{"product_id":"metastructural-unification-mathematics-volume-unifying-algebra-geometry-and-probability-9781764309721","title":"Metastructural Unification ( Mathematics Volume ): Unifying Algebra, Geometry and Probability","description":"\u003cp\u003e • Author(s): John Chang\u003cbr\u003e • Publisher: Universal Publishing\u003cbr\u003e • Publisher Imprint: Universal Publishing\u003cbr\u003e • BISAC: Research \u0026amp; Methodology\u003c\/p\u003e\u003cp\u003e\u003cb\u003eIntroduction to\u003c\/b\u003e\u003cb\u003e《\u003c\/b\u003e\u003cb\u003eMetastructural Unification ( Mathematics Volume ): \u003c\/b\u003e\u003cb\u003e \u003c\/b\u003e\u003cb\u003eUnifying Algebra, Geometry, and Probability\u003c\/b\u003e\u003cb\u003e》\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eThis book is not a collection of papers addressing isolated mathematical problems, but a systematic work that seeks to unify algebra, geometry, and probability at the structural level. The author proposes a unified structural grammar centered on the triad \u003cb\u003eDot - - Line 1 - Circle Ο\u003c\/b\u003e, revealing the intrinsic isomorphic relationships among the three foundational mathematical languages across different levels.\u003cbr\u003eGuided by a \u003cb\u003ering-structured framework\u003c\/b\u003e, the book develops mathematical problems through multiple hierarchical layers.\u003cbr\u003eAt the \u003cb\u003eThird-Ring level\u003c\/b\u003e, it systematically examines represent-tative problems such as the generalized Goldbach conjecture, Fermat's Last Theorem, the \u003ci\u003eabc\u003c\/i\u003e conjecture, as well as the Poincar� problem, geodesics, prime number distributions, and spectral statistics, demonstrating their unity in structural roles.\u003cbr\u003eAt the \u003cb\u003eFourth-Ring level\u003c\/b\u003e, the discussion advances to selected topics including the Langlands program, higher-order \u003ci\u003eL\u003c\/i\u003e-functions, noncommutative geometry, Ricci flow, many-body random systems, and high-dimensional spectral statistics, revealing a unified mechanism underlying \u003cb\u003eexistence, stability, and generation\u003c\/b\u003e.\u003cbr\u003eThe central thesis of this book is that algebra, geometry, and probability are not parallel disciplines, but manifestations of the same structure expressed in different languages. Through unified formulations and structural closure analysis, the author presents a clear path from local conditions to global structures, offering a new perspective on the deep unifying principles of modern mathematics.\u003cbr\u003eThis book is intended for readers interested in foundational mathematical structures, cross-domain unification theories, and advanced mathematical thought. \u003cp\u003e\u003c\/p\u003e","brand":"Universal Publishing","offers":[{"title":"Paperback","offer_id":47594056581271,"sku":"9781764309721","price":2014.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781764309721.webp?v=1774984540","url":"https:\/\/atlanticbooks.com\/products\/metastructural-unification-mathematics-volume-unifying-algebra-geometry-and-probability-9781764309721","provider":"Atlantic Books","version":"1.0","type":"link"}