# गणित

ढाँचा:Nep

**गणित** सङ्ख्या, संरचना, दिक र परिवर्तनआदिको वैज्ञानिक अध्ययन हो ।

यस्ता शिर्षकहरूको अध्ययन गर्ने हुनाले गणितले वस्तु र धारणाहरूबारे बयान गर्न अमूर्त (सरलतम,कम विशिष्ट) वस्तुहरूको प्रयोग गर्दछ । यसको सरलतम उदाहरण सङ्ख्या हो । यथार्थ जगतमा २ वटा र २ वटा स्याउ जोडदा ४ वटा स्याउ हुन्छ ,२ वटा र २ वटा ईट जोडदा ४ वटा ईट हुन्छ ,अतएव गणितमा यस कथनलाई सामान्यिकरण गरी यस्तो कथन बनाइन्छ :२+२=४ । यसलाई अंकगणित भनिन्छ ।

एउटा अर्को सरल उदाहरण समूह सिद्धान्तबाट हेरौ ।.यदि सबै काला चरा काला छन र एउटा चरा कालो छैन भने त्यो कालो चरा होइन । यदि सबै हिउ सेतो हुन्छ. र सेतो नहुने अर्को कुनै कुरो छ भने त्यो हिउ होइन।.गणितमा यस्तो अवधारणालाई अमूर्त बनाउदै हामी भन्छौ :यदि **अब**को एउटा उपसमूह हो भने **-ब-अ**को उपसमूह हो । उदाहरणका लागि, यदि तपाइसंग भएको वस्तु कालो छैन भने त्यो कालो चरा हुन सक्दैन ।

यसरी कुनै कुरा अभिव्यक्त गर्नका लागि सामान्य मार्ग पहिल्याइ सकेपछि गणितले एकै पटकमा धेरै समस्याहरू हल गर्ने गर्दछ ।हुन त हिउं र कालो चराको उदाहरण गणित बिना पनि बुझ्न सकिन्छ तर जटिलतर समस्याहरू भने गणितको सहयोगले सजिलै बुझ्न सकिन्छ । कहिलेकांहि गणितले यथार्थ जगतमा अहिलेसम्म भेउ नपाइएका अवधारणा र नियमहरूका बारेमा पनि अध्ययन गर्ने गर्दछ । यस्ता अध्ययनका नतिजाहरू यथार्थ जगतलाई राम्रोसँग बुझ्नका लागि पछि उपयोगी हुन्छन ।

गणित भन्ने शब्द संस्कृतबाट आएको हो।

गणितिय prediction is the basis of [रा[hard science]], wदछ ।hich almost always uses equationतबारेs to preथार्थ जगतमाdict events in physics. The philosनभनेophy of science explores this. However, creatingदछ । mathematics is clearly a [[human छsciencएउ The philosophy of mathematics explores these issues, and others regarding how mathematics fits into संगphilवधारणाosophy, ethics अण्य्व्यैअइक्क्तार्and real life.

थ == Important themes in mathematics ==

अले

ओगिHere is a possible grouping of mathematical areas and topics.

### मात्रा

गिन्ती, नाप, र नाप पत्ता लगाउने तरीकाको विषय हो।
कहिलेकंहि

|  |  |  |  |  |
| --- | --- | --- | --- | --- |
|  WIKINIUM\_MATH\_PH\_0  |  WIKINIUM\_MATH\_PH\_2  |  WIKINIUM\_MATH\_PH\_4  |  WIKINIUM\_MATH\_PH\_6  |  WIKINIUM\_MATH\_PH\_8  |
| प्राकृतिक सङ्ख्या | पूर्णाङ्क | अनुपातीय सङ्ख्या | वास्तविक सङ्ख्या | संयुक्त सङ्ख्या |

अंक – प्राकृतिक सङ्ख्या – पूर्णाङ्क – अनुपातीय सङ्ख्या – वास्तविक सङ्ख्या – संयुक्त सङ्ख्या – Hypercomplex numbers – Quaternions – Octonions – Sedenions – Hyperreal numbers – Surreal numbers – Ordinal numbers – Cardinal numbers – *p*-adic numbers – पूर्णाङ्कको अनुक्रम – गणितीय अचल – सङ्ख्याका नाम – अनन्तता – आधार
### परिवर्तन

Ways to express and handle change in mathematical functions, and changes between numbers.

|  |  |  |  |
| --- | --- | --- | --- |
|  WIKINIUM\_MATH\_PH\_10  |  |  |  WIKINIUM\_MATH\_PH\_12  |
| अंकगणितीय | क्याल्कुलस | भेक्टर क्याल्कुलस | गणितीय एनालाईसिस |
|  WIKINIUM\_MATH\_PH\_14  |  |  |
| Differential equations | Dynamical systems | Chaos theory |

अंकगणित – Calculus – Vector calculus – विश्लेषन – Differential equations – Dynamical systems – Chaos theory – List of functions
### संरचना

आकार, symmetry, र गणितीय संरचनाको बारेमा विचार उल्लेख गर्ने।
अमूर्त वीजगणित – अङ्क सिद्धान्त – वीजगणितीय ज्यामिती – समूह सिद्धान्त – Monoids – विश्लेषन – Topology – रेखीय वीजगणित – लेखचित्र सिद्धान्त – विश्व वीजगणित – Category सिद्धान्त – Order सिद्धान्त – नाप सिद्धान्त
### Spatial relations

A more visual variant of mathematics.

|  |  |  |  |  |
| --- | --- | --- | --- | --- |
|  |  |  |  |  |
| Topology | ज्यामिती | Trigonometry | Differential geometry | Fractal geometry |

Topology – ज्यामिती – Trigonometry – वीजगणितीय ज्यामिती – Differential ज्यामिती – Differential topology – वीजगणितीय topology – रेखीय वीजगणित – Fractal ज्यामिती
### Discrete mathematics

Discrete mathematics is about objects, which can only have specific states.

|  |  |  |  |
| --- | --- | --- | --- |
|  |  |  |  |
| Naive set theory | Theory of computation | Cryptography | Graph theory |

Combinatorics – Naive set theory – Theory of computation– Cryptography – Graph theory
### गणितको प्रयोग जीवनमा

Applied mathematics uses the full knowledge of mathematics to solve real-world problems.
Mechanics – Numerical analysis – Optimization – Probability – Statistics – Financial mathematics – Game theory – Mathematical biology – Cryptography – Information theory – Fluid dynamics
### प्रसिद्ध साध्यहरू

These theorems have interested mathematicians and non-mathematicians.
Pythagorean theorem – Fermat's last theorem – Goldbach's conjecture – Twin Prime Conjecture – Gödel's incompleteness theorems – Poincaré conjecture – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's identity – Church-Turing thesis
### Important theorems and conjectures

*See list of theorems, list of conjectures for more*

These are theorems and conjectures that have changed the face of mathematics throughout history.
Riemann hypothesis – Continuum hypothesis – P=NP – Pythagorean theorem – Central limit theorem – Fundamental theorem of calculus – Fundamental theorem of algebra – Fundamental theorem of arithmetic – Fundamental theorem of projective geometry – classification theorems of surfaces – Gauss-Bonnet theorem
### Foundations and methods

Progress in understanding the nature of mathematics also influence the way mathematicians study their subject.
Philosophy of mathematics – Mathematical intuitionism – Mathematical constructivism – Foundations of mathematics – Set theory – Symbolic logic – Model theory – Category theory – Logic – Reverse Mathematics – Table of mathematical symbols
### गणित र यसको इतिहास

*See also list of mathematics history topics*

Mathematics in history and the history of mathematics.
History of mathematics – Timeline of mathematics – Mathematicians – Fields medal – Abel Prize – Millennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Mathematical abilities and gender issues
### गणित र अरु विधा

Mathematics and architecture – Mathematics and education – Mathematics of musical scales
## गणितिय औजार

Tools, that are used to do mathematics or to calculate.
Old:

* Abacus
* Napier's bones, Slide Rule
* Ruler and Compass
* Mental calculation

New:

* Calculators and computers
* Programming languages
* Computer algebra systems (listing)
* Internet shorthand notation
* statistical analysis software
	+ SPSS
	+ SAS programming language
	+ R programming language