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Beyond Calculus: Modernizing System Modeling and Computational Methods

Authors:
Pavel Loskot

Keywords: abstract algebra; algebraic geometry; algebraic topol- ogy; calculus; curriculum; mathematical object; modeling

Abstract:
Mathematical modeling has been used for centuries to create understanding of natural phenomena, and recently, to enable constructing man-made systems. Computational models in engineering are mostly based on calculus and linear algebra, and they are now well-established. However, the rapidly rising complexity of modern intelligent and autonomous systems calls for rethinking the present modeling strategies to allow beyond calculus modeling with different levels of abstractions, semantics, and information granularity. This vision paper offers a non-mathematical outline of selected advanced mathematical topics, which can be adopted not only to enhance modeling methods in engineering, but also to modernize engineering curricula by bridging the gap between engineering and mathematics. The key idea is to allow algebraic manipulations of mathematical objects, and assigning numerical values to these objects, so they can be used as natural data structures within mathematical models.

Pages: 20 to 26

Copyright: Copyright (c) IARIA, 2026

Publication date: March 8, 2026

Published in: conference

ISSN: 2519-8432

ISBN: 978-1-68558-360-6

Location: Valencia, Spain

Dates: from March 8, 2026 to March 12, 2026