गणित
From Wikipedia
गणित is the study of सङ्ख्या, structure (how things are organized), space (where things are) and change.
Because गणित looks at such general topics, it uses abstract (simpler, less specific) descriptions of objects to talk about things. The simplest example of this is numbers. In the real world two apples plus two apples makes four apples, two bricks plus two bricks makes four bricks so in mathematics this becomes the general statement "two plus two equals four". This is arithmetic.
Another very simple example comes from set theory. If all blackbirds are black and one bird is not black it is not a blackbird. If all snow is white and another thing is not white it is not snow. In math we make this idea abstract by saying: if A is a subset of B then "not B" is a subset of "not A". For example, if you have something that is not black, it cannot be a blackbird.
By finding a general way to say something mathematics solves many problems at the same time. The examples of snow and blackbirds are easy to understand without math, but harder situations can be much easier to understand with math. Sometimes mathematics studies rules or ideas which have not yet been found in the real world. Often if the rules are chosen because they are simple, later on they are found in the real world and studying the rules helps us understand the world better.
The word "mathematics" comes from the Greek μάθημα (máthema) and means "science, knowledge, or learning". Often it is abbreviated to maths (math in American English), especially when describing arithmetic, geometry or basic algebra as taught to teenagers (as pupils).
गणितिय prediction is the basis of hard science, which almost always uses equations to predict events in physics. The philosophy of science explores this. However, creating mathematics is clearly a human science. The philosophy of mathematics explores these issues, and others regarding how mathematics fits into philosophy, ethics and real life.
Contents |
[परिवर्तन्] Important themes in mathematics
- See also: List of mathematics topics
Here is a possible grouping of mathematical areas and topics.
[परिवर्तन्] Quantity
- This is about counting and measuring and the ways to find such measurements.
-
Natural numbers Integers Rational numbers Real numbers Complex numbers
- Number – Natural number – Integers – Rational numbers – Real numbers – Complex numbers – Hypercomplex numbers – Quaternions – Octonions – Sedenions – Hyperreal numbers – Surreal numbers – Ordinal numbers – Cardinal numbers – p-adic numbers – Integer sequences – Mathematical constants – Number names – Infinity – Base
[परिवर्तन्] Change
- Ways to express and handle change in mathematical functions, and changes between numbers.
-
Arithmetic Calculus Vector calculus Analysis 
Differential equations Dynamical systems Chaos theory
- Arithmetic – Calculus – Vector calculus – Analysis – Differential equations – Dynamical systems – Chaos theory – List of functions
[परिवर्तन्] Structure
- Express ideas of size, symmetry, and mathematical structure.
- Abstract algebra – Number theory – Algebraic geometry – Group theory – Monoids – Analysis – Topology – Linear algebra – Graph theory – Universal algebra – Category theory – Order theory – Measure theory
[परिवर्तन्] Spatial relations
- A more visual variant of mathematics.
-
Image:Koch curve.GIF Topology Geometry Trigonometry Differential geometry Fractal geometry
- Topology – Geometry – Trigonometry – Algebraic geometry – Differential geometry – Differential topology – Algebraic topology – Linear algebra – Fractal geometry
[परिवर्तन्] Discrete mathematics
- Discrete mathematics is about objects, which can only have specific states.
-
Image:Fsm moore model door control.jpg 
Naive set theory Theory of computation Cryptography Graph theory
- Combinatorics – Naive set theory – Theory of computation– Cryptography – Graph theory
[परिवर्तन्] Applied mathematics
- 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
[परिवर्तन्] Famous theorems and conjectures
- 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
[परिवर्तन्] 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
[परिवर्तन्] 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
[परिवर्तन्] History and the world of mathematicians
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
[परिवर्तन्] Mathematics and other fields
- Mathematics and architecture – Mathematics and education – Mathematics of musical scales
[परिवर्तन्] Mathematical tools
- 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
