Hall代数:民国时期的中学数学课本:英文

PART I Chapter I. GENERALIZED ARITHMETIC. SYMBOLS. SUBSTITUTION Signs of operation and their use (pp. 1, 2). Product, Factor Coefficient (pp. 5, 6). Power, Index (pp. 7, 8). Algebraical Expression (p. 10) Chapter II. NEOATIVE QWNaUzS. ADDITION. SIMPLE BRACKETS Concrete Illustrations (pp. 13-16). Addition of Like Terms (pp 16-19). Easy Problems (pp. 19-21). Brackets (pp. 21-23) Addition of Unlike Terms (pp. 23-25). Dimension and Degree (pp. 25, 26) Chapter III. SVBTRAm Subtraction of Simple Expressions (pp. 28, 29). Subtraction of Compound Expressions (pp. 29-31). Commutative and Associative Laws for Addition and Subtraction (p. 31) Miscellaneous Examples I Chapter IV. MTneLIeATION Simple Expressions, Multiplication by a Negative Quantity, Rule of Signs (pp. 34, 35). Commutative and Associative Laws for Multiplication (p. 35). Law of Indices (p. 37). Compound Expressions, Distributive Law (pp. 38--41). Products by Inspection (pp. 42, 43) Chapter V. DwsIo Simple Expressions (p. 44). Index Law (p. 45). Compound Expressions (pp. 45-48) Chapter VI. BRACKV.TS Removal of Brackets (pp. 49-52). Insertion of Brackets (pp. 52-53) Miscellaneous Examples II Chapter VII. R.wsio oF EL'MTY RCES Important Cases in Multiplication and Division (pp. 56-58) Fractional Coefficients (pp. 58-60). Compound Terms and Coefficients (pp. 61-63). Roots, Substitutions (pp. 63-66) Chapter VIII. SrMPLE EQUATIONS Identity, Equation of Condition (p. 67). Use of the Fundamental Axioms (p. 69). Verification of Solutions (p. 69). Transposition of Terms (p. 72) Chapter IX. SYMBOLICAL EXPRESSION. FORMULAE Easy Examples (pp. 77-81). Formation of Equations (pp. 81, 82) Formulae and their Use (pp. 83-87) Chapter X. SOLUTION OF PROBLEMS Chapter XI. GRAPHS Axes, Coordinates, Plotting Points (pp. 95-100). Graph of a Function. Linear Graphs (pp. 100-107). Applications of Graphs (pp. 100-I10). Non-linear Graphs (pp. 111-113) Graphs of Statistics (pp. 113-119) Miscellaneous Examples III Chapter XII. SIMULTANEOUS EQUATIONS Agebraical Methods (pp. 122-127). Graphical Treatment (pp. 127 131). Simultaneous Equations with Three Unknowns (pp. 132 133) Chapter XIII. PROBLEMS LEADING TO SIMULTANEOUS EQUATIONS Chapter XIV. RESOLUTION INTO FACTORS (--4 First Course) Chapter XV. HARDER CASES OF MULTIPrICATION AND DMSION Harder Cases of Compound Expressions, Detached Coefficients (pp. 148-153). Important Cases in Division (p. 153). Functional Notation, Remainder Theorem (pp. 155-157) Chapter XVI. INVOLUTION AND EVOLUTION Rules of Signs in Involution (p. 158). Square of a Multinomial (pp. 159, 160). Cube of a Binomial (pp. 160, 161). Rules of Signs in Evolution, Imaginary Quantities (pp. 161, 162). Square Root of Compound Expressions (pp. 163-167). Cube Root (p. 167) Chapter XVII. HARDER CASES OF RESOLUTION rSTO FACTORS Trinomials (pp. 169-171). Harder Cases of previous types (pp. 171-173). Method of Completing the Square (pp. 173 174). Miscellaneous Factors (pp. 174, 175). Converse Ap plications, Identities (pp. 176, 177). Solution of Quadratic Equations by Factors (pp. 177-179) Miscellaneous Examples IV Chapter XVIII. HIGHEST COMMON FACTOR H.C.F. by Factors (pp. 183-185). Long Rule for H.C.F. (pp 186-189). General Proof of Rule (p. 190) Chapter XIX. FCTIONS Reduction to Lowest Terms (pp. 191-194). Multiplication and Division (pp. 194--197) Chapter XX. Low-sT COMMON [ULTIPL:8 L.C.M. by Factors (pp. 198, 199). General Method (p. 200) Chapter XXI. AurrioN AND SUBTRACTION OF FRACTIONS Chapter XXII. Msc,.,.,Nxous F2ACTIONS Complex Fractions, Continued Fractions, Inexact Division (pp 211-215). Further Illustrative Examples (pp. 215-218) Chapter XXIII. HARDER EQUATIONS AND PROBLEMS Illustrative Examples (pp. 219-221). Missing and Extraneous Roots (pp. 221, 222). Literal Coefficients (pp. 224-227) Harder Problems (pp. 228-233). Examples on Formulae and Literal Equations (pp. 234-239) Miscellaneous Examples V Chapter XXIV. GRAPHS OF QUADRATIC