## Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, AnalysisWhen the mathematician Felix Klein first went to university, he was surprised at just how little what he had learned up to that point was relevant to his new studies. Professors had their own interests, and these they conveyed without regard for the math students of the future that these prospective secondary schoolteachers would one day instruct. Elementary Mathematics from an Advanced Standpoint was written to help remedy that problem. Though highly regarded as one of the finest mathematical minds of his day, Professor Klein took a great deal of interest in guiding teachers and "reducing the gap between the school and the university." Readers will come away impressed at the clarity of Klein's writing, and the ease with which he conveys complex mathematical ideas. Divided into three parts-arithmetic, algebra, and analysis-and covering such topics as complex numbers, real equations, and logarithmic and exponential functions, Klein's classic is essential reading for math instructors and students planning to become math instructors. German mathematician FELIX KLEIN (1849-1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Geometry and Famous Problems of Elementary Geometry. |

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### Contents

1 | |

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 |

Concerning Infinitesimal Calculus Proper | 207 |

Transcendence of the Numbers e and as | 237 |

The Theory of Assemblages | 250 |

269 | |

### Other editions - View all

Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra ... Felix Klein Limited preview - 2004 |

### Common terms and phrases

according actually algebraic angles appear apply arbitrary assemblages axis beginning branch calculation called circle coefficients complex concept concerning connection consider considerations construction continuous convergence corresponding course curve decimal defined definite detail determined differential direction discussion division edition element entire equal equation essential example expression fact factors field finite follows formula fractions function fundamental geometric give given important infinitely instruction integral interesting known limit logarithm mathematics means mention method multiplication namely natural negative normal numbers obtain once operations origin plane positive possible precisely present problem proof quantities question rational relation remarkable represent result roots rotation satisfy schools sense separate sides simple solution space sphere surface tables theorem theory things transformation triangle trigonometric unit values volume zero