Foundations of Analysis over Surreal Number Fields is popular PDF and ePub book, written by N.L. Alling in 1987-04-01, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Foundations of Analysis over Surreal Number Fields can be Read Online from any device for your convenience.
Foundations of Analysis over Surreal Number Fields Book PDF Summary
In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given. Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand.
Detail Book of Foundations of Analysis over Surreal Number Fields PDF
- Author : N.L. Alling
- Release : 01 April 1987
- Publisher : Elsevier
- ISBN : 9780080872520
- Genre : Mathematics
- Total Page : 391 pages
- Language : English
- PDF File Size : 8,8 Mb
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