NeutroGeometry and NeutroAlgebra: A Mathematical Framework for the Sustainable Development of College Music Education in the New Era

Abstract

This paper develops a precise and rigorous mathematical framework for 
NeutroGeometry and NeutroAlgebra, aiming to support the sustainable development of 
college music education in the new era. These theories generalize classical algebraic and 
geometric structures by introducing partial truth, indeterminacy, and partial falsehood, 
reflecting the dynamic and flexible nature of musical learning and performance. We 
define the fundamental laws, establish key equations, and provide clear examples. 
Additionally, we propose innovative extensions to these concepts, showing how they can 
transform the evaluation and growth of college music education to be more adaptive, 
creative, and sustainable. 

DOI: 10.5281/zenodo.15588316