Intermediate Algebra - by William L. Hart- PDF book (1948)

Intermediate Algebra 

Intermediate Algebra




Excerpt from the introduction:

The book offers a collegiate substitute for third-semester high school algebra. The text was designed for a college student who will study it either (1) as a preliminary to taking college algebra, or (2) as terminal work hi algebra which is intended as a prerequisite for elementary courses in various fields of natural or social science, or in business administration.

A suitable selection of content from the book would provide a satisfactory algebraic foundation for a first course in trigonometry or in the mathematics of investment. In the case of a student of the assumed preparation, the text provides sufficient material for a substantial course utilizing from 40 to 60 class hours.

The plan of the text was based on the assumption that the typical student involved is of mature age but studied his elementary algebra so long ago that practically all fundamentals must be taught as if they were relatively new material for him. Hence, the early chapters of the book present a mature but frankly elementary treatment of the foundations of algebraic technique with a generous amount of discussion and problem material. Also, appropriate refresher work on arithmetic is provided incidentally hi the algebraic problems and explicitly in an early optional chapter devoted to computation.


The tempo of the discussion in the text is gradually increased until, in the later chapters, distinctly collegiate speed is attained so that the student will find it easy to make the transition into a substantial second course devoted to college algebra. 

The text makes no attempt to present material that custom dictates as primarily within the sphere of college algebra, although such material frequently may enter the most substantial courses in third-semester algebra at the secondary level. However, in the interest of efficiency and mathematical simplicity, the terminology and general viewpoint of the text is distinctly collegiate. Emphasis is laid on the logical sequence of topics, the accuracy of definitions, and the completeness of proofs.


Adult nature of the presentation. The discussion in the text is couched at a level suitable to the maturity of college students. Hence, the available space and assumed class time are utilized mainly to explain and illustrate the mathematical principles involved and only the necessary minimum attention is devoted to the artificial motivation of the type which might properly be expanded for younger students. Terminology.

Some contents of the book:

1. THE FUNDAMENTAL OPERATIONS 1
2. INTRODUCTION TO FRACTIONS AND EXPONENTS 22
Review of Chapters 1 and 2 46
3. DECIMALS AND ELEMENTS OP COMPUTATION 48
4. LINEAR EQUATIONS IN ONE UNKNOWN 68
5. SPECIAL PRODUCTS AND FACTORING 82
6. ADVANCED TOPICS IN FRACTIONS 104
Review of Chapters 4, cmd 6 118
’ 7. RECTANGULAR COORDINATES AND GRAPHS 119
8 . SYSTEMS OP LINEAR EQUATIONS 131
9. EXPONENTS AND RADICALS 142
10. ELEMENTS OP QUADRATIC EQUATIONS 170
11. ADVANCED TOPICS IN QUADRATIC EQUATIONS 186
12. THE BINOMIAL THEOREY 204
RATIO, PROPORTION, AND VARIATION 210
14. PROGRESSIONS t ^ 221
15. LOGARITHMS 240
16. SYSTEMS INVOLVING QUADRATICS 262


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