## Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis"Makes the reader feel the inspiration that comes from listening to a great mathematician." "Bulletin, " American Mathematical Society A distinguished mathematician and educator enlivens abstract discussions of arithmetic, algebra, and analysis by means of graphical and geometrically perceptive methods. His three-part treatment begins with topics associated with arithmetic, including calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers. Algebra-related subjects constitute the second part, which examines real equations with real unknowns and equations in the field of complex quantities. The final part explores elements of analysis, with discussions of logarithmic and exponential functions, the goniometric functions, and infinitesimal calculus. 1932 edition. 125 figures." |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Arithmetic | 6 |

The First Extension of the Notion of Number | 22 |

Concerning Special Properties of Integers | 37 |

Real Equations with Real Unknowns | 87 |

Equations in the field of complex quantities | 101 |

Logarithmic and Exponential Functions | 144 |

The Goniometric Functions | 162 |

HI Concerning Infinitesimal Calculus Proper | 207 |

Transcendence of the Numbers e and n | 237 |

The Theory of Assemblages | 250 |

269 | |

### Common terms and phrases

according algebraic numbers analysis analytic analytic functions angles appear applications arbitrary arithmetic assemblages axis biquadratic equation branch points circle coefficients commutative law complex numbers concept connection consider continuous functions continuum convergence coordinates corresponding course cubic equation decimal definite denumerable determined differential dihedron division edition elementary example expression fact factor finite number follows formula fractions fundamental Gauss geometric give goniometric hyperbola icosahedron infinitesimal calculus integers integral intuition irrational number lectures Leibniz Leipzig linear logarithm logical mathematicians mathematics Mathematische Annalen means method multiplication negative numbers normal curve notion obtain octahedron operations parabola parameter plane polynomial positive power series precisely prime numbers problem proof quaternion rational functions rational numbers real numbers real roots relation remarkable Riemann surface rotation and expansion schools solution sphere spherical triangle tangent Taylor's theorem theorem theory of numbers transformation trigonometric series values variable vector vertices zero

### References to this book

Handbook of International Research in Mathematics Education Lyn D. English No preview available - 2002 |