Leseprobe
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Fearless Symmetry
Avner Ash, Robert Gross
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them.
Hidden symmetries were first discovered nearly two hundred years ago by French mathematician évariste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination.
The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.
Kundenbewertungen
Galois theory, Frey curve, Quadratic formula, Permutation, Pure mathematics, Matrix group, Identity matrix, Conjecture, Root of unity, Identity element, Quadratic function, Theorem, Fermat's Last Theorem, Discrete group, Modular arithmetic, Variable (mathematics), Modular form, Empty set, Number theory, Prime number, Polynomial, Riemann hypothesis, Real number, Zorn's lemma, Prime factor, Associative property, Sign (mathematics), Geometry, Abc conjecture, Significant figures, Morphism, Simultaneous equations, Tetrahedron, Group representation, Rational number, Algebraic integer, Special case, Quadratic equation, Algebraic equation, Dot product, Elliptic curve, Wiles's proof of Fermat's Last Theorem, Commutative property, P-adic number, Solution set, Cohomology, Pythagorean theorem, Addition, Quadratic reciprocity, Divisibility rule, Representation theory, Counting, Scientific notation, Algebraic number, Equation, System of polynomial equations, Natural number, Diophantine equation, Big O notation, Absolute Galois group, Integer, Reciprocity law, Z-matrix (mathematics), Complex multiplication, Complex number, Conjugacy class, Galois group, Inverse Galois problem, Mathematician, Mathematics