INTERMEDIATE ALGEBRA

By C. LIMAU

RELATIONS AND FUNCTIONS SETS OF REAL NUMBERS AND THE CARTESIAN COORDINATE PLANE SETS OF NUMBERS THE CARTESIAN COORDINATE PLANE DISTANCE IN THE PLANE EXERCISES ANSWERS RELATIONS GRAPHS OF EQUATIONS INTRODUCTION TO FUNCTIONS FUNCTION NOTATION MODELING WITH FUNCTIONS FUNCTION ARITHMETIC GRAPHS OF FUNCTIONS GENERAL FUNCTION BEHAVIOR TRANSFORMATIONS LINEAR AND QUADRATIC FUNCTIONS LINEAR FUNCTIONS ABSOLUTE VALUE FUNCTIONS QUADRATIC FUNCTIONS INEQUALITIES WITH ABSOLUTE VALUE AND QUADRATIC FUNCTIONS REGRESSION POLYNOMIAL FUNCTIONS GRAPHS OF POLYNOMIALS THE FACTOR THEOREM AND THE REMAINDER THEOREM REAL ZEROS OF POLYNOMIALS FOR THOSE WISHING TO USE A GRAPHING CALCULATOR FOR THOSE WISHING NOT TO USE A GRAPHING CALCULATOR COMPLEX ZEROS AND THE FUNDAMENTAL THEOREM OF ALGEBRA RATIONAL FUNCTIONS INTRODUCTION TO RATIONAL FUNCTIONS GRAPHS OF RATIONAL FUNCTIONS RATIONAL INEQUALITIES AND APPLICATIONS VARIATION FURTHER TOPICS IN FUNCTIONS FUNCTION COMPOSITION INVERSE FUNCTIONS OTHER ALGEBRAIC FUNCTIONS EXPONENTIAL AND LOGARITHMIC FUNCTIONS INTRODUCTION TO EXPONENTIAL AND LOGARITHMIC FUNCTIONS PROPERTIES OF LOGARITHMS EXPONENTIAL EQUATIONS AND INEQUALITIES LOGARITHMIC EQUATIONS AND INEQUALITIES APPLICATIONS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS APPLICATIONS OF EXPONENTIAL FUNCTIONS APPLICATIONS OF LOGARITHMS HOOKED ON CONICS INTRODUCTION TO CONICS CIRCLES PARABOLAS ELLIPSES HYPERBOLAS SYSTEMS OF EQUATIONS AND MATRICES SYSTEMS OF LINEAR EQUATIONS: GAUSSIAN ELIMINATION SYSTEMS OF LINEAR EQUATIONS: AUGMENTED MATRICES MATRIX ARITHMETIC SYSTEMS OF LINEAR EQUATIONS: MATRIX INVERSES DETERMINANTS AND CRAMER’S RULE DE?NITION AND PROPERTIES OF THE DETERMINANT CRAMER’S RULE AND MATRIX ADJOINTS PARTIAL FRACTION DECOMPOSITION SYSTEMS OF NON-LINEAR EQUATIONS AND INEQUALITIES SEQUENCES AND THE BINOMIAL THEOREM SEQUENCES SUMMATION NOTATION MATHEMATICAL INDUCTION SELECTED ANSWERS THE BINOMIAL THEOREM CHAPTER IN GENERAL, THERE ARE THREE WAYS TO DESCRIBE SETS THEY ARE WAYS TO DESCRIBE SETS 1 THE VERBAL METHOD: USE A SENTENCE TO DE?NE A SET 2 THE ROSTER METHOD: BEGIN WITH A LEFT BRACE ‘{’, LIST EACH ELEMENT OF THE SET ONLY ONCE AND THEN END WITH A RIGHT BRACE ‘}’ 3 THE SET-BUILDER METHOD: A COMBINATION OF THE VERBAL AND ROSTER METHODS USING A “DUMMY VARIABLE” SUCH AS X FOR EXAMPLE, LET S BE THE SET DESCRIBED VERBALLY AS THE SET OF LETTERS THAT MAKE UP THE WORD “SMOLKO” A ROSTER DESCRIPTION OF S WOULD BE {S, M, O, L, K} NOTE THAT WE LISTED ‘O’ ONLY ONCE, EVEN THOUGH IT 1 TO BE READ AS ‘GOOD, SOLID FEEDBACK FROM COLLEAGUES’ 2FOR A MORE THOUGHT-PROVOKING EXAMPLE, CONSIDER THE COLLECTION OF ALL THINGS THAT DO NOT CONTAIN THEMSELVES - THIS LEADS TO THE FAMOUS RUSSELL’S PARADOX