbers Around Us. 20. How to Multiply am by an or Why Our Definition is Convenient. 21. The Rule of Multiplication for Powers. 22. Formula for Short Multiplication: The Square of a Sum. 23. How to Explain the Square of the Sum Formula to Your Younger Brother or Sister. 24. The Difference of Squares. 25. The Cube of the Sum Formula. 26. The Formula for (a + b)4. 27. Formula for (a + b)-5, (a + b)6... and the Pascal Triangle. 28. Polynomials. 29. A Digression: When Are Polynomials Equal?. 30. How Many Monomials Do We Get?. 31. Coefficients and Values. 32. Factoring. 33. Rational Expressions. 34. Converting Rational Expression into the Quotient of Two Polynomials. 35. Polynomial and Rational Fractions in One Variable. 36. Division of Polynomials in One Variable; the Remainder. 37. The Remainder When Dividing by x - a. 38. Values of Polynomials and Interpolation. 39. Arithmetic Progressions. 40. The Sum of an Arithmetic Progression. 41. Geometric Progressions. 42. The Sum of a Geometric Progression. 43. Different Problems about Progressions. 44. The Well Tempered Clavier. 45. The Sum of an Infinite Geometric Progression. 46. Equations. 47. A Short Dictionary. 48. Quadratic Equations. 49. The Case p = 0. Square Roots. 50. Rules for Square Roots. 51. The Equation x2 + px + q = 0. 52. Vieta's Theorem. 53. Factoring ax2 + bx + c. 54. A Formula for ax2+ bx + c = 0 (where a = 0). 55. One More Formula Concerning Quadratic Equations. 56. A Quadratic Equation Becomes Linear. 57. The Graph of the Quadratic Polynomial. 58. Quadratic Inequalities. 59. Maximum and Minimum Values of a Quadratic Polynomial. 60. Biquadratic Equations. 61. Symmetric Equations. 62. How to Confuse the Student on the Exam. 63. Roots. 64. Non-integer Powers. 65. Proving Inequalities. 66. Arithmetic and Geometric Means. 67. The Geometric Mean Does Not Exceed the Arithmetic Mean. 68. Problems About Maximum and Minimum. 69. Geometric Illustrations. 70. The Arithmetic and Geometric Mean of Several Numbers. 71. The Quadratic Mean. 72. The Harmonic Mean.
