Mathematics - simple.LinkFang.org

Mathematics


Mathematics is the study of numbers, shapes and patterns. The word comes from the Greek word "μάθημα" (máthema), meaning "science, knowledge, or learning", and is sometimes shortened to maths (in England, Australia, Ireland, and New Zealand) or math (in the United States and Canada).[1] The short words are often used for arithmetic, geometry or simple algebra by students and their schools.

Mathematics includes the study of:

Mathematics is useful for solving problems that occur in the real world, so many people besides mathematicians study and use mathematics. Today, some mathematics is needed in many jobs. People working in business, science, engineering, and construction need some knowledge of mathematics.[2][3]

Contents

Problem-solving in mathematics


Mathematics solves problems by using logic. One of the main tools of logic used by mathematicians is deduction. Deduction is a special way of thinking to discover and prove new truths using old truths. To a mathematician, the reason something is true (called a proof) is just as important as the fact that it is true, and this reason is often found using deduction. Using deduction is what makes mathematics thinking different from other kinds of scientific thinking, which might rely on experiments or on interviews.[4]

Logic and reasoning are used by mathematicians to create general rules, which are an important part of mathematics. These rules leave out information that is not important so that a single rule can cover many situations. By finding general rules, mathematics solves many problems at the same time as these rules can be used on other problems.[5] These rules can be called theorems (if they have been proved) or conjectures (if it is not known if they are true yet).[6] Most mathematicians use non-logical and creative reasoning in order to find a logical proof.[7]

Sometimes, mathematics finds and studies rules or ideas that we don't understand yet. Often in mathematics, ideas and rules are chosen because they are considered simple or neat. On the other hand, sometimes these ideas and rules are found in the real world after they are studied in mathematics; this has happened many times in the past. In general, studying the rules and ideas of mathematics can help us understand the world better. Some examples of math problems are addition, subtraction, multiplication, division, calculus, fractions and decimals. Algebra problems are solved by evaluating certain variables. A calculator answers every math problem in the four basic arithmetic operations.

Areas of study in mathematics


Number

Mathematics includes the study of numbers and quantities.It is a branch of science the deals with logic of shape,quantity and arrangement. Most of the areas listed below are studied in many different fields of mathematics, including set theory and mathematical logic. The study of number theory usually focuses more on the structure and behavior of the integers rather than on the actual foundations of numbers themselves, and so is not listed in this given subsection.
\({\displaystyle 0,1,2,3,\ldots }\) \({\displaystyle \ldots ,-1,0,1,\ldots }\) \({\displaystyle {\frac {1}{2}},{\frac {2}{3}},0.125,\ldots }\) \({\displaystyle \pi ,e,{\sqrt {2}},\ldots }\) \({\displaystyle 1+i,2e^{i\pi /3},\ldots }\)
Natural numbers Integers Rational numbers Real numbers Complex numbers
\({\displaystyle 0,1,\ldots ,\omega ,\omega +1,\ldots ,2\omega ,\ldots }\) \({\displaystyle \aleph _{0},\aleph _{1},\ldots }\) \({\displaystyle +,-,\times ,\div }\) \({\displaystyle >,\geq ,=,\leq ,<}\) \({\displaystyle f(x)={\sqrt {x}}}\)
Ordinal numbers Cardinal numbers Arithmetic operations Arithmetic relations Functions, see also special functions

Structure

Many areas of mathematics study the structure that an object has. Most of these areas are part of the study of algebra.
Number theory Abstract algebra Linear algebra Order theory Graph theory

Shape

Some areas of mathematics study the shapes of things. Most of these areas are part of the study of geometry.
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

Applied mathematics

Applied mathematics uses mathematics to solve problems of other areas such as engineering, physics, and computing.
Numerical analysisOptimizationProbability theoryStatistics – Mathematical finance – Game theoryMathematical physicsFluid dynamics - computational algorithms

Famous theorems


These theorems have interested mathematicians and people who are not mathematicians.

