Like most people, learning math was a long journey. We started by knowing the names of the numbers, counting little balls and toys, and define several arithmetic operations and build our problem solving skills through countless arithmetic drills and eventually do more symbolic manipulation in high school algebra and so on. Most priviledged students end their math journey in single variable calculus.
My math journey ended in undergraduate level. I was a math major who basically chose a few classes out of a list of rarely ever offered classes from the catalog and I graduated. The real math question that every math major should ask is this: "how am I going to make a living." Of course we can be *real* good and become professors which in turn create even more math majors. I ended up doing programming for a living. I am not a PhD/professor material.
It has been quite some time since my college years. I learned a great deal but I also forgot a great deal! One day Fermat's Last Theorem came to my mind. All I remember was it was a hard theorem that no one can prove for hundreds of years, but I don't recall what it is! One day I tried to recall what I know about calculus, I know derivative of sine is cosine, but I don't remember why! I cannot let my knowlege slip away.
Most math books fall into 2 catagories: way too easy and way too difficult. That book that says "College Algebra" thick text is title inflation. That stuff is nothing "college" about it. A harder-working 16-year-old should be able to handle that. That yellow covered stuff titled "Modern Algebra" or "Introduction to " are outrageously difficult and only for the real hardcore graduate students.And there are those especially targeted for less motivated students, which contains good materials, but often they are too short and too narrow a topic. Those also belong to the way too easy category.
Math has no boundary. I see Arithmetics/Algebra/Geometry/Trig/Calculus as one continuous subject.
Of course, calculus itself is a BIG topic if we go into great details and provide lots of homework problems. A typical textbook has a 1000 pages. That is enough to intimidate many students. Calculus is also HARD. It does require some math maturity to grasp. The slow slow pace of typical high school that take entire year to cover basic algebra and geometry concepts will have a hard time catching up. But they don't have to be just reading textbooks. They can do some fun readings outside their text.
I tried hard and couldn't find many books that cover all these topics. Actually I found one, a very well written book, titled "Mathematics: from the birth of numbers", by Jan Gullberg. This is it! It covers a broad number of topics (beyond typical high school stuff) but at a whopping size of 1093 pages.
I'd like to see a smaller one, that go over math topics in a fun way, without all that drills. Rather than looking for one, why don't I simply WRITE one? I'll present what I know, discover interesting topics that I didn't know, and relearn anything that I forgot. Here it is.
I want to write a book that I wanted to read when I was 16.
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