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The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990's. As early as the 1960's, 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 high school and college students. These same ideas, this development, are available in the following 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.
Author Bio
Gelfand, I.M. : Rutgers the State University of New Jersey Central Office
Shen, A. : Institute of Problems of Information Transportation, Moscow
1. Introduction
2. Exchange of terms in addition
3. Exchange of terms in multiplication
4. Addition in the decimal number system
5. The multiplication table and the multiplication algorithm
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 a m by a n , 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. Formulas for (a +b ) 5 , (a +b ) 6 ,... and Pascal's 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 a rational expression into the quotient of two polynomials
35. Polynomials 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 glossary
48. Quadratic equations
49. The case p = 0. Square roots
50. Rules for square roots
51. The equation x 2 +px + q =0
52. Vieta's theorem
53. Factoring ax 2 +bx +c
54. A formula for ax 2 +bx +c =0(where a does not equal 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 students on an 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 means of several numbers
71. The quadratic mean
72. The harmonic mean
I.M. Gelfand and A. Shen
ISBN13: 978-0817636777The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990's. As early as the 1960's, 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 high school and college students. These same ideas, this development, are available in the following 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.
Author Bio
Gelfand, I.M. : Rutgers the State University of New Jersey Central Office
Shen, A. : Institute of Problems of Information Transportation, Moscow
Table of Contents
1. Introduction
2. Exchange of terms in addition
3. Exchange of terms in multiplication
4. Addition in the decimal number system
5. The multiplication table and the multiplication algorithm
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 a m by a n , 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. Formulas for (a +b ) 5 , (a +b ) 6 ,... and Pascal's 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 a rational expression into the quotient of two polynomials
35. Polynomials 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 glossary
48. Quadratic equations
49. The case p = 0. Square roots
50. Rules for square roots
51. The equation x 2 +px + q =0
52. Vieta's theorem
53. Factoring ax 2 +bx +c
54. A formula for ax 2 +bx +c =0(where a does not equal 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 students on an 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 means of several numbers
71. The quadratic mean
72. The harmonic mean