Mathematical Elegance: An Approachable Guide to by Steven Goldberg

By Steven Goldberg

The center of arithmetic is its splendor; how it all matches jointly. regrettably, its good looks usually eludes the majority of people who find themselves intimidated by means of worry of the trouble of numbers. Mathematical Elegance treatments this. utilizing hundreds and hundreds of examples, the writer provides a view of the mathematical panorama that's either available and fascinating.

At a time of shock that American adolescence are bored via math, there's renewed curiosity in bettering math talents. Mathematical Elegance stimulates scholars, in addition to these already skilled within the self-discipline, to discover many of the unforeseen pleasures of quantitative considering. Invoking mathematical proofs well-known for his or her simplicity and brainteasers which are enjoyable and illuminating, the writer leaves readers feeling exuberant—as good as confident that their IQs were raised via ten points.

A host of anecdotes approximately recognized mathematicians humanize and supply new insights into their lofty topics. Recalling such vintage works as Lewis Carroll’s Introduction to Logic and A Mathematician Reads the Newspaper via John Allen Paulos, Mathematical Elegance will energize and enjoyment a large viewers, starting from intellectually curious scholars to the enthusiastic common reader.

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This series does have a limit: 1. You can forever get closer and closer (and, taking the series as a whole, consider the total to be 1), but you can never get a total past 1. It is not always easy to tell from inspection whether a series has a limit. As Martin Gardner points out, consider the ubiquitous “Â�harmonic series,” 1/2 + 1/3 + 1/4 + 1/8 . . The terms become increasingly smaller, leading one to suspect that the series (like 1/2 + 1/4 + 1/8 + 1/16) approaches a limit. It certainly seems to.

Judy Is a Bank Teller, But Is she a Feminist? Judy is thirty-three, unmarried, and quite assertive. A magna cum laude graduate, she majored in political science in college and was deeply involved in campus social affairs, especially in antidiscrimination and antinuclear issues. Which statement is more probable? (a) Judy works as a bank teller. (b) Judy is active in the feminist movement and works as a bank teller. Most people, correctly perceiving that Judy may well be a feminist, choose (b). But note that if (b) is true, then (a) must also be true.

39 5 Believe It or Not Start Counting However large the number of physical things (remember, the number of particles in the universe is way, way below 10100), the numbers appearing in analyses of the universe and its parts is much, much greater. In refuting the Austrian physicist and philosopher Ludwig Boltzman’s claim that molecules in an enclosed space will forever increase, mathematician Henri Poincaré showed that the molecules will return to their original state, thereby decreasing entropy.

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