To me the function table examples were eye opening. I wish I got this point of view earlier both when I was starting out with mathematics but also when I was starting out with programming.
When you focus on just one function application at a time you might miss the beauty and the patterns in the overall picture.
Oh man thanks for posting this. After seeing a few APL references in comments today, it reminded me to go look for this exact book by Ken Iversen. Lo and behold, I just sit down to peruse HN.... And this link is right above the fold. Sweet.
Content of PDF (12 MB): Scan of K.E. Iverson's Elementary Algebra, 178 pp., published by IBM in 1971 (Technical Report 320-3001, Philadelphia Scientific Center)
P.S. Uncorrected (mostly) OCR of Preface:
PREFACE The present text treats the usual topics expected in a second course in high school algebra. It differs from conventional treatments in the following respects ;
1. The notation used is simple and precise and applies to arrays (vectors and matrices) in a simple and form manne r.
2. Arrays are used extensively to give a view Of functions by g the patterns produced by applying them to vectors They are also used to clarify cs whi ch use vectors directly , such as linear functions and polynomials
3. The precision Of the notation permits an algorithmic treatment Of the material. In parti , e expression in the book can be executed directly by simply typing it on an appropriate computer terminal. Hence if a computer is available, it can be used by students for individual or collective exploration of relevant mathematical functions in the manner discussed in Berry al Even if a computer is not availab the treatment pres s the essen of computer programming in a mathematical 1 i e , as the precise definition and cation Of functions
4. The algorithmic approach is the same as that used in my Elementary Functions, a text which can be used as a continuation in topics such as the slope ( derivative) of functions, and the hyperbolic, exponential , and logarithmic functions
5. The organization of topics follows a pattern suggested by considering algebra as a language; in particular , the treatment of formal is deferred much work has been done in the reading and writing of algebraic sentences These matters are discussed fully in the Appendix a , and any teacher may be well—advised to begin by reading this appendix.
The pace of the text is perhaps best suited to a second year course, but it can also be used for a first year course the early con all Of the essentials such as the introduction Of the negative and rational numbers When used as a second year text, th ese early chapters can serve not only as a brief review, but also as an introduction to the notation used.
This text grew out of a summer project undertaken in 1969 in collaboration with my colleagues Adin Falkoff and Paul Berry of IBM, and with five high school teachers—— M John Brown, now of Dawson College, Montreal; Mr. Nathaniel of Belmont Hill School, Belmont, Massachusetts; Miss Bates Linda Al vord, Of Scotch P High School, Scotch plains N.J.; and Sisters Helen Wilxman and Barbara Brennan, of Mary I:nmaculate School , Ossining , 1 am indebted to all Of N.Y. these people for much fruitful discussion, and particularly to Messrs. Falkoff and Berry for helping to set and maintain the direction Of the project.
