- 数形与对称性--数论几何和群论导论(英文)/国外优秀数学著作原版系列
- - 作者：(美)黛安·L.赫尔曼//小保罗·J.萨利|责编:杜莹雪//李兰静
  - 出版社：哈尔滨工业大学
  - ISBN：9787560399713
  - 出版日期：2022/05/01
  - 页数：456
- 售价：51.2

内容大纲
本书的前半部分着重于数论，以算术规则（整数的规则）作为开始。作者之后呈现了所有整除性、素数和模算术的基本思想和应用。同时介绍了群的抽象记号，并且包含了许多例子。数论的最后一个话题由有理数、实数及无穷的思想组成。在几何方面，本书涵盖了多边形和多面体，包括正多边形和正多面体的构造。它通过观察平面上的图案来研究镶嵌，特别是那些由正多边形及正多边形的集合组成的图形。本书同时研究了这些图形和图案的对称群，解释了这些群是如何在几何和数论中同时出现的。
作者介绍
目录
Preface
0 Warm-up: The Triangle Game
  Practice Problem Solutions and Hints
  Exercises
  The Beginnings of Number Theory
  1.1 Setting the Table: Numbers, Sets, and Functions
    Numbers and Number Systems
    Sets
    Functions
    Math Words
  1.2 Rules of Arithmetic
  1.3 A New System
  1.4 One's Digit Arithmetic
  Practice Problem Solutions and Hints
  Exercises
2 Axioms in Number Theory
  2.1 Consequences of the Rules of Arithmetic
    Cancelation for Addition
    Properties of-1 and 0
    Cancelation for Multiplication
    Subtraction and Division
  2.2 Inequalities and Order
    Order and Other Number Systems
    Well-Ordering
  Practice Problem Solutions and Hints
  Exercises
3 Divisibility and Primes
  3.1 Divisibility
  3.2 Greatest Common Divisor
  3.3 Primes
    Formulas for Primes
    Twin Primes and Triple Primes
    Other Conjectures about Primes
  Practice Problem Solutions and Hints
  Exercises
4 The Division and Euclidean Algorithms
  4.1 The Division Algorithm
    The Division Algorithm with a Negative Dividend
  4.2 The Euclidean Algorithm and the Greatest Common Divisor
  4.3 The Fundamental Theorem of Arithmetic
    Why We Don't Call 1 a Prime
    Prime Factorization and the GCD
  Practice Problem Solutions and Hints
  Exercises
5 Variations on a Theme
  5.1 Applications of Divisibility
    Fibonacci Numbers
    Sum and Number of Divisors
    Perfect Numbers
  5.2 More Algorithms

    Rational Arithmetic and Least Common Multiples
    Egyptian Fractions
  Practice Problem Solutions and Hints
  Exercises
6 Congruences and Groups
  6.1 Congruences and Arithmetic of Residue Classes
  6.2 Groups and Other Structures
    Cyclic Groups
    Rings
    Zero Divisors and Fields
  Practice Problem Solutions and Hints
  Exercises
7 Applications of Congruences
  7.1 Divisibility Tests
    Divisibility by Powers of 2
    Divisibility by Powers of 5
    Divisibility by 3 and 9
    Divisibility by 11
    Divisibility by 7, 11, and 13
  7.2 Days of the Week
    Calculating from the First Date of Any Year
    How to Find the Day of the Week
  7.3 Check Digits
    ISBNs and UPC Numbers
  Practice Problem Solutions and Hints
  Exercises
  Rational Numbers and Real Numbers
  8.1 Fractions to Decimals
  8.2 Decimals to Fractions
  8.3 Infinity
  8.4 Rational Numbers
  8.5 Irrational Numbers
  8.6 How Many Real Numbers?
  Practice Problem Solutions and Hints
  Exercises
9 Introduction to Geometry and Symmetry
  Practice Problem Solutions and Hints
  Exercises
IO Polygons and Their Construction
  10.1 Polygons and Their Angles
    Triangles
    Quadrilaterals
    n -gons
  10.2 Constructions
  Practice Problem Solutions and Hints
  Exercises
  Symmetry Groups
  11.1 Symmetric Motions of the Triangle
  11.2 Symmetric Motions of the Square
    Reflections and Rotations

    Impossible Motions
    Economy of Notation Revisited
  11.3 Symmetries of Regular n-gons
  Practice Problem Solutions and Hints
  Exercises
12 Permutations
  12.1 Symmetric Motions as Permutations
    Permutations and the Motions of the Square
  12.2 Counting Permutations and Symmetric Groups
  12.3 Even More Economy of Notation
    Transpositions
  Practice Problem Solutions and Hints
  Exercises
13 Polyhedra
  13.1 Regular Polyhedra
  13.2 Euler's Formula
  13.3 Symmetries of Regular Polyhedra
    Rotations of the Tetrahedron
    Tetrahedron "Flips," or Reflections
    Economy of Notation
    Rotations of the Cube
    Cube "Flips," or Reflections
  13.4 Reflections and Rotations
    Symmetries of the Octahedron
    The Dodecahedron and the Icosahedron
  13.5 Variations on a Theme: Other Polyhedra
    Prisms and Pyramids
    Other Convex and Nonconvex Polyhedra
    Diagrams (Nets) for Making Polyhedra
  Practice Problem Solutions and Hints
  Exercises
14 Graph Theory
   14.1 Introduction
   14.2 The KSnigsberg Bridge Problem
   14.3 Colorability and Planarity
   14.4 Graphs and Their Complements
   14.5 Trees
  Practice Problems Solutions and Hints
  Exercises
15 Tessellations
   15.1 Tessellating with a Single Shape
  15.2 Tessellations with Multiple Shapes
  15.3 Variations on a Theme: Polyominoes
  15.4 Frieze Patterns
    Symmetry Groups
    The Four Symmetric Motions
    Classification of Friezes
    The Seven Symmetries
  15.5 Infinite Patterns in Two and Three Dimensions .
  Practice Problem Solutions and Hints

  Exercises
16 Connections
  16.1 The Golden Ratio and Fibonacci Numbers
    The Golden Ratio and Geometry
    Constructing the Golden Ratio
    Fibonacci Numbers
  16.2 Constructible Numbers and Polygons
    Constructing √a
    Constructible Polygons
    Gauss's Construction of a Regular Pentagon
    Constructing Other Regular n-gons
  Practice Problem Solutions and Hints
  Exercises
A Appendix: Euclidean Geometry Review
  Part 1
  Part 2
Glossary
Bibliography
Index
编辑手记

内容大纲

作者介绍

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