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This lecture is the first part of a mini-course by Carsten Schneider on "Summation theory of difference rings and applications," recorded at the Centre International de Rencontres Mathématiques during the thematic meeting "Enumerative combinatorics and effective aspects of differential equations" in February 2025. Explore the summation package Sigma with emphasis on parameterized telescoping and recurrence solving for indefinite nested sums defined over nested products. Learn about the underlying difference ring theory and how these summation tools can be applied to solve complex problems in enumerative combinatorics, number theory, and elementary particle physics. The video includes chapter markers and keywords for easy navigation, and is part of CIRM's Audiovisual Mathematics Library which offers additional features like abstracts, bibliographies, and Mathematics Subject Classification.
