Monday, June 23, 2014

Skimpression of Book 2

     The first book I reviewed was Euler: The Master of Us All William Dunham. I liked how the author presented the book so I decided to read (skim) another one of his books, Journey Through genius. The book is a nice read, it gives a broad view of the some of the greatest mathematicians, and their works, who ever lived. The book reads in chronological order, so you get a taste of each generation of mathematicians. This means the book starts out at around 300 B.C where was still young. Therefore, the first five chapters talk a lot about old school geometry, which I'm not really a fan of so I skimmed through those pretty fast. Though, the first chapters talks a little bit about transcendental numbers (numbers that are not solutions to any polynomial equation with integer coefficients); so I read that and it was pretty interesting. Then chapter 6 discusses Cardano and his cubic formula. It's a good chapter, but the first book I read discussed Cardano pretty extensively so I didn't spend to much time on chapter 6.
     No book about mathematical, or scientific, geniuses would be complete without Issac Newton (chapter 7). So in that chapter you get to learn more about him and his works. The author gives a good explanation of Newton's binomial theorem, which is so widely used in many areas of mathematics; so it's worth it to read and understand his explanation.
     Then the author gives two good chapters on Leonhard Euler himself. I pretty much knew everything he had to say in them; but, if you haven't read about Euler, the two chapters should convince you to learn more about him (and read Euler: The Master of Us All). 
     Now comes the good stuff, chapter 11: The Non-Denumerability of the Continuum. One of my favorite subjects in math is infinity. This chapter discusses Georg Cantor and his great work on infinite sets. If you don't know much on cardinality, you will love this chapter. The concepts of countability and different levels of infinity is so mind blowing, I just love Cantor's work. Though, many mathematicians of his time thought he was crazy for coming up with this stuff. I just want to give them a good punch in stomach.
     Then we have chapter 12, which is essentially a continuation of chapter 11, which means it's awesome. This chapter has Cantor's proof that the cardinality of any set A is always smaller than the cardinality of the power set of A. This theorem is powerful because it works for infinite sets as well. Though, the actual proof in the book was long and a bit difficult to understand. Georg Cantor was like Euler in a way, he helped other mathematicians not be so scared of infinity, as Euler did with imaginary numbers.
     Overall, this is a fine read for anyone interested in mathematics, and science overall. William Dunham touches upon pretty much all my favorite (and maybe yours) mathematicians. He gives a number of proofs, so there is plenty to learn in this book; it's not just a leisure read. I would actually recommend giving this book to any freshman math or science major; it would inspire them to keep working hard in their field. Personally, I would read any book by William Dunham, he's a good author.

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