《美國中學數學（套裝共4冊）》是2011年4月出版的圖書，作者是雷伊。
基本介紹
- 書名：美國中學數學（套裝共4冊）
- 作者：雷伊
- ISBN：9787542635266
- 頁數：1419頁
- 定價：116.00元
- 出版時間：2011-4
- 副標題：美國中學數學
內容簡介,目錄,作者簡介,
內容簡介
《美國中學數學(套裝共4冊)(代數+幾何)》內容簡介：We are honored and happy to bring this set of math textbooks by Joseph Ray. These popular books sold more than any other arithmetic in America, in fact over 120 million copies and are still used in modern American schools and families. As you can see, this set of textbooks is organized in an orderly manner around the discipline of arithmetic itself.
Ray emphasized critical thinking in his classroom. He believed that his students needed to learn how to apply what they learned to real-life situations. Rather than giving his pupils simple problems to solve, he preferred word problems. Students can increase their reading comprehension skills, and learn to think.
The science of Algebra, properly taught, stands among the first of those studies essential to both the great objects of education. In a course of instruction properly arranged, it naturally follows Arithmetic, and should be taught immediately after it. The pupil should acquire both a practical and theoretical knowledge of the subject While every page is the result of the author's own reflection, and the experience of many years in the school-room.
目錄
《美國中學數學·代數（上冊）》目錄：
DEFINITIONS
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
ALGEBRAIC THEOREMS
FACTORING
GREATEST MON DIVISOR
LEAST MON MULTIPLE
ALGEBRAIC FRACTIONS
CASE I. TO REDUCE A FRACTION TO ITS LOWEST TERMS
CASE II. TO REDUCE A FRACTION TO AN ENTIRE OR MIXED QUANTITY
CASE TO REDUCE A MIXED QUANTITY TO THE FORM OF A FRACTION
CASE IV. TO REDUCE FRACTIONS OF DIFFERENT
DENOMINATORS TO EQUIVALENT FRACTIONS HAVING A MONDENOMINATOR
CASE Ⅴ. ADDITION AND SUBTRACTION OF FRACTIONS
CASE Ⅵ. MULTIPLICATION OF FRACTIONS
CASEⅦ. DIVISION OF FRACTIONS
SIMPLE EQUATIONS.
DEFINITIONS AND ELEMENTARY PRINCIPLES
SIMPLE EQUATIONS CONTAINING ONE UNKNOWN QUANTITY
AXIOMS
TRANSPOSITION
TO CLEAR AN EQUATION OF FRACTIONS
SOLUTION OF SIMPLE EQUATIONS CONTAINING ONE UNKNOWN QUANTITY
QUESTIONS PRODUCING SIMPLE EQUATIONS, CONTAINING
ONE UNKNOWN QUANTITY
TO ELIMINATE BY PARISON
TO ELIMINATE BY ADDITION AND SUBTRACTION
GENERAL RULE FOR ELIMINATION BY ADDITION AND
SUBTRACTION
SUPPLEMENT TO SIMPLE EQUATIONS
GENERALIZATION
RULE, FOR FINDING TWO QUANTITIES, WHEN THEIR SUM
AND DIFFERENCE ARE GIVEN
GENERAL PROBLEMS
NEGATIVE SOLUTIONS
DISCUSSION OF PROBLEMS
PROBLEM OF THE COURIERS
CASES OF INDETERMINATION IN SIMPLE EQUATIONS, AND IMPOSSIBLEPROBLEMS
OF POWERS, ROOTS, AND RADICALS
CASE I. TO RAISE A MONOMIAL TO ANY GIVEN POWER
CASE II. TO RAISE A POLYNOMIAL TO ANY POWER
CASE III. TO RAISE A FRACTION TO ANY POWER
QUADRATIC EQUATIONS
DEFINITIONS AND ELEMENTARY PRINCIPLES
PURE QUADRATICS
QUESTIONS PRODUCING PURE QUADRATIC EQUATIONS AFFECTED QUADRATICEQUATIONS
TO SOLVE AN AFFECTED QUADRATIC EQUATION
PROGRESSIONS AND PROPORTION
ARITHMETICAL PROGRESSION
GEOMETRICAL PROGRESSION
TO FIND THE SUM OF A GEOMETRICAL SERIES
RATIO AND PROPORTION
PROPORTION
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
ALGEBRAIC THEOREMS
FACTORING
GREATEST MON DIVISOR
LEAST MON MULTIPLE
ALGEBRAIC FRACTIONS
CASE I. TO REDUCE A FRACTION TO ITS LOWEST TERMS
CASE II. TO REDUCE A FRACTION TO AN ENTIRE OR MIXED QUANTITY
CASE TO REDUCE A MIXED QUANTITY TO THE FORM OF A FRACTION
CASE IV. TO REDUCE FRACTIONS OF DIFFERENT
DENOMINATORS TO EQUIVALENT FRACTIONS HAVING A MONDENOMINATOR
CASE Ⅴ. ADDITION AND SUBTRACTION OF FRACTIONS
CASE Ⅵ. MULTIPLICATION OF FRACTIONS
CASEⅦ. DIVISION OF FRACTIONS
SIMPLE EQUATIONS.
