(In the third edition, the Dedekind cut construction is sent to an appendix for pedagogical reasons.) Chapter 2 discusses the topological properties of the real numbers as a metric space. In Chapter 1, he constructs the real and complex numbers and outlines their properties. Rudin's text was the first modern English text on classical real analysis, and its organization of topics has been frequently imitated. It has been translated into several languages, including Russian, Chinese, Spanish, French, German, Italian, Greek, Portuguese, and Polish. The text was revised twice: first in 1964 (second edition) and then in 1976 (third edition). It was an esthetic pleasure to work on it." Rudin noted that in writing his textbook, his purpose was "to present a beautiful area of athematics in a well-organized readable way, concisely, efficiently, with complete and correct proofs. He completed the manuscript in the spring of 1952, and it was published the year after. After completing an outline and a sample chapter, he received a contract from McGraw Hill. Martin, who served as a consulting editor for McGraw Hill, that there were no textbooks covering the course material in a satisfactory manner, Martin suggested Rudin write one himself. Moore instructor, Rudin taught the real analysis course at MIT in the 1951–1952 academic year.
0 Comments
Leave a Reply. |