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Geometry: Seeing, Doing, Understanding 3e , 2e Elementary Algebra and Geometry are fairly standard secondary school curricula for those subjects. A number of the topics covered in A Human Endeavor e.
Nor is its topic being particularly recommended for inclusion, indiscriminately, into the school curriculum. However, it should convey some of the breadth and depth found close to the traditional school and college curricula, and encourage the reader not only to follow up on some of the historical and technical references, but to pull out pen and paper to tackle some problems of special interest. Some of the mathematics will be difficult, but I believe that it will all be accessible.
The intended audience consists of students at both high school and college who wish to go beyond the usual curriculum, as well as teachers who wish to broaden their mathematical experience and discover possible material for use with their regular or enriched students. In particular, I am concerned about two groups of students.
There are those who romp through the school curriculum in mathematics while they have yet to complete other subjects. A standard response to this situation is to accelerate them, either into calculus or into college prematurely. While this is undoubtedly appropriate for some, my experience is that very often such acceleration is counterproductive and leads to an unsettled academic experience.
Then there are those who get caught up in contest activity. It is now possible to spend much of the spring semester preparing for and writing contests, and this may have some value.
However, there are some for whom contests are not congenial and others who emphasize the short-term goal of solving problems and winning contests at the expense of proper mathematical growth.
What seems to be needed is a mathematical enrichment which starts with school mathematics, broadens it and yet is sufficiently down-to-earth that the student can explore it in an elementary way with pencil and paper or calculator. This book covers algebra, but it covers it much more deeply than typical high school courses. It would be appropriate, as Barbeau suggests, as enrichment reading for a high school student who is too advanced for the usual curriculum but has not been accelerated through it.
Many of the problems are taken from various math contests. In addition to being useful cubic equations do come up and not knowing how to solve one is embarrassing , I find these techniques to be very instructive as examples of how you could go about solving problems.
Since they are in the public domain, you can find them available online for free. PDFs are available on archive.
TCWAG BY LEITHOLD PDF
The calculus with analytic geometry