Mathematics     Last updated on 2010     8     25, a full moon day;

Time.Space.Action: SYN, ASYN, ... , Mathematics, some people like, some people dislike, you do not need several years of learning mathematics to know 5W1H of mathematics, but you may need a few hours of teaching from a genuine math teacher to understand all about mathematics; After understanding all about mathematics, and then time to do your ...  Do your own math, bring a common calculator, press 2, i.e. in ACT1 stage, and then press square root sign, and then keep pressing again and again √ square root 22 times, and notice that result prompts 1, and then try to mathematically prove that HOW a calculator slices time period, WHY only 22 times, WHERE is 2 * 7, and so on ... ; In Korea, average high school students can do math without using calculator, can perform up to 99 * 99; Try to compete math to Korea's new generation ... ; Try to compete, try to participate in the world's open math contests; Since 1985, 1 + 1 = 1 can be proved by algebra, therefore be very careful in equations, formulations, ... ;   The following information contents express the current up-to-date basic-understanding of mathematics;

2 inconsistencies in math are problems of infinity and problems of "cracks" WHICH kill symmetries;   Consider the image which represents dark, earth, sun altogether, this one & only the Sun [ just before noise in ACT2, the red line at top, visible by space imaging there is nothing out there except 4 planet prediction, just before dawn in ACT1, ... ] image might be the 1st crack of our universe's cracks, and yellow colored character represents the Earth, approx. 35+ years old information of the Sun in our universe; Only restricted people from higher civilization can solve ... ; The whole character Red + Yellow is king. And, notice that especially in this "the 1st crack of our universe", the gap exists, and the 1 gap might be for 1 tangent a@t 1 time of our universe a@t 1 dimension IFF dimensional hyperspace craft's retrospective in 1D. WHY red color as the 1st crack of our universe? Human beings perceive? also read Buddha Abhidhamma.

 

K-Theory and its D-branes, M-Theory and its strings, Unified Strings theory, ... , are all try to prove particles' vectors bundles ... ;

 

NCG, Non Commutative Geometry: common usages are "metric-tensor" to determine 2 points in space's length for each abstract notion of manifold, quantum field theory and its space-time, billions dollars cost so called non-trivial quantum relationship in commutation is NCG; Nuclear power of Western civilization was in 20th century only; To accomplish the ACT 2 stage, all nuclear power must be destroyed unconditionally;

 

Super Symmetry & Super Gravity, must learn Chinese characters, because i.e. artificial energies, artificial lights, pressure machine engines, gravity machines, MRI(s) and PMD, remote-virtual-electricity, vertical EM scanner(s) and reflector(s), laser(s), ... , since 1980s ;

Characteristic classes, Fiber bundles, and Index theorems, ... , are related to dimensional space, hyperspace, ... ; Symmetry for each dimension; And very advanced, very limited, very classified, ... ;

Also see: Relational Algebra, RDBMS, since 1970s, along with index theorems ... ;

 

Homology vs. Homotopy  

Homological common usages are 1D circle, 2D circular disk, boundary, chains, homotopy complexes, simplexes, ... ;

Homotopy is a relation between 2 mappings; Homotopy common usages are contractibility, hole [also see: worm=hole], homotopic mapped loop, homotopy groups, loop, path, ... ; In Java language, 2 common mappings are JPA inheritance mapping, and JPA relationship mapping;

Remark: after understanding a path to be integrated, partially differential to each Left, and Right as a chain(s), and then try to understand 2-spin strings interaction, ... ; Also see: Pairs of sticks;

ACT2 and ACT3 objects are ACT2 2 and 3 vector directions [also see: sony.net], ACT2 and ACT3 2*5 JUN time, ACT1 and ACT2 2*7 lunar co-existences [full moon day & no moon day, also see: \Info\Help\usamyanmar.htm], ACT3 3 to 1 dimensions, ACT1, ACT2 and ACT3 4 planets prediction [2500+ years old information in Buddha calendar], ACT2 distance to SUN < distance to MOON, ... , and,  

ACT2 and ACT3 subjects are ACT2 2 times daily tidal water [also see: globalsuzuki.com], ACT1 holes as no existence of the SUN, ACT3 horizontal and sectional gray scales [also see: \Info\index.htm], ACT1 and ACT2 stars as no existence of the SUN [also see: ntspace.jp], ACT3 very very very dark environment [also see: 4PP + JUN = 6, and 6 has been defined in Abhidhamma], ... ;

 

Differential Forms vs. Differential Geometry

Differential Forms: common usages are dynamics, integral-able conditions, ... ;

Differential Geometry: common usages are coordinate systems, covariant derivatives, metrics, curvature in coordinate, curvature in non-coordinate, ... ;

 

Lie Groups: common usages are differentiable-manifold, killed vectors, lie-algebras representations, lie-derivatives, lie-matrix representations, ... ; Also see: 2-point distance to n-point distance;

IFF ACT2 ACT3 space mathematicians, also see: 2,3 dimensional distribution formula designing and engineering, [ for near future ACT2 space public traveling ... ];

 

Analysis of Complex vs. Analysis of Real

Real: common usages are real function as isomorphism, real function as fix-point(s), and real function as mapping; Topologies such as neighborhoods, homeomorphisms, invariants, sets, ... ;

Complex: common usages are complex variables, space, strings representing as functions, surfaces, ... ; Also see: Complexity Region;

 

Probability & Statistics

Quantum mechanics in physics proposed, and demanded probability and statistics; Common usages are mean, quantitative counting of distinguishable objects, qualitative counting of distinguishable objects, quantitative counting of indistinguishable objects, qualitative counting of indistinguishable objects, variance, ... ;

 

Approximation Method

Fuzzy set was condemned in 20th century by western nations, but unofficially, however eastern nations accepted; In 21st century, so many proofs of so many new technologies make people around the globe convince that fuzzy set is the way to do controls; Whenever a problem cannot be solved, approximation method is needed; Large perturbation +, saddle-point integration, series' expansions in power, small perturbation -, ... are not in exact-closed-form, therefore, cleverly guessing of approx. ... ;

 

Differential Equation: Ordinary vs. Partial

Function of 2 variables can be defined as y = f(x)   OR   x = f(y); WHERE y can be defined by function of x,   OR   x can be defined by function of y; IFF y = f(x) can also be written as dy = f'(x) dx, to do increment-approximation of the given function y = f(x) as d derivative of the function times  times = * = x = multiplication, ...  the increment of independent variable;

For example, dx = f'(t)dt means increment-approximation time t assuming that orbital synchronization time t of the given function i.e. x = f(t) as d derivative of the function * the increment of independent variable in 3-to-1 dimension as x,  WHERE in our universe, 3 planets' almost tangent valued gravitational waves cause 1 earth's full moon day ... ; In this case, derivative dt is partially calculated for partially delay time, partially artificial energies, partially artificial lights, and so on ... ; Also see: Time . Space's 3 for 3 dots in our universe ... ;

 

Algebra: Linear

linear equation must be express 1st, i.e. ai1 x1 + ai2 x2 + ai3 x3 + ... + ain-1 xn-1 + ain xn = ci; And then express the displacements either in matrices, or in vectors; Properties of abstract matrices are asymmetric, characteristic equation, determinant, inverse, symmetric, unitary, ... ;

 

Geometry: Analytical

Algebra and geometry; Geometric entities such as conic-sections, planes [such as: 2D plane, 3D plane, Polar plane, spherical coordinate, XY coordinate, XY plane, ... ], Sphere think circle in 2D becomes sphere in 3D, so called solid geometric entity, ... ; 5W1H algebraic equations for each geometric entity is called analytical geometry;

 

Multiple Variables vs. Single Variable

Multiple variables' abstract functions, i.e. f(i, j, k, ...); Thus d derivatives becomes in partial, or/and, in a whole; In 2D, 3D space, integration of a path, integration onto a surface, are all based on directional d derivatives; Also see: evolute, and understand a curve's tangent(s) cause another curve, after understanding the directional d derivatives, partially or/and whole functionalities become designers' mathematicians' engineers' developers' 5W1H ...  concepts, ideas, logics, and so on ... ;

Single variable's abstract functions;

 

Trigonometry

Common usages are right-triangle(s), trigonometric functions of sine, cosine, tangent, ... ;

 

Geometry

2D, 3D, ... , Common usages are geometric shapes in 2D, geometric shapes in flat, 2D XY planes, similarity, symmetry, ... ;

 

Algebra

Linear equation of form y = ax + b;

Quadratic equation of from y = ax2 + bx + c;

For advanced mathematicians only: solve and prove that the statement 1 + 1 = 1 can be proved by algebra, in a characteristic of Space.Action's 2-spin-strings, however, WHEN Time.Space concerns in ACT2, or ACT3 stages, HOW to prove 2 fuzzy sets { ... can also be proved as 1 f(x) of 1 fuzzy set { ... ; Question is whether Time.Space OR Timeless?

For Monbusho level developers only: 2500+ years old Myanmar's original document has been based on 7, and 2 * 7, in lunar orbits, 22 times of square root of 2, result prompts 1, mathematically prove that the 4 Planets Prediction diff in Space Time vs. Natural Time; WHY 22 times, HOW 2 and 7 relates to each other, ...

 

Basic mathematics Be very careful, since 1985, 1+1=1 can be mathematically proved by algebra

Analytical skill enhancement by studying relationship among point, line, angle, and plane; Parallel, NOT parallel proofs; Postulated parallel; Decision and reasoning skill enhancement of fuzzy logic, illogical logic, logical logic, relative truth logic, universal truth logic; Direct proof vs. indirect proof [Also see: ACT1 Theoretical Law To ACT2]; Triangle congruence, property, and similarity; Equality property of triangle vs. Inequality property of triangle; Equilateral triangle, Isosceles triangle, centralized triangle; ASA SAS SSS triangle congruence; Quadrilateral & polygon; Polygon property; Quadrilateral property; Area analysis of perimeter of quadrilateral; Circle vs. arc, angle, chord, tangent, ... ;

Linear equation vs. Linear expression; Slope form; Intercept form; Slope form AND Intercept form; Linear equation represents graph; Structure of Equation vs. System of Equation; Simultaneous equation & its Graph; Inconsistent system; Dependent System; Polynomial; Monomial vs. Polynomial; Simplified polynomial; Polynomial adding; Polynomial subtracting; Polynomial multiplying; Polynomial dividing; Polynomial pattern; Factor; Composite number; Prime number; Square number; Monomial factor vs. Polynomial factor; Diff of 2 square factoring; Quadratic equation, expression, function; Quadratic solution, by factoring, graphing, square rooting, squaring, formulating, ... ;

2D geometric figures; Point, and then displacement of points, Line; Plane & Coordinate; Angle; Triangle; Quadrilateral; 2D area vs. 2D perimeter geometric figure; Area vs. Perimeter; Unit & Dimensional Area; Parallelogram area vs. Parallelogram perimeter; Trapezoid area vs. Trapezoid perimeter; Circle, Cycle, Eccentric cycle; 22/7 circular part & its measurement; 3D geometric figures; Polyhedral; Platonic solid & sphere; Surface area vs. Volume [Balancing: non-object vs. object]; Dimensional state of solid; Symmetry vs. Balance; Symmetrical line & Tessellation; Kinetic motive rotation; Reflection, Glide reflection, and basic translational energy; [ACT3 coordinate-less D number];

Fundamental mathematical operations; Algebraic thoughts; Variables; Exponents; Large number vs. Small Number; Operational orders; Distributive property vs. Others; Integer; Coordinated integer graph; Integer's origin; Integer adding; Integer subtracting; Integer multiplying; Integer dividing; Absolute value vs. relative value; Real number; Rational number; Factoring; Squares and Square Roots; Irrational number; Pi is 22/7 [also see: ACT3 108 configuration & C108.GIF], pairs of sticks; Real number; Equation becomes structural by using variable; Solution oriented IQ enhancement by solving basic equations; Equation represents graph; Equivalent object balancing equation of LEFT = RIGHT; Algebra application; Ratio vs. Proportion; Area vs. Perimeter; Problem solving skill enhancement of time, distance, and rate, traditional concept of Time.Space.Action;

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