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Author: John L. Casti

Rating: 7/10

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Mathematics has come a long way in the last couple of centuries and seems that the most recent developments are too complex to discuss outside a limited circle of experts.

Is it possible then to explain to a broader audience the importance and essence of some of the later 20th century mathematical developments? This was the challenge the author set for himself, and for the most part he succeeds meeting it in this book. As the title indicates, he covers five main topics ("Golden Rules" as he calls them) in areas ranging from Game Theory (Min Max Theorem) to Optimization Theory (the Simplex Method). I appreciated the fact that he not only explains the basic theory (in high-level terms of course), but that he also complemented this with examples of practical applications for the theories. While many in the mathematics field profess that Mathematics should not be "subservient" to other sciences and it's practicalities, I always found Mathematics at its best when it finds a relationship with practice; even if that takes her a couple of years... This is certainly not a book that any person will enjoy. As the author himself warned, there is a basic mathematical foundation needed to understand the material; but one year of college-level Calculus and Algebra should suffice for most of it. This places the book within the reach of most readers with a college-level science education. I enjoyed the material, and while it doesn't give you enough depth to fully understand the theories, it does broaden your horizons and suggests paths for further study. Recommended.

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