Elementary Mathematics from a Higher Standpoint: Volume I: Arithmetic, Algebra, Analysis

by Felix Klein

First Arithmetic. I. Calculating with Natural Numbers.- II. The First Extensions of the Notion of a Number.- III. Concerning Special Properties of Integers.- IV. Complex Numbers.- V. Concerning the Modern Development and the General Structure of Mathematics.- Second Algebra. I. Real Equations with Real Unknowns.- II. Equations in the Field of Complex Quantities.- Third I. Logarithmis and Exponential Functions.- The Goniometric Functions.- III. Concerning Infitesimal Calculus Proper.- I. Transcendence of the Numbers e and pi.- II. Set Theory.- Appendix.- Index of Names.- Index of Contents.

Genres: Mathematics, Algebra

334 pages, Paperback

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.