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rusczyk r art problem solving introd algebra 2007

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Textbook in PDF format Learn the basics of algebra from former USA Mathematical Olympiad winner and Art of Problem Solving founder Richard Rusczyk. Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more! How to Use This Book Acknowledgements Follow the Rules Numbers Order of Operations When Does Order Matter? Distribution and Factoring Equations Summary X Marks the Spot Expressions Arithmetic with Expressions Distribution, Subtraction, and Factoring Fractions Summary One-Variable Linear Equations Solving Linear Equations I Solving Linear Equations II Word Problems Linear Equations in Disguise Summary More Variables Evaluating Multi-Variable Expressions Still More Arithmetic Distribution and Factoring Fractions Equations Summary Multi-Variable Linear Equations Introduction to Two-Variable Linear Equations Substitution Elimination Word Problems More Linear Equations in Disguise More Variables Summary Ratios and Percents Basic Ratio Problems More Challenging Ratio Problems Conversion Factors Percent Percentage Problems Summary Proportion Direct Proportion Inverse Proportion Joint Proportion Rate Problems Summary Graphing Lines The Number Line and the Cartesian Plane Introduction to Graphing Linear Equations Using Slope in Problems Find the Equation Slope and Intercepts Comparing Lines Summary Introduction to Inequalities The Basics Which Is Greater? Linear Inequalities Graphing Inequalities Optimization Summary Quadratic Equations - Part 1 Getting Started With Quadratics Factoring Quadratics I Factoring Quadratics II Sums and Products of Roots of a Quadratic Extensions and Applications Summary Special Factorizations Squares of Binomials Difference of Squares Sum and Difference of Cubes Rationalizing Denominators Simon's Favorite Factoring Trick Summary Complex Numbers Numbers, Numbers, and More Numbers! Imaginary Numbers Complex Numbers Summary Quadratic Equations - Part 2 Squares of Binomials Revisited Completing the Square The Quadratic Formula Applications and Extensions Summary Graphing Quadratics Parabolas Circles Summary More Inequalities Quadratic Inequalitie Beyond Quadratics The Trivial Inequality Quadratic Optimization Summary Functions The Machine Combining Functions Composition Inverse Functions Problem Solving with Functions Operations Summary Graphing Functions Basics Transformations Inverse Functions Revisited Summary Polynomials Addition and Subtraction Multiplication Summary Exponents and Logarithms Exponential Functions Show Me the Money Interesting Problems What is a Logarithm? Summary Special Functions Radicals Absolute Value Floor and Ceiling Rational Functions Piecewise Defined Functions Summary Sequences & Series Arithmetic Sequences Arithmetic Series Geometric Sequences Geometric Series Telescoping Summary Special Manipulations Raising Equations to Powers Self-similarity Symmetry Summary Hints to Selected Problems Index

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Rusczyk R. The Art of Problem Solving. Introd. to Algebra 2007.pdf 104.6 MB

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rusczyk r art problem solving introd algebra 2007

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