Fearless Symmetry: Exposing the Hidden Patterns of Numbers.FEARLESS SYMMETRY: Exposing the Hidden Patterns of Numbers AVNER ASH AND ROBERT GROSS Mathematics is an ever-evolving discipline, but Ash and Gross assert that many non-mathematicians are under the impression that everything that can be solved has been solved. The authors, math professors at Boston College Boston College, main campus at Chestnut Hill, Mass.; coeducational; Jesuit; est. and opened 1863. Actually a university, the school's Chestnut Hill campus comprises colleges of arts and sciences and business administration, the graduate school, and schools of nursing , outline current research in mathematics and tell why it should hold interest even for people outside scientific and technological fields. The book's main focus is number theory, so readers will benefit from having studied calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value. before embarking. On the other hand the authors outline the basics of complex numbers and modular arithmetic (mathematics) modular arithmetic - (Or "clock arithmetic") A kind of integer arithmetic that reduces all numbers to one of a fixed set [0..N-1] (this would be "modulo N arithmetic") by effectively repeatedly adding or subtracting N (the "modulus") until the result is within this . Ash and Gross describe current research in number theory and explain how the rules of mathematics lead to proofs such as that for Fermat's last theorem Fermat's last theorem Statement that there are no natural numbers x, y, and z such that xn + yn = zn, in which n is a natural number greater than 2. . For their more ambitious readers, they offer math exercises. Princeton, 2006, 272 p., hardcover, $24.95. |
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