DEFINITIONS AND ELEMENTARY PRINCIPLES
SIMPLE EQUATIONS CONTAINING ONE UNKNOWN QUANTITY
AXIOMS
TRANSPOSITION
TO CLEAR AN EQUATION OF FRACTIONS
SOLUTION OF SIMPLE EQUATIONS CONTAINING ONE UNKNOWN QUANTITY
QUESTIONS PRODUCING SIMPLE EQUATIONS, CONTAINING
ONE UNKNOWN QUANTITY
TO ELIMINATE BY PARISON
TO ELIMINATE BY ADDITION AND SUBTRACTION
GENERAL RULE FOR ELIMINATION BY ADDITION AND
SUBTRACTION
SUPPLEMENT TO SIMPLE EQUATIONS
GENERALIZATION
RULE, FOR FINDING TWO QUANTITIES, WHEN THEIR SUM
AND DIFFERENCE ARE GIVEN
GENERAL PROBLEMS
NEGATIVE SOLUTIONS
DISCUSSION OF PROBLEMS
PROBLEM OF THE COURIERS
CASES OF INDETERMINATION IN SIMPLE EQUATIONS, AND IMPOSSIBLEPROBLEMS
OF POWERS, ROOTS, AND RADICALS
CASE I. TO RAISE A MONOMIAL TO ANY GIVEN POWER
CASE II. TO RAISE A POLYNOMIAL TO ANY POWER
CASE III. TO RAISE A FRACTION TO ANY POWER
QUADRATIC EQUATIONS
DEFINITIONS AND ELEMENTARY PRINCIPLES
PURE QUADRATICS
QUESTIONS PRODUCING PURE QUADRATIC EQUATIONS AFFECTED QUADRATICEQUATIONS
TO SOLVE AN AFFECTED QUADRATIC EQUATION
PROGRESSIONS AND PROPORTION
ARITHMETICAL PROGRESSION
GEOMETRICAL PROGRESSION
TO FIND THE SUM OF A GEOMETRICAL SERIES
RATIO AND PROPORTION
PROPORTION
《美國中學數學·代數（下冊）》目錄：
Ⅰ.DEFINITIONS1
ADDITION9
SUBTRACTION.11
MULTIPLICATION..17
DIVISION24
Ⅱ.ALGEBRAIC THEOREMS.32
FACTORING.37
GREATEST MON DIVISOR41
LEAST MON MULTIPLE.47
Ⅲ.ALGEBRAIC FRACTIONS49
Ⅳ.SIMPLE EQUATIONS68
Ⅴ.SUPPLEMENT TO SIMPLE EQUATIONS103
Ⅰ.GENERALIZATION.103
Ⅱ.NEGATIVE SOLUTIONS108
Ⅲ.DISCUSSION OF PROBLEMS110
Ⅳ.PROBLEM OF THE COURIERS.111
Ⅴ.A SIMPLE EQUATION HAS BUT ONE ROOT.117
Ⅵ.EXAMPLES INVOLVING THE SECOND POWER OF THE
UNKNOWN QUANTITY117
Ⅵ.OF POWERS,ROOTS,RADICALS,AND LNEQUALITIES..118
Ⅰ.INVOLUTION,OR FORMATION OF POWERS118
Ⅱ.EXTRACTION OF THE SQUARE ROOT127
Ⅲ.EXTRACTION OF THE CUBE ROOT139
Ⅳ.EXTRACTION OF THE FOURTH ROOT,SIXTH ROOT,NTH
ROOT,ETC148
Ⅴ.RADICAL QUANTITIES151
Ⅵ.THEORY OF FRACTIONAL EXPONENTS.166
Ⅶ.EQUATIONS CONTAINING RADICALS169
Ⅷ.INEQUALITIES.171
Ⅶ.QUADRATIC EQUATIONS176
AFFECTED QUADRATIC EQUATIONS181
TRINOMIAL EQUATIONS.202
SIMULTANEOUS QUADRATIC EQUATIONS CONTAINING TWO
OF MORE UNKNOWN QUANTITIES210
AFFECTED EQUATIONS.214
Ⅷ.RATIO,PROPORTION,AND PROGRESSIONS226
PROPORTION229
GEOMETRICAL PROGRESSION249
Ⅸ.PERMUTATIONS,BINATIONS,AND BINOMIAL
THEOREM259
Ⅹ.INDETERMINATE COEFFICIENTS:BINOMIAL THEOREM,
GENERAL DEMONSTRATION:SUMMATION AND
INTERPOLATION OF SERIES270
THEOREM270
BINOMIAL THEOREM275
THE DIFFERENTIAL METHOD OF SERIES283
PILING OF CANNON BALLS AND SHELLS..288
INTERPOLATION OF SERIES.292
INFINITE SERIES..295
RECURRING SERIES.299
REVERSION OF SERIES.303
Ⅺ.CONTINUED FRACTIONS:LOGARITHMS:EXPONENTIAL
EQUATIONS:INTEREST,AND ANNUITIES.306
CONTINUED FRACTIONS306
LOGARITHMS.314
PUTATION OF LOGARITHMS322
NAPERIAN,OF HYPERBOLIC LOG ARITHMS.327
SINGLE AND DOUBLE POSITION331
EXPONENTIAL EQUATIONS333
INTEREST AND ANNUITIES.335
Ⅻ.GENERAL THEORY OF EQUATIONS341
TRANSFORMATION OF EQUATIONS.352
LIMITS OF THE ROOTS OF EQUATIONS.363
STURM’S THEOREM.367
ⅩⅢ.RESOLUTION OF NUMERICAL EQUATIONS374
《美國中學幾何》目錄：
THE NATURE, DIVISIONS, AND METHOD OF THE SCIENCE
DETERMINATE GEOMETRY
INDETERMINATE GEOMETRY BOOK I PLANE CO-ORDINATES
PART I THE REPRESENTATION OF FORM BY
ANALYTIC SYMBOLS
CHAPTER 1. THE OLDER GEOMETRY: BILINEAR AND
POLAR CO-ORDINATES
THE POINT
THE RIGHT LINE
PAIRS OF RIGHT LINES
THE CIRCLE
THE ELLIPSE
THE HYPERBOLA
THE PARABOLA
LOCUS OF SECOND ORDER IN GENERAL
CHAPTER 2. THE MODERN GEOMETRY: TRILINEAR
AND TANGENTIAL CO-ORDINATES
TRILINEAR CO-ORDINATES
TANGENTIAL CO-ORDINATES
PART II. THE PROPERTIES OF CONICS.
