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Algebra

Auteur : I M Gelʹfand; A Shen
Éditeur: Boston : Birkhäuser, ©1993.
Édition/format:   Livre imprimé : AnglaisVoir toutes les éditions et tous les formats
Résumé:

The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. Adding three apples to five apples is  Lire la suite...

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Type d’ouvrage: Ressource Internet
Type de document: Livre, Ressource Internet
Tous les auteurs / collaborateurs: I M Gelʹfand; A Shen
ISBN: 0817637370 9780817637378 0817636773 9780817636777 3764337370 9783764337377 3764336773 9783764336776
Numéro OCLC: 28547046
Description: 153 pages : illustrations ; 24 cm
Contenu: Exchange of terms inaddition --
Exchange of terms in multiplication --
Addition in the decimal number system --
Multiplication table and the multiplication algorithm --
Division algorithm --
Binary system --
Commutative law --
Use of parentheses --
Distributive law --
Letters in algebra --
Addition of negative numbers --
Dealing with fractions --
Powers --
Big numbers around us --
Negative powers --
Small numbers around us --
How to multiply a(to the mth power) by a(to the nth power), or why our definition is convenient --
Formula for short multiplication: the square of a sum --
How to explain the square of the sum formula to your younger brother or sister --
Difference of squares --
Cube of the sum formula --
Formal for (a+b) to the fourth power --
Formulas for (a+b) to the fifth power, (a+b) to the sixth power,...pascal's traingle --
Polynomials --
Digression: when are polynomials equal? --
How many monomials do we get? --
Coefficients and values --
Factoring --
Rational expressions --
Converting a rational expression into the quotient of two polynomials --
Polynomial and rational fractions in one variable --
Division of polynomials in one variable; the remainder --
Remainder when dividing by x-a --
Values of polynomials, and interpolation --
Arithmetic progressions --
Sum of an arithmetic progression --
Geometric progressions --
Sum of a geometric progression --
Different problems about progressions --
Well-tempered clavier --
Sum of an infinite geometric progression --
Equations --
Short glossary --
Quadratic equations --
Case p=0. square roots --
Rules for square roots --
Equation x(to the second power) +px+q=0 --
Vieta's theorem --
Factoring ax(to the second power)+bx+c --
Formula for ax(to the second power)+bx+c=) (where a does not equal 0) --
One mroe formula concerning quadratic equations --
Quadratic equation becomes linear --
Graph of the quadratic polynomial --
Quadratic inequalities --
Maximum and minimum values of a quadratic polynomials --
Biquadratic equations --
Symmetric equations --
How to confuse students on an exam --
Roots --
Non-integer powers --
Proving inequalities --
Arithmetic and geometric means --
Geometric mean does not exceed the arithmetic mean --
Problems about maximum and minimum --
Geometric illustrations --
Arithmetic and geometric means of several numbers --
Quadratic mean --
Harmonic mean
Responsabilité: I.M. Gelʹfand, A. Shen.
Plus d’informations:

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Synopsis de l’éditeur

"The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy Lire la suite...

 
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