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Mathematics is full of small marvels that a standard course never has time for. Math Vignettes I gathers dozens of them into short, self‑contained explorations — vignettes — that carry the curious reader across a remarkably wide sweep of the subject, from the different kinds of numbers we count with to the cryptography that keeps modern messages secret. Prerequisites are kept to a minimum and listed for each section, and the emphasis is always on insight and intuition, so you can open the book almost anywhere your curiosity points.
Inside you'll find the golden ratio and the Fibonacci sequence, complex numbers and quaternions, continued fractions and nested radicals, Diophantine puzzles from Pell's equation to Ramanujan's taxicab number, random walks and the gambler's ruin, Markov chains and queues, game theory, linear and integer programming (including the traveling salesman problem), number theory, and the ideas behind modern encryption — Caesar ciphers through RSA, hashing, and blockchain. This is a survey rather than a textbook: it favors worked examples, historical context, and pointers for further study over long proofs and problem sets. Many of the topics rarely appear in an undergraduate curriculum, so even readers with a technical background are likely to meet something new. This second edition revises and corrects the text throughout.
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