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. |
Contents
6 | |
22 | |
Concerning Special Properties of Integers | 37 |
Complex Numbers | 49 |
Concerning the Modern Development and the General Structure | 77 |
Real Equations with Real Unknowns | 87 |
Equations in the field of complex quantities | 101 |
The tetrahedral the octahedral and the icosahedral equations | 120 |
Setting up the Normal Equation | 129 |
Solution in Terms of Radicals | 138 |
Logarithmic and Exponential Functions | 144 |
The Goniometric Functions | 162 |
Concerning Infinitesimal Calculus Proper | 207 |
Transcendence of the Numbers e and я | 237 |
The Theory of Assemblages 4 | 250 |
269 | |
Other editions - View all
Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra ... Felix Klein Limited preview - 2004 |
Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra ... Felix Klein Limited preview - 2007 |
Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra ... Felix Klein No preview available - 2004 |
Common terms and phrases
a₁ according algebraic numbers angles appear arbitrary arithmetic assemblages axis biquadratic equation branch points C₁ calculation called circle coefficients commutative law complex numbers connection consider continuous functions continuum convergence coordinates corresponding course cubic equation decimal definite denumerable determined differential dihedron division elementary example expression fact factors finite number follows formula fractions function fundamental Gauss geometric give goniometric hyperbola infinitesimal calculus integers integral intuition irrational number Leibniz Leipzig limit linear logarithm mathematicians mathematics Mathematische Annalen means method multiplication negative numbers normal curve notion obtain octahedron operations parabola parameter plane polynomial positive possible power series precisely prime numbers problem proof quaternion rational functions rational numbers real numbers real roots relation Riemann surface rotation and expansion schools solution sphere tangent Taylor's theorem theorem theory of numbers transformation trigonometric series values variable vertices w₂ zero