Applied Algebra II (Tt) by Thomas J. McHale; Paul T. WitzkeReview by: Anton GlaserThe Mathematics Teacher, Vol. 74, No. 1 (January 1981), pp. 72-73Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27962317 .

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NEW publications

Code: Tj = Textbook, junior high

Ts Textbook, senior high Tt = Textbook, two-year college

L = Library

= Professional S =

Supplementary student reading

Algebra?Programmed: Part 3, 2d ed. (Tt), Robert

H. Alwin, Robert D. Hackworth, and Joseph W.

Howland. 1980, xii + 596 pp., $15.95 paper. ISBN

0-13-021931-2. Prentice-Hall, Englewood Cliffs, NJ

07632.

This latest edition of a second half of an elementary

algebra course is composed of relatively clear tele

graphic explanations followed by a handful of exer

cises and an abundance of well-structured, self-eval

uative tests.

The text covers traditional topics with a somewhat

increased emphasis on exponents, polynomials, and

the arithmetic of square roots. The units on sets, func

tions, slope, and scientific notation are particularly ef

fective. Considerable space is devoted to logarithms, but the topic is developed in such a way that the logic is compatible with that of the hand-held calculator.

Unfortunately, the authors do not envision the stu

dent using a calculator for lengthy computations, and

they include a lengthy unit on arithmetic operations with logarithms.

An additional feature of this second edition is a

concluding chapter devoted to applications. The prob lems are uninspiring and painfully familiar: boats go

ing downstream, grocers mixing nuts, cars overtaking one another, and so on. Were the applications to be

interspersed wherever appropriate and designed to

keep the student interested and aware of the useful ness of the concepts studied, this aspect of the pro

grammed text would be more effective and valuable.

Programmed texts are ultimately collections of reci

pes. This is one of the more readable and competent,

although conventional, books.?Myra R. Lipman, Pace University, New York, NY 10038.

Algebra and Trigonometry (Ts, Tt), Walter Fleming and Dale Varberg. 1980, xvi + 521 + A34 + 13 pp., $17.95 cloth. ISBN 0-13-021824-3. Prentice-Hall,

Englewood Cliffs, NJ 07632.

The book is instructive but not rigorous and techni

cal. Clear and precise guidance is given for the many

problems and word problems. There is a substantial amount of reading required,

and the book is not dull. The chapters are introduced

with anecdotes, quotations, and historical facts. Often, the introductions are humorous. Each chapter has a

summary and a review problem set. Formulas for ge

ometry, algebra, and trigonometry are easily found on

the inside covers. Answers for odd-numbered prob lems are given.

This is a very good book and highly recommended

for use.?Julia J. Grice, Roosevelt High School, Wash

ington, DC 20011.

Algebra and Trigonometry: Functions and Appli cations (Ts, Tt), Paul A. Foerster. 1980, 602 pp., $15.00 cloth. ISBN 0-201-02475-6. Addison-Wes

ley, Reading, MA 01867.

This is a unique text, rigorous in theory and rich in

applications. End-of-chapter problems create mathe

matical models of real-world situations and employ several mathematical concepts in a single context.

There are over 250 such applications in the book with

titles like "Diesel Car vs. Gasoline Car Problem" (lin ear systems), "Louisiana Purchase Problem" (geomet ric series), and "Why Mammals Are the Way They Are" (joint variations); they are imparted with a sense

of humor, pragmatism, and curiosity. The book is designed for a course in intermediate

algebra, advanced algebra, and trigonometry. (The three chapters on trigonometry are adapted from the

author's equally impressive Trigonometry: Functions

and Applications.) Two appendices cover a review of

computer programming and mathematical induction.

Many of the application problems are appropriate for

calculator or computer solutions; answers to all odd

numbered problems are given. This is a book to be read. Concepts tests completing

each chapter require the student to think, write, and

synthesize unfamiliar material. As a basic text, it is

appropriate for the above average algebra student. As a source of application problems for all, it is peer less.?William Jacob Bechern, Greenwich High School,

Greenwich, CT 06830.

Applied Algebra II (Tt), Thomas J. McHale and Paul

T. Witzke. 1980, 444 pp., $12.95 paper. ISBN

0-201-04775-6. Addison-Wesley Publishing Co.,

Reading, MA 01867.

The book is in programmed learning form and was

reproduced from camera-ready copy supplied by the

authors. Was it field-tested? There is no mention of it

in the preface or the press release. Good field-testing, with appropriate revisions, would have eliminated

some awkward layout, such as the minus sign that runs into a radical and makes it look like the principal root. The book would also have been better if the au

thors had stuck to standard mathematical terminol

ogy, instead of introducing such concepts as complete and incomplete complex numbers. Some statements

72 Mathematics Teacher

This content downloaded from 211.28.229.160 on Sat, 13 Sep 2014 06:45:48 AMAll use subject to JSTOR Terms and Conditions

are false, such as "jc = y/x2 "

(try ? ?

