Mathematics is not a spectator sport數(shù)學(xué)不是一種觀賞性體育項(xiàng)目

內(nèi)容概要

It is often said that mathematics and music go together, and that people with a special aptitude for mathematics often have similar gifts in music.  Some music is very profound, and listeners find that there is far more in it than they appreciated at a first hearing.  A similar point can be made about an understanding of mathematics.　　This book introduces the reader to various topics in mathematics and is intended for precocious high school students and college students just beginning their study of mathematics.  The topics discussed in this book include a variety of results in number theory involving squares, and also complex numbers, early algebraic ideas such as the Euclidean algorithm, geometrical constructions created by the Greeks, and more recent topics such as group theory.

書籍目錄

Preface1  Squares  1．1 Square and Triangular Numbers  1．2 Pythagoras’S Theorem  1．3 The Equation a2+b2=C2  1．4 Sum of TWO Squares  1．5 Complex Numbers2 Numbers。Numbers Everywhere  2．1 Difierent Bases  2．2 Congruences  2．3 Continued Fractions  2．4 The Euclidean Algorithm  2．5 Infinity3 Fibonacci Numbers  3．1  Recurrence Relations  3．2 Fibonacci and Lucas Numbers  3．3 The Golden Section4 Prime Numbers  4．1  Introduction  4．2 The Distribution ofPrimes   4．3 Large Primes  4．4 The Riemann Hypothesis5 Choice and Chance  5．1  Arrangements and Permutations  5．2 Binomial Coemcients  5．3 Probability．6  Geometrical Constructions  6．1  Ruler and Compasses    6．2 Unsolvable Problems  6．3 Properties of the Triangle  6．4 Coordinate Geometry  6．5 Regular Polyhedra7 The Algebra of Groups  7．1  Introduction  7．2  Groups  7．3 Subgroups  7．4 Permutation Groups  7．5 Further Material  7．6 Groups of Small order  7．7 Dihedral and Polyhedral GroupsReferencesIndex

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