FUNCTIONS Equations of the forms y = x2, y -- ax + bx + c, Graphical Solution of f(x)=0, Turning Points, Maximum and Minimum Values (pp. 246-251). Hyperbola, Asymptote, Circle, Miscellaneous Graphical Examples (pp. 252-255) Chapter XXV. QUADRATIO EQUATIONS A-D FUNCTIONS Standard Form, Solution by Factorization (pp. 256, 257) Solution by Completing the Square (pp. 257-260). Solution by Formula, Graphical Illustrations (pp. 261-263). The Dis eriminant, Summary of Methods (pp. 263, 264). Combination of Two Graphs (pp. 265, 266). Equations of Higher Degree (pp. 267, 268). Miscellaneous Examples on Quadratic Equations and Functions, Table of Square Roots (pp. 268 269) Chapter XXVI. SMULTrOUS EQUATIONS OF THE SECOND OR HIGHER DEGRE Typical Solutions (pp. 270, 271). Graphical Illustrations (pp 272, 273). Further Typical Solutions, Miscellaneous Solutions in brief (pp. 274-276) Chapter XXVII. PROBLEMS LEADING TO QUADRATIO EQUATIONS Chapter XXVIII. GPmCAL PROBLEMS Miscellaneous Examples VI PART II Chapter XXIX. ARITHMETIC, HARMONIC, AND GEOMETRIC PROGRESSION Chapter XXX. THE THEORY OF INDICES Positive Integral Indices. Fundamental Theorems (pp. 327, 328) Fractional and Negative Indices (pp. 328-337) Chapter XXXI. SURDS D IRRATIONAL QVANTrrIES Simple Surds (pp. 338-343). Compound Surds (pp. 343-345) Properties of Quadratic Surds (pp. 346-348). Irrational Equa tions (pp. 348-350) Chapter XXXII. LOGARITHMS Graph of y2x (pp. 352, 353). General Propositions (pp. 354 356). Common Logarithms (pp. 356-359). Graph of y:10s (pp. 360, 361). Use of Four-Figure Tables (pp. 362-369). Tables (pp. 370-373) Miscellaneous Examples VII Chapter XXXIII. RATIO AND PROPORTION Chapter XXXIV. VARIATION Direct and Inverse Variation (pp. 391-395). Joint Variation (pp 396, 397). Graphical Illustration (p. 398) Chapter XXXV. TEE THEORY OF QUADRATIC EQUATmS AND FUICTIONS Number and Character of Roots, Discriminant (pp. 401-405) Properties of a Quadratic Function (p. 405). Quadratics with a Common Root (p. 407). Variations in Sign and Value of Quadratic Functions (pp. 408-412) Chapter XXXVI. A CHAPTER FOR REVISION. MSCELLaNEOUS THEOREMS AND EXAMPLES Harder Factors and Identities (pp. 414-419). Applications of the Remainder Theorem. Symmetrical and Alternating Functions (pp. 420--422). Undetermined Coeficients (pp. 423-427) Chapter XXXVII. THE PROGRESSIONS AND SOME ALLIED SERIES Arithmetico-Geometric Series (pp. 428, 429). Sum of Squares and of Cubes of the Natural Numbers (pp. 430-432). Further Exercises on the Progressions (pp. 432-435) Chapter XXXVIII. HARDER GRAPHS Graph of y=x2 (pp. 436, 437). Graphs of Miscellaneous Curves Gradient of a Curve (pp. 438-443). Practical Applications (pp. 444-416) Miscellaneous Examples VHI Chapter XXXIX. PERMUTATIONS AND COMBINATIONS Definitions, General Principles (pp. 457-459). Permutations unlike things (pp. 460, 461) ; things not all different (pp. 462 463) ; things which may be repeated (pp. 463, 464). Combina tions (pp. 465-468). Miscellaneous Examples in Permutations and Combinations (pp. 469-472) Chapter XL. MATHEMATICAL INDUCTION Chapter XLI. THE BINOMIAL THEOREM Expansion of (x+a)n when n is a Positive Integer (pp. 476-478) The Binomial CoeMcients. General Term. Greatest Term (pp. 479-485). Binomial Theorem for Negative and Fractional Indices (pp. 488-494). Approximations (pp. 495-499) Chapter XLII. PARTIAL FRACTIONS Miscellaneous Examples IX Chapter XLIII. THE USE OF EXPONENTIAL AND LOGARITHMIC SERIES Exponential Theorem (p. 510). Logarithmic Series (pp. 511-517) Chapter XLIV. COMPOUND INTEREST AND ANNUITIES Chapter XLV. SCALES OF NOTATION Integers (pp. 524, 525). Radix Fractions (p. 526). Some Properties of Numbers (pp. 527-529) Chapter XLVI. EASY INEQUALITIES Chapter XLVII. M,SCELLANEOUS EQUATIONS Equations in One Unknown (pp. 534-538). Equations in Two or More Unknowns (pp. 539-542). Indeterminate Equations (pp. 543-546) Miscellaneous Examples X Examples from Recent Examination Papers Answer 编辑手记