CHAPTER 1. THE RIGHT LINE
CHAPTER 2. THE CIRCLE
CHAPTER 3. THE ELLIPSE
THE CURVE REFERRED TO ITS AXES
THE CURVE REFERRED TO ANY TWO CONJUGATES
THE CURVE REFERRED TO ITS FOCI
AREA OF THE ELLIPSE
EXAMPLES ON THE ELLIPSE
CHAPTER 4. THE HYPERBOLA.
THE CURVE REFERRED TO ITS AXES
THE CURVE REFERRED TO ANY TWO CONJUGATES
THE CURVE REFERRED TO ITS FOCI
THE CURVE REFERRED TO ITS ASYMPTOTES
AREA OF THE HYPERBOLA
EXAMPLES ON THE HYPERBOLA
CHAPTER 5. THE PARABOLA
THE CURVE REFERRED TO ITS AXIS AND VERTEX
THE CURVE IN TERMS OF ANY DIAMETER
THE CURVE REFERRED TO ITS FOCUS
AREA OF THE PARABOLA
EXAMPLES ON THE PARABOLA
CHAPTER 6. THE CONIC IN GENERAL
BOOK II CO-ORDINATES IN SPACE
CHAPTER 1. THE POINT
CHAPTER 2. LOCUS OF FIRST ORDER IN SPACE
CHAPTER 3. LOCUS OF SECOND ORDER IN SPACE
《美國中學數學·代數（上下冊）（答案）》
作者簡介
編者：（美國）雷伊（Joseph Ray）
Joseph Ray was born on November 25, 1807, in Ohio County, Virginia.He at tended local schools and quickly proved himself to be anadept student.By the time he was sixteen, he had begun a careeras ateacher. In 1825, Ray enrolled in Franklin College in New Athens,Ohio. While a student at Franklin College, Ray studied medicineunderJoel Martin. Upon graduating from college in1828, Ray enrolledin the Medical College of Ohio, located in Cincinnati. During thewin terhe attended college, and during the summers, hetaughtschool. He graduated in 1831. Ray is most famous for authoring mathe matical text books. By the end of the nieenth century,Ray'stexts had bee the most widely used math books in the UnitedStates, with sales approaching120 million copies. For a time, theywere the most used textbooks across all disciplines.WilliamMcGuffey, a colleague of Ray's at Woodward College,eventually produced a series of Englis hreaders. Ray was a memberof the Ohio State Teachers Association and served as thatorganization'spresident in 1853. In 1854, he became anassociateeditor for The Ohio Journal of Education. He died on April11, 1855, from tuberculosis.
Joseph Ray was born on November 25, 1807, in Ohio County, Virginia.He at tended local schools and quickly proved himself to be anadept student.By the time he was sixteen, he had begun a careeras ateacher. In 1825, Ray enrolled in Franklin College in New Athens,Ohio. While a student at Franklin College, Ray studied medicineunderJoel Martin. Upon graduating from college in1828, Ray enrolledin the Medical College of Ohio, located in Cincinnati. During thewin terhe attended college, and during the summers, hetaughtschool. He graduated in 1831. Ray is most famous for authoring mathe matical text books. By the end of the nieenth century,Ray'stexts had bee the most widely used math books in the UnitedStates, with sales approaching120 million copies. For a time, theywere the most used textbooks across all disciplines.WilliamMcGuffey, a colleague of Ray's at Woodward College,eventually produced a series of Englis hreaders. Ray was a memberof the Ohio State Teachers Association and served as thatorganization'spresident in 1853. In 1854, he became anassociateeditor for The Ohio Journal of Education. He died on April11, 1855, from tuberculosis.
