High school algebra; advanced course

H. E. (Herbert Ellsworth) Slaught

Description

*MWl»t!aWUMflOMMM:c«Mm COURSADVANCED LENNESSLAUGHT & w«a»owMM»M»Miii»mmwwmnMnni>tiMi*nl inriiliwwiimiwimiwiwuiMHnwmnmiiirtwiiiiiiiiiiiiHiiiiiiiiir IN MEMORIAM FLOR1AN CAJOR1 C^^trv-t:(T^w'cc^ HIGH SCHOOL ALGEBRA Hbvancefc Course BY H. E. SLAUGHT, Ph.D. ASSOCIATE PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF CHICAGO N. LENNES, Ph.D. J. INSTRUCTOR IN MATHEMATICS IN THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JHHc Boston ALLYN AND BACON 1908 COPYRIGHT, 1908, BY H. E. SLAUGHT AND N. J. LENNES. m M Sm m. : PREFACE Advanced Course of the High School AlgebraThe contains a review of all topics treated in the Elementary Course, to- gether with such additional topics are required to make itas amply sufficient to meet the entrance requirements of any technical school. Its development is uponcollege or based the following important considerations The pupil has had one year's course in algebra, involv-1. a ing constant application of its elementary processes to the solution of concrete problems. This has invested the pro- cesses themselves with an interest which now makes them a proper object of study for their own sake. 2. The pupil has, moreover, developed in intellectual ma- turity and is, therefore, able to comprehend processes of with abstract numbers which were entirely beyondreasoning his reach in the first year's course. This is particularly true with the moreif, in the meantime, he has learned to reason concrete forms of geometry.

Sujets

• Álgebra

Informations

• Publié par: les_archives_du_savoir
• Nombre de lectures: 10
• Langue: English
• Poids de l'ouvrage: 10 Mo

Extrait

*MWl»t!aWUMfl<M>OMMM:c«Mm
COURSADVANCED
LENNESSLAUGHT &
w«a»owMM»M»Miii»mmwwmnMnni>tiMi*nl
inriiliwwiimiwimiwiwuiMHnwmnmiiirtwiiiiiiiiiiiiHiiiiiiiiirIN MEMORIAM
FLOR1AN CAJOR1C^^trv-t:(T^w'cc^HIGH SCHOOL ALGEBRA
Hbvancefc Course
BY
H. E. SLAUGHT, Ph.D.
ASSOCIATE PROFESSOR OF MATHEMATICS IN THE UNIVERSITY
OF CHICAGO
N. LENNES, Ph.D.
J.
INSTRUCTOR IN MATHEMATICS IN THE MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
JHHc
Boston
ALLYN AND BACON
1908COPYRIGHT, 1908,
BY H. E. SLAUGHT
AND N. J. LENNES.
m M Sm m.:
PREFACE
Advanced Course of the High School AlgebraThe contains
a review of all topics treated in the Elementary Course, to-
gether with such additional topics are required to make itas
amply sufficient to meet the entrance requirements of any
technical school. Its development is uponcollege or based
the following important considerations
The pupil has had one year's course in algebra, involv-1. a
ing constant application of its elementary processes to the
solution of concrete problems. This has invested the pro-
cesses themselves with an interest which now makes them
a proper object of study for their own sake.
2. The pupil has, moreover, developed in intellectual ma-
turity and is, therefore, able to comprehend processes of
with abstract numbers which were entirely beyondreasoning
his reach in the first year's course. This is particularly true
with the moreif, in the meantime, he has learned to reason
concrete forms of geometry.
In consequence the treatmentof these considerations,
throughout is from a more mature point of view than in the
given inElementary Course. The principles of algebra are
the form of theorems the proofs of which are based upon a
definite set of axioms.
As in the Elementary Course, the important principles are
used at once in the solution of concrete and interesting prob-
lems, which, however, are here to the pupil's greateradapted
maturity and experience. But relatively greater space and
emphasis are given manipulation of standard algebraicto the
iii
msosisiIV PREFACE
forms, such as the student is likely to meet in later work in
mathematics and andphysics, especially such as were too com-
plicated for the Elementary Course.
The division of the High School Algebra into two distinct
courses has made it possible to give in the Advanced Course
a more thorough treatment of the elements of algebra than
could be given if the book were designed for first-year classes.
It has thus become possible to lay emphasis upon the pedagogic
of viewing each subject second in mannerimportance a time a
more profound than is possible on a first view.
Attention is specifically called to the following points :
The scientific treatment of axioms in Chapter I.
The clear and simple treatment of equivalent equations in
Chapter III.
discussion by formula, well graph, of incon-The as as by
40sistent and dependent systems of linear equations, pages
to I I.
The unusually complete treatment of factoring and the
and simple exposition of the process of findingclear general
the Highest Common Factor, in Chapter V.
careful discrimination stating and applying theThe in
theorems on powers and roots in Chapter VI.
treatment in VI 1,The unique of quadratic equations Chapter
giving a lucid exposition in concrete and graphical form of
coincident,distinct, and imaginary roots.
The concise treatment of radical expressions in Chapter X,
especially— innovation much needed in this connec-and an
solution of whichtion— the rich collection of problems, in the
radicals are applied.
H. E. SLAUGHT.
N. .1. LENNES.
' \iim
< II I< \M> I'.OSTON,
April, L908.CONTENTS
CHAPTER I
FUNDAMENTAL LAWS
PAGE
Axioms of Addition and' Subtraction 1 of Multiplication and Division
Theorems on Addition and Subtraction on Multiplication and Division .
CHAPTER II
FUNDAMENTAL OPERATIONS
Definitions 11
Addition and Subtraction of Monomials . 12 and of Polynomials . 15
Removal of Parentheses 17....
Multiplication and Division of Monomials 18 and of Polynomials 21
CHAPTER III
INTEGRAL EQUATIONS OF THE FIRST DEGREE IN ONE
UNKNOWN
25Definitions
Equivalent Equations 27
Problems in One Unknown 32
CHAPTER IV
INTEGRAL LINEAR EQUATIONS IN TWO OR MORE VARIABLES
Indeterminate Equations ... ..... .36
38Simultaneous in Two VariablesVI CONTENTS
PAGE
and DependentInconsistent Equations 43
in .More than TwoSystems Variables 45
Problems in Two or More Unknowns 47
CHAPTER V
FACTORING
Expression of Two, Three, or Four Terms 52
Factors found by Grouping 55 found by the Factor Theorem u
Solution of Equations by Factoring . 60
Common Factors and Multiples Gl
CHAPTER VI
POWERS AND ROOTS
Definitions ....... 69
Theorems on Powers and Roots 73
Roots of Polynomials 77.....
Roots of Arabic Numbers
CHAPTER VII
QUADRATIC EQUATIONS
Exposition by means of Graphs 83
Distinct, Coincident, and 87Imaginary Roots
Simultaneous Quadratics .... 90
Special Methods of Solution 96
Higher Equations involving Quadratics 106
andRelations between the Roots Coefficients L08
Formation of Equations with Given Roots 110
Problems involving Quadratics . 112
VIIICHAPTER
ALGEBRAIC FRACTIONS
FractionsReduction of ..... 11G
Addition and Fractions 120Subtraction of