Pythagorean theoremFermat's last theoremGoldbach's conjectureTwin Prime ConjectureGödel's incompleteness theoremsPoincaré conjectureCantor's diagonal argumentFour color theorem – Zorn's lemma – Euler's IdentityChurch-Turing thesis

These are theorems and conjectures that have greatly changed mathematics.

Riemann hypothesisContinuum hypothesisP Versus NPPythagorean theoremCentral limit theoremFundamental theorem of calculusFundamental theorem of algebraFundamental theorem of arithmetic – Fundamental theorem of projective geometry – classification theorems of surfaces – Gauss-Bonnet theoremFermat's last theorem - Kantorovich theorem

Foundations and methods


Progress in understanding the nature of mathematics also influences the way mathematicians study their subject.

Philosophy of Mathematics – Mathematical intuitionism – Mathematical constructivism – Foundations of mathematics – Set theory – Symbolic logic – Model theory – Category theoryLogic – Reverse Mathematics – Table of mathematical symbols

History and the world of mathematicians

Mathematics in history, and the history of mathematics.

History of mathematics – Timeline of mathematics – MathematiciansFields medalAbel PrizeMillennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Mathematics and gender

Awards in mathematics


There is no Nobel prize in mathematics. Mathematicians can receive the Abel prize and the Fields Medal for important works.[8][9]

The Clay Mathematics Institute has said it will give one million dollars to anyone who solves one of the Millennium Prize Problems.

Mathematical tools


There are many tools that are used to do mathematics or to find answers to mathematics problems.

Older tools
Newer tools

References


  1. Waldman, Katy (2014-12-08). "Why Do Brits Say Maths and Americans Say Math?" . Slate. ISSN 1091-2339 . Retrieved 2018-07-30.
  2. "Thinking of a Career in Applied Mathematics? | SIAM" . www.siam.org. Retrieved 2018-07-30.
  3. Wigner, Eugene (February 1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" . Communications in Pure and Applied Mathematics. 13: 1–14.
  4. "The science checklist applied: Mathematics" . undsci.berkeley.edu. Retrieved 2018-08-05.
  5. "The Role of Generalization in the Advanced Mathematical Thinking" . AMS Grad Blog. 2016-08-21. Retrieved 2018-08-07.
  6. Houston, Kevin (2009). How to Think Like a Mathematician. Cambridge University Press. p. 99. ISBN 978-0-521-71978-0.
  7. Thurston, William (April 1994). "On proof and progress in mathematics" (PDF). Bulletin of the American Mathematical Society. 30: 161–177. arXiv:math/9404236 – via arXiv.
  8. Ronan, Mark (2014-08-13). "The Fields Medal is the greatest prize in maths" . ISSN 0307-1235 . Retrieved 2018-08-07.
  9. Bellos, Alex (2018-03-20). "Abel Prize 2018: Robert Langlands wins for 'unified theory of maths'" . the Guardian. Retrieved 2018-08-07.

Related pages


Other websites









Categories: Mathematics




Information as of: 28.10.2020 07:10:18 CET

Source: Wikipedia (Authors [History])    License : CC-by-sa-3.0

Changes: All pictures and most design elements which are related to those, were removed. Some Icons were replaced by FontAwesome-Icons. Some templates were removed (like “article needs expansion) or assigned (like “hatnotes”). CSS classes were either removed or harmonized.
Wikipedia specific links which do not lead to an article or category (like “Redlinks”, “links to the edit page”, “links to portals”) were removed. Every external link has an additional FontAwesome-Icon. Beside some small changes of design, media-container, maps, navigation-boxes, spoken versions and Geo-microformats were removed.

Please note: Because the given content is automatically taken from Wikipedia at the given point of time, a manual verification was and is not possible. Therefore LinkFang.org does not guarantee the accuracy and actuality of the acquired content. If there is an Information which is wrong at the moment or has an inaccurate display please feel free to contact us: email.
See also: Legal Notice & Privacy policy.