TL;DR
This paper introduces transseries as a comprehensive mathematical framework extending real numbers, highlighting their algebraic, combinatorial, and analytic structures, and explaining their applications across various mathematical fields.
Contribution
It provides a beginner-friendly exposition of transseries, detailing their structure, operations, and relevance for non-specialist mathematicians.
Findings
Transseries form a large ordered field extending real numbers.
They incorporate operations like exponential, logarithm, derivative, and integral.
Transseries are applicable in asymptotic analysis, model theory, and computer algebra.
Abstract
From the simplest point of view, transseries are a new kind of expansion for real-valued functions. But transseries constitute much more than that--they have a very rich (algebraic, combinatorial, analytic) structure. The set of transseries is a large ordered field, extending the real number field, and endowed with additional operations such as exponential, logarithm, derivative, integral, composition. Over the course of the last 20 years or so, transseries have emerged in several areas of mathematics: asymptotic analysis, model theory, computer algebra, surreal numbers. This paper is an exposition for the non-specialist mathematician. All a mathematician needs to know in order to apply transseries.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.