1). The press release claims that the book "is appropriate as the pri

mary text in a one-semester course in developmental mathematics for the technical science major or stu

dents enrolled in technician/training programs." These students deserve something better.?Anton Gla

ser, Pennsylvania State University, Abington, PA

19001.

Assessing Competencies for Calculus: A Self

Correcting Workbook (S), Raymond McGivney, James McKim, and Benedict Pollina. 1980, 48 pp. ISBN 0-534-00856-9. Wadsworth Publishing Co.,

Belmont, CA 94002.

An illustrated workbook with programmed exer

cises excerpted from various calculus texts.?Law

rence Adler, ?orwell Junior High School, Norwell, MA

02061.

Background Math for a Computer World, 2d ed.

(L), Ruth Ashley and Nancy B. Stern. 1980, xi +

308 pp., $7.95 paper. ISBN 0-471-08086-1. John

Wiley & Sons, 605 Third Ave., New York, NY

10016.

This book is one in a series of Wiley self-teaching

guides. The format of the book is programmed in

struction. Each chapter concludes with a self-test on

the contents of the chapter. The book concludes with

a final test on all the material in the book. Answers to

all questions are provided in the text.

The author intends the book for people with little

formal training in mathematics who find themselves

working with computers. The author has selected top ics that she feels the reader needs to know to survive

in the computer world. These topics include binary, octal, and hexadecimal number systems; logic for

computers; flowcharts; trigonometric functions; prob

ability; statistics; linear equations; matrix algebra; se

quences and series; interest and mortgage problems; and game theory.

As you might expect from the wide range of topics included, the development of each topic is quite shal low.

This book could be useful to persons who have had formal mathematics courses in the past and feel they need a quick review of major topics.?Bruce De

Young, Ramsey High School, Ramsey, NJ 07446.

Barron s How to Prepare for the High School

Equivalency Examination (GED): The Mathe

matics Test, Vol. 1: Arithmetic (L), Anthony Prindle and Eugene J. Farley. 1979, xii + 60 pp., $2.25 paper.

Barron s How to Prepare for the High School

Equivalency Examination (GED): The Mathe

matics Test, Vol. 2: Algebra (L), Anthony Prindle

and Eugene J. Farley. 1979, iv + 57 pp., $2.25 pa

per. Barron s How to Prepare for the High School

Equivalency Examination (GED): The Mathe

matics Test, Vol. 3: Geometry, Tables &

Graphs, Word Problems (L), Anthony Prindle

and Eugene J. Farley. 1979, iv + 59 pp., $2.25 pa

per. Barron's How to Prepare for the High School

Equivalency Examination (GED): The Mathe matics Test, Vol. 4: Model Exams (L), Anthony Prindle and Eugene J. Farley. 1979, iv + 76 pp., $2.25 paper. Barron's Educational Series, 113

Crossways Park Dr., Woodbury, NY 11797.

These four volumes will be helpful to the student

who learned the material well once and who only needs a review. The instructional material is some

what wordy, and there are several instances of mathe

matical errors throughout the text. Although these er

rors are minor, they may cause difficulty with the

conscientious reader for whom the books are in

tended. For example, in a discussion cf prime and

composite numbers, no mention of zero is made; an

improper fraction is defined on one page as "one

where the numerator is greater than or equal to the

denominator" and four pages later there is a note, "Remember that the numerator of an improper frac

tion is larger than the denominator"; and other errors

appear in the sequencing of material (using a skill be

fore it is taught), inclusion of topics (some are omitted

in instruction but assumed in future explanations), and the use of new, undefined words (invert, divider

for divisor, etc.). There are practice tests with solutions at the end of

each section, probably the most valuable portions of

these booklets. Volume 4, Model Exams, would be

useful for anyone planning to take the High School

Equivalency Examination. It contains test-taking hints, information on applying for the exam and state

requirements, as well as a diagnostic test and a prac tice test (with solutions) keyed to instructional sec

tions in the first three volumes.?Sandra Pryor Clark

son, Hunter College of CUNY, New York, NY 10021.

Calculus: A Modeling Approach, 2d ed. (Ts, Tt), Marvin L. Bittinger. 1980, xi + 544 pp., $17.95 cloth. ISBN 0-201-01247-2. Addison-Wesley Pub

lishing Co., Reading, MA 01867.

This is an updated and expanded edition of a pre vious work. The introductory level text is aimed at the

business, premedicai, social science, or behavioral sci

ence major. The subjects are to be covered in a two

semester course, but a fast-paced, one-semester treat

ment could be given to many chapters. The concept of

mathematical modeling and the application of func

tions to real situations is paramount in the writing of

this text. Many exercises and examples point out func

tions and relationships that are not included in begin

ning courses. Quite a few of the problem selections are

excellent and unique. The text is very readable, uses a

minimum of notation, and has well-chosen graphs and photos.

Proofs are included for major theorems, but the em

phasis is on an intuitive approach, not rigor. Many times a problem is solved by the student through trial

and error before seeing the standard calculus method.

January 1981 Ti

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