Transseries for beginners

@misc{citeulike:2320051, abstract = {The differential field of transseries was discovered independently in various parts of mathematics: asymptotic analysis, model theory, computer algebra, surreal numbers. Some feel it was surprisingly recent for something so natural. Roots of the subject go back to E'calle working in asymptotic analysis, Dahn and Go"ring working in model theory, Geddes \& Gonnet working in computer algebra, Kruskal working in surreal numbers. They arrived at eerily similar mathematical structures. But in fact no knowledge of model theory or asymptotic analysis or computer algebra or surreal numbers is required in order to understand this new, beautiful, complex object. This paper is not on the applications. But on the algebraic, analytic, combinatorial structure of the set of transseries. I am convinced it is elementary but very rich, and worth study in its own right.}, author = {Edgar, G. A. }, citeulike-article-id = {2320051}, eprint = {0801.4877}, keywords = {algebra, asymptotic, power-series, transseries}, month = {Jan}, posted-at = {2008-05-14 08:22:08}, priority = {2}, title = {Transseries for beginners}, url = {http://arxiv.org/abs/0801.4877}, year = {2008} }

TY - ELEC ID - citeulike:2320051 L3 - citeulike-article-id:2320051 TI - Transseries for beginners N2 - The differential field of transseries was discovered independently in various parts of mathematics: asymptotic analysis, model theory, computer algebra, surreal numbers. Some feel it was surprisingly recent for something so natural. Roots of the subject go back to E'calle working in asymptotic analysis, Dahn and Go"ring working in model theory, Geddes & Gonnet working in computer algebra, Kruskal working in surreal numbers. They arrived at eerily similar mathematical structures. But in fact no knowledge of model theory or asymptotic analysis or computer algebra or surreal numbers is required in order to understand this new, beautiful, complex object. This paper is not on the applications. But on the algebraic, analytic, combinatorial structure of the set of transseries. I am convinced it is elementary but very rich, and worth study in its own right. KW - algebra KW - asymptotic KW - power-series KW - transseries AU - Edgar, GA PY - 2008/Jan/31/ UR - http://arxiv.org/abs/0801.4877 ER -