Mathematics

Ii papyrus rhind se puraana Egypt me mathematics ke jaankari mile hae

Mathematics (jiske chhota kar ke "maths" nai to "math" bola jaae hae), ginti (number), dhaancha (shape) aur namuuna (pattern) ke adhyan hae. Ii sabd Greek μάθημα (máthema) se aais hae, jiske matlab vigyan, gyaan, nai to sikhnaa hae.

Mathematics me adhyan karaa jaae hae:

• Ginti: jisme chij ke kaise gina jaae, bhi hae.
• Dhaancha (structure):chij ke kaise bandobast (organize) karaa gais hae, lekin ii bhi ki ii kaise rahaa hoi. Iske jaada kar ke algebra bola jaae hae.
• Place: jahaan chij hae, ii kaise arrange karaa gais, jisme iske dhaancha ke arrangement bhi hae. Iske jaada kar ke geometry bola jaae hae.
• Change: kaise chij ke biich me antar (difference) hae. Iske jaada kae ke Mathematical analysis bola jaae hae.

Applied math, asli dunia me problem ke solve kare me kaamil (useful) hae. Jon log business, vigyan, engineering aur construction me kaam kare hae, mathematics ke kaam me laae hae.

Mathematics me samasya ke suljhaana (problem solving)

Mathematics, logic ke kaam me laae ke samasya ke sulghae hae.Ek khaas aujaar jiske mathematician log kaam me laae hae, deduction. Deduction me puraana sachchaai ke kaam me laae ke nawaa sachchaai ke khoja jaae hae. Deduction ke kaam me laana, uu chij hae jon mathematics ke duusra rakam ke vigyanik soch (scientific thinking) se different hae, kaaheki usme experiment nai to interview pe nirbhar rahaa jaae hae.

Mathematician log logic aur reasoning ke kaam me laae ke general niyam (rule) banae hae, jon mathematics ke khaatir jaruri hae. Ii niyam uu jaankari ke nikaal de hai jon jaruri nai hae, tab ek niyam dher haalaat me kaam me laawa jaae sake hae. General niyam ke paae se, mathematicians dher samasya ke suljhaae sake hae, kaaheki ii niyam duusra samaya me bhi kaam me laawa jaae sake hae. Ii niyam ke theorem bola jaae hae (agar iske saabit kar dewa gais hae), nai to conjecture bola jaae hae. Jaada mathematicians non-logical aur creative reasoning ke kaam me laae ke logical proof ke paae hae.

Areas of study in mathematics

Ginti

Mathematics me ginti aur quantities ke adhyan karaa jaae hae. Ii vigyan ke ek hissa hae jisme logic of shape, quantity, aur arrangement hae. Niche dewa gais areas ke mathematics ke dher field me adhyan karaa jaae hae, jisme set theory aur mathematical logic hae. Number theory ke adhyan jaada kar ke integer ke structure aur behavior ke adhyan kare hae .

$1,2,3,\ldots$	$\ldots ,-1,0,1,\ldots$	${\frac {1}{2}},{\frac {2}{3}},0.125,\ldots$	$\pi ,\tau ,e,{\sqrt {2}},\ldots$	$1+i,2e^{i\pi /3},\ldots$
Natural numbers	Integers	Rational numbers	Real numbers	Complex numbers
$0,1,\ldots ,\omega ,\omega +1,\ldots ,2\omega ,\ldots$	$\aleph _{0},\aleph _{1},\ldots$	$+,-,\times ,/$	$<,\leq ,=,\geq ,>$	$f(x)={\sqrt {x}}$
Ordinal numbers	Cardinal numbers	Arithmetic operations	Arithmetic relations	Functions, see also special functions

Structure

Structural mathematics objects' and constructions' ke shape aur integrity ke adhyan kare hae. Isme algebra aur calculus hae.

Number theory	Abstract algebra	Linear algebra	Order theory	Graph theory

Shape

Mathematics ke kuchh hussa chij ke dhaancha ke adhyan kare hae, Ii sab jaada kar ke geometry ke adhuan ke hissa hae.

Topology	Geometry	Trigonometry	Differential geometry	Fractal geometry

Change

Some areas of mathematics study the way things change. Most of these areas are part of the study of analysis.

Calculus	Vector calculus	Analysis
Differential equations	Dynamical systems	Chaos theory