《A COLLEGE ALGEBRA》

PART FIRST—NUMBERS1

Ⅰ.THE NATURAL NUMBERS—COUNTING，ADDITION，AND MUL-TIPLICATION1

Ⅱ.SUBTRACTION AND THE NEGATIVE16

Ⅲ.DIVISION AND FRACTIONS27

Ⅳ.IRRATIONAL NUMBERS39

Ⅴ.IMAGINARY AND COMPLEX NUMBERS70

PART SECOND—ALGEBRA79

Ⅰ.PRELIMINARY CONSIDERATIONS79

Ⅱ.THE FUNDAMENTAL OPERATIONS93

Ⅲ.SIMPLE EQUATIONS IN ONE UNKNOWN LETTER110

Ⅳ.SYSTEMS OF SIMULTANEOUS SIMPLE EQUATIONS127

Ⅴ.THE DIVISION TRANSFORMATION155

Ⅵ.FACTORS OF RATIONAL INTEGRAL EXPRESSIONS176

Ⅶ.HIGHEST COMMON FACTOR AND LOWEST COMMON MULTIPLE196

Ⅷ.RATIONAL FRACTIONS213

Ⅸ.SYMMETRIC FUNCTIONS245

Ⅹ.THE BINOMIAL THEOREM252

Ⅺ.EVOLUTION260

Ⅻ.IRRATIONAL FUNCTIONS.RADICALS AND FRACTIONAL EXPONENTS271

ⅩⅢ.QUADRATIC EQUATIONS298

ⅩⅣ.DISCUSSION OF THE QUADRATIC EQUATION.MAXIMA AND MINIMA304

ⅩⅤ.EQUATIONS OF HIGHER DEGREE WHICH CAN BE SOLVED BY MEANS OF QUADRATICS309

ⅩⅥ.SIMULTANEOUS EQUATIONS WHICH CAN BE SOLVED BY MEANS OF QUADRATICS317

ⅩⅦ.INEQUALITIES340

ⅩⅧ.INDETERMINATE EQUATIONS OF THE FIRST DEGREE342

ⅩⅨ.RATIO AND PROPORTION.VARIATION347

ⅩⅩ.ARITHMETICAL PROGRESSION354

ⅩⅪ.GEOMETRICAL PROGRESSION357

ⅩⅫ.HARMONICAL PROGRESSION362

ⅩⅩⅢ.METHOD OF DIFFERENCES.ARITHMETICAL PROGRES-SIONS OF HIGHER ORDERS.INTERPOLATION364

ⅩⅩⅣ.LOGARITHMS374

ⅩⅩⅤ.PERMUTATIONS AND COMBINATIONS393

ⅩⅩⅥ.THE MULTINOMIAL THEOREM408

ⅩⅩⅦ.PROBABILITY409

ⅩⅩⅧ.MATHEMATICAL INDUCTION424

ⅩⅩⅨ.THEORY OF EQUATIONS425

ⅩⅩⅩ.CUBIC AND BIQUADRATIC EQUATIONS483

ⅩⅩⅪ.DETERMINANTS AND ELIMINATION492

ⅩⅩⅫ.CONVERGENCE OF INFINITE SERIES520

ⅩⅩⅩⅢ.OPERATIONS WITH INFINITE SERIES539

ⅩⅩⅩⅣ.THE BINOMIAL，EXPONENTIAL，AND LOGARITHMIC SERIES553

ⅩⅩⅩⅤ.RECURRING SERIES560

ⅩⅩⅩⅥ.INFINITE PRODUCTS564

ⅩⅩⅩⅦ.CONTINUED FRACTIONS566

ⅩⅩⅩⅧ.PROPERTIES OF CONTINUOUS FUNCTIONS577

INDEX591