شمېرپوهنه

Euclid, "د آتن ښوونځی" يو منظر، د رافايل د اثرونو څخه.

شمېر پوهنه د هغوسکالوګانو(موضوعاتو) لکه کميت، جوړښت، تشيال او بدلون په هکله زده کړې ته وايي خو ځينې بيا داسې يو ځانګړی تعريف لري چې شمېرپوهنه د ټولو پوهنو بدن دی او بنسټ يې تعليلي دليل دی چې په اکسزيوم او تعريفونو پېل کېږي.

شمېرپوهنه په ټوله نړۍ کې د ساينس په بېلابېلو ډګرونو کې کارول کېږي لکه انجنيری، څېړنه، طب او اقتصاد. دا د ساينس هغه ډګرونه دي چې مونږ ته د نورو زېږونو الهام په ورکړې سره سره په شمېرپوهنه کې د لا نورو لاس ته راوړنو جوګه کوي. نوې شمېرپوهنه هم د ځانه زېږېدلې، پرته له دې چې کومه ځانګړې کارونه په پام کې وي.

شمېرپوهنه چې د رياضياتو د علومو په مانا ده، يو پښتو ويکه ده چې د شمېر او پوهنې يو تړنګ (ترکيب) دی. په انګليسي ژبې کې د (Mathematics) يا مېتامېټکس د شمېرپوهنې انډول دی او دا ويۍ بيا د پخواني يوناني ژبې لغت μάθημα يا (máthēma) نه اخيستل شوی او په مانا د ساينس، علوم يا زده کړې دی. خو په همدې توګه بياد μαθηματικός يا (mathēmatikós) د زده کړې لېوال په مانا دی. په انګليسي ژبه کې بيا کله نا کله د math او يا هم maths لنډون هم کارېدلی.

تاريخ

آر ليکنه: [[د شمېر پوهنې تاريخ|د شمېر پوهنې تاريخ]]

Pythagoras (c.570-c.495 BC) has commonly been given credit for discovering the Pythagorean theorem. Well-known figures in Greek mathematics also include Euclid, Archimedes, and Thales.

الهام، بوب او کارېدونکې شمېرپوهنه، او ښکلاپېژندنه

مشتق

په شمېرپوهنه کې اصلي موضوعګانې

کميت يا کچه

کميت او يا هم چې په پښتو کچه بلل کېږی په شمېرلو او مېچ کول پېلېږي.

$1, 2, \ldots$	$\ldots, -1, 0, 1, \ldots$	$\frac{1}{2}, \frac{2}{3}, 0.125,\ldots$	$\pi, e, \sqrt{2},\ldots$	$i, 3i+2, e^{i\pi/3},\ldots$
طبيعي ګڼونه	Integerونه	ناطق ګڼونه	ريښتن ګڼونه	پېچلي ګڼونه

Number – Hypercomplex numbers – Quaternions – Octonions – Sedenions – Hyperreal numbers – Surreal numbers – Ordinal numbers – Cardinal numbers – p-adic numbers – Integer sequences – Mathematical constants – Number names – Infinity – Base

جوړښت

Pinning down ideas of size, symmetry, and mathematical structure.

$36 \div 9 = 4$		96px
رياضي	Number تيوري	Abstract الجبر	د ډلې تيوري	Order تيوري

Monoids – Rings – Fields – Linear algebra – Algebraic geometry– Universal algebra

تشيال

A more visual approach to mathematics.

Geometry	Trigonometry	Differential geometry	Topology	Fractal geometry

Algebraic geometry – Differential topology – Algebraic topology – Linear algebra – Combinatorial geometry – Manifolds

ونج يا بدلون

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

		$\frac{d^2}{dx^2} y = \frac{d}{dx} y + c$
Calculus	Vector calculus	Differential equations	Dynamical systems	Chaos theory

Analysis – Real analysis – Complex analysis – Functional analysis – Special functions – Measure theory – Fourier analysis – Calculus of variations

بنسټونه او مېتودونه

Approaches to understanding the nature of mathematics.

$P \Rightarrow Q$
Mathematical logic	Set theory	Category theory

Foundations of mathematics – Philosophy of mathematics – Intuitionism – Constructivism – Proof theory – Model theory – Reverse mathematics

Discrete mathematics

Discrete mathematics involves techniques that apply to objects that can only take on specific, separated values.

$[1,2,3][1,3,2]$ $[2,1,3][2,3,1]$ $[3,1,2][3,2,1]$
Combinatorics	Theory of computation	Cryptography	Graph theory

Computability theory – Computational complexity theory – Information theory

کارندويه شمېرپوهنه

کارندويه شمېرپوهنه، په حقيقي نړۍ کې د ورځينيو مسايلو د حل لپاره يو بشپړه پوهنه ده.

Mathematical physics – Mechanics – Fluid mechanics – Numerical analysis – Optimization – Probability – Statistics – Mathematical economics – Financial mathematics – Game theory – Mathematical biology – Cryptography – Mathematics and architecture – Mathematics of musical scales

اهمې قضيې

These theorems have interested mathematicians and non-mathematicians alike.

See list of theorems for more

Pythagorean theorem – Fermat's last theorem – Gödel's incompleteness theorems – Fundamental theorem of arithmetic – Fundamental theorem of algebra – Fundamental theorem of calculus – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's identity – classification theorems of surfaces – Gauss-Bonnet theorem – Quadratic reciprocity – Riemann-Roch theorem.

Important conjectures

See list of conjectures for more

These are some of the major unsolved problems in mathematics.

Goldbach's conjecture – Twin Prime Conjecture – Riemann hypothesis – Poincaré conjecture – Collatz conjecture – P=NP? – open Hilbert problems.

تاريخ او د شمېرپوهانو نړۍ

See also list of mathematics history topics

History of mathematics – Timeline of mathematics – Mathematicians – Fields medal – Abel Prize – Millennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Mathematics education – Mathematical abilities and gender issues

شمېرپوهنيز اوزارونه

Old:

• Abacus
• Napier's bones, slide rule
• Ruler and compass
• Mental calculation

New:

• شمېرنی او کمپيوټر
• Programming languages
• Computer algebra systems (listing)
• Internet shorthand notation
• statistical analysis software
  • SPSS
  • SAS programming language
  • R programming language

دا هم وګورۍ

• شمېرپوهنيزې لوبې
• Mathematical problem
• شمېرپوهنيز چوکاټونه
• چوکاټونه

سرچينې

• Benson, Donald C., The Moment Of Proof: Mathematical Epiphanies (1999).
• Courant, R. and H. Robbins, What Is Mathematics? (1941);
• Davis, Philip J. and Hersh, Reuben, The Mathematical Experience. Birkhäuser, Boston, Mass., 1980. A gentle introduction to the world of mathematics.
• Boyer, Carl B., History of Mathematics, Wiley, 2nd edition 1998 available, 1st edition 1968 . A concise history of mathematics from the Concept of Number to contemporary Mathematics.
• Gullberg, Jan, Mathematics--From the Birth of Numbers. W.W. Norton, 1996. An encyclopedic overview of mathematics presented in clear, simple language.
• Hazewinkel, Michiel (ed.), Encyclopaedia of Mathematics. Kluwer Academic Publishers 2000. A translated and expanded version of a Soviet mathematics encyclopedia, in ten (expensive) volumes, the most complete and authoritative work available. Also in paperback and on CD-ROM.
• Kline, M., Mathematical Thought from Ancient to Modern Times (1973).
• Pappas, Theoni, The Joy Of Mathematics (1989).