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Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics. Mathematical notations include relatively simple symbolic representations, such as numbers 1 and 2, function symbols sin and +; conceptual symbols, such as lim, dy/dx, equations and variables; and complex diagrammatic notations such as Penrose graphical notation and Coxeter-Dynkin diagrams.


A mathematical notation is a writing system used for recording concepts in mathematics.

  • The notation uses symbols or symbolic expressions which are intended to have a precise semantic meaning.
  • In the history of mathematics, these symbols have denoted numbers, shapes, patterns, and change. The notation can also include symbols for parts of the conventional discourse between mathematicians, when viewing mathematics as a language.

The media used for writing are recounted below, but common materials currently include paper and pencil, board and chalk (or dry-erase marker), and electronic media. Systematic adherence to mathematical concepts is