Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis

by Felix Klein

When 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.

Genres: Mathematics, Algebra

274 pages, Hardcover

First published January 1, 1924

Reviews

[Erickson · Rating 5 out of 5]

Very good book, advanced explanations for many things either taken for granted or new perspectives to look at things. Interesting things like impossibility to inscribe heptagon using compass and straightedge, transcendence of e and pi, etc are included with proofs, highly accessible with the presentation style.

Though in my case some topics are not quite understood e.g. Riemann surfaces due to lack of training, nonetheless the book is highly insightful. Recommended for advanced readers or those interested in advanced mathematics.