Mathematics الرياضيات

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Browsing Mathematics الرياضيات by Author "Ahmad Zeyad Mahmoud Al-Awawdeh"

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    Dynamic Set Theory and Extensions on Lagrange Squares: New Theorems, Philosophical Insights and Applications
    (Al-Quds University, 2025-05-14) Ahmad Zeyad Mahmoud Al-Awawdeh; أحمد زياد محمود العواودة
    This thesis presents an innovative mathematical and philosophical development by establishing a connection between Lagrange Four Square Theorem and five well-known sequences: the sequence of natural numbers, square numbers, cubic numbers, triangular numbers, and the Fibonacci sequence. This integration resulted in the construction of five new sequences, each of which has been rigorously analyzed and accompanied by fourteen original theorems, all proven within a strict methodological framework.. This thesis reflects a multifaceted approach that bridges the rigorous structure of number theory with the philosophical perspective of mathematics. It introduces a novel principle in the philosophy of mathematics, termed "coexistence of opposites within a single entity", which opens new horizons for understanding contradiction and integration within the mathematical framework itself. Furthermore, the research establishes connections with fundamental issues in the philosophy of mathematics. The developed sequences were also utilized in various applied domains, including a reimagining of the classical game of chess based on the framework of Lagrange’s foursquare theorem, as well as the resolution of real-world problems in fields such as physics, cryptography, economics, and engineering—demonstrating the practical value of the proposed theorems. In the concluding part of the thesis, a new theoretical framework proposed under the title ―Dynamic Set Theory,‖ which reimagines mathematical sets as mutable entities rather than fixed ones—contrasting with the classical perspective established by Cantor. The logical, philosophical, and algebraic foundations of this approach presented, positioning it as a fertile ground for future research.