Between Elementary and Advanced Mathematics I

In mathematics, there are many topics that cannot be found in school and university standardized textbooks. Those topics are ignored mostly because they are not considered to be foundational mathematics, and are not usually needed in science and technology. It's a pity that some important and really nice topics are ignored as well. And as a result, many students are unaware ofthese nice results and the equally interesting techniques behind them. The aim of this book is to introduce to the reader a few of such interesting mathematical topics that are normally ignored by textbooks. Do you know why 1+1/22+1/32+... =π2/6?

Do you know the secrets of the equation x3-3x+1=0?

Do you know how to compute cos(2π/17)?

Do you know how to solve the integer equation x2+y2=z2?

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If you have mastered high school mathematics, and, optionally, knows a little bit of calculus and linear algebra, find the answers in this book.