Macro and Micro Mathematics' Matrix Tables: Digital, Relational and Behavioral Mathematics, A systemic approach to Matrix Analysis

ISBN-13: 9781480176966 / Angielski / Miękka / 2013 / 344 str.

Roy Hubbert

Opis

"Macro and Micro Mathematics: Digital, Relational and Behavioral Mathematics" and its supplemental text, "Macro and Micro Mathematics' Matrix Tables," are research based texts, targeted at mathematicians, college students, professors, libraries and math enthusiasts in general. Digital Mathematics is the foundation that supports Relational and Behavioral Mathematics, and includes studies of principles, which are fundamentally the embodiment of progression and regression analyses with regard to sequences, arrays and matrices. Digital Mathematics authors, legislates and enforces bylaws that govern the digital microcosm of all numeric expressions. Relational Mathematics governs the formation of internal and external relationships that exist among components of mathematical entities at their differential, sequential, composite and peripheral layers, and is divided between Micro and Macro-Mathematics. Micro Mathematics is limited to the study of internal relationships among components within the same mathematical entity; conversely, Macro Mathematics is limited to the study of external relationships among components of two or more mathematical entities. Behavioral Mathematics is the study of integers' patterns of behavior in mathematical operations. The most outstanding aspect of Digital Mathematics is its comprehension of interrelations among progression and regression, sequences, arrays and matrices. Discussions offered by Digital Mathematics occur within digital arenas where grouping constraints (comparable to associative, distributive, and commutative laws) only permit, numeric expressions with linear, variable or cumulative progression and regression as operants ("operant" is used instead of "operator"), and mathematical operations that produce similar numeric expressions as sums, differences, products and quotients. What distinguish Digital Mathematics from other publications involving matrices are its digital bylaws (i.e. digitization, de-digitization and grouping constraints), equivalences, composite to augment ratios (CARs) and operants' augment ratios (OARs). a) Digitization is the bridge between the digital and conventional domains; through digitization, the integers' digitized multiplication products were discovered, which are arrays that possess the same composite, sequential and differential attributes as their digital predecessors; arrays, in Digital Mathematics are as crucial as integers are in conventional mathematics. A lack of understanding regarding sequences and arrays' interrelationships with matrices has been a major hindrance to progress in the area of Matrix Analysis. b) Disclosures of sequences' intrinsic characteristics and systematic digital structures were provided by the discovery of de-digitization. c) Grouping constraints as digital bylaws enforce the associative, commutative, and distributive properties of integers and progressive numeric expressions, which ensure their predictability in mathematical operations. d) Equivalences, (i.e. differential, sequential and composite) offer disclosures of the functional and structural architecture of progressive numeric expressions, and integers' innate and formed relationships that occur in the formation and production of sequences, arrays and matrices. e) Composite to argument ratios (CARs) disclose the organizational structure of sequences, arrays and matrices within each digital domain. f) Operants' augment ratios (OARs) allow progressive numeric expressions, as operants, to be properly identified so their behavior in mathematical operations can be recognized and observed.