**
MATH** a.k.a. ** Mathematics**
Last updated on
2017/2560
1
12,
a full
moon day;

in Mathematics, relationship between 2 numbers is; Radical102;

division operator; Also see: Operator IFF Mathematics; Radical286;

Time.Space.Action: SYNC,
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.

IFF problems of infinity exists (e.g.

floating points
of square root 2 ≡ decimal expansion ≡
problems of infinity
a.k.a. SQRT2;

floating points
of square root 3 ≡ decimal expansion ≡
problems of infinity a.k.a. SQRT3),

use
mantissa point
doko
WHERE truncating points
are at e.g. (2^3) a.k.a. 8, (2^4) a.k.a. 16, (2^5) a.k.a. 32, (2^6) a.k.a. 64,
(2^7) a.k.a. 128, (2^8) a.k.a. 256, (2^9) a.k.a. 512,
1K a.k.a. (2^10) a.k.a. 1024, (2^11) a.k.a. 2048, (2^12) a.k.a. 4096, (2^13)
a.k.a. 8192, (2^14) a.k.a. 16384, (2^15) a.k.a. 32768, (2^16) a.k.a. 65536,
(2^17) a.k.a. 131072, (2^18) a.k.a. 262144, (2^19) a.k.a. 524288, (2^20) a.k.a.
1048576, ... ; notice that C
Sequence Number (structural)
WHICH is
beyond (dimensional, directional, numerological)
starts at 2^20, 2^30, 2^40, ... ; also notice that
20 (i.e.
middle
JUN) water drops
alike characters, inside the catalog of syllables
(**NIPPON**, also see:
Nippon
Syllabary);

__ K-Theory__ and its D-branes,

__ NCG__, Non Commutative Geometry: common usages
are "metric-tensor" to determine

__ 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 ... ;

For basic understanding of WHAT is super symmetry, also see: Monbusho level knowledge enhancement idea ♯ 146; Super Symmetry;

two; Radical7;

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
**object**s are (2 and 3)
vector directions, __
ACT2 and
ACT3__ 2*5 JUN time,

IFF (2*6) dimensional, also see: 8;

**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** (also known as language of
symmetry; also
read the book: Page 103, Beyond Einstein, Michio Kaku and Jennifer Thompson,
1995): 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 ... ];

O means **O**rthogonal;
catalog
groups
of
types
into
7;
1
class
is called O (N);
atom
itself is O (
3); In 1800s, Sophus Lie
(Norwegian)
discovered a set of symmetries called SU (N) WHICH rotates complex number e.g.
SU (1) with 1 photon, e.g. SU (2) with 1 photo and 1 neutron;
Notice THAT prior to superstrings (1 word would be "spin"); (SU
(2) x U (1)) with 1 electron and 1 neutrino; SU (3) rotates
3 sub nuclear
particles; SU (
5), the smallest GUT theory (1 electron, 1 neutrino, 3 quark);
IFF N (quark) and then SU (N); E (N) WHERE N <= 8 also known
as E(8) group, and superstrings' symmetry begins, and higher dimensions begins
e.g. 8, 10, 26, ... ; Unified Theory adapted Lie
Groups in 1900s;

But, since 2000s,
this DOMAIN
has implemented (e.g. C Sequence Number) both
10 (2*5,
dassa,
10, ... ,
dassa became desu thousand years ago) and
26
(numerological dimension) for thousands
of years
in software approach (hardware approach is intentionally left for oriental e.g.
NIPPON; notice that
Myanmar
has been __non-semi-conductor nation__ and
this DOMAIN developer is out of hardware design knowledge e.g. HOW to embed
Idea Processor into GPS ? e.g. HOW to embed
GPS into computer? e.g. HOW to embed all
basic calculator, dictionary,
and translator to be AI ? ) e.g.
web
site as
Triangulation
System in the Internet,
therefore, please do not change its
aesthetics (also see:
philosophy);
Therefore, 21st century's power e.g. Gravity & IT, e.g. Manmade Global
Weather (service),
e.g. directional gravity for elevating automotives, ... are military top secrets
... , therefore, NOT available to public; WHICH is beyond stars are groups in
constellations (also known as
Lie Groups);

2100s predictions: gene therapy systems, gravity dimension computers, teleportation methods, ... ; There will be Rakhine (an ethnic tribe of Union of Myanmar) for sure WHO will ... ;

**
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, ... ;

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. ... ;

IFF distance approximation, also see: Monbusho level knowledge enhancement 1, idea ♯ 178, Distance Approximation with C Sequence Number, Math approach, HOW gravity spots as induction in 1 computer ... ;

**Differential Equation: Ordinary vs. Partial**

Function of 2 variables can be defined as y = f (x) OR x = f (y); doko 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, d x = f' (t) d t 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 d t 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. a_{i1} x_{1}
+ a_{i2} x_{2} + a_{i3} x_{3} + ... + a_{in-1}
x_{n-1} + a_{ in} x_{ n}
= c_{ i}; 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, X Y coordinate, X Y 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;

mathematical operators, also see: AI FONT;

**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;

**
Transform**: patterns
can be transformed
to-and-from between analog and digital; doko
WHERE analog is a.k.a. harmonic motion, and digital is a.k.a. discrete (isolated
set of
points
(
dots));
Schematic Symbols'
SHARP 's

**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
form y = ax^{2} + 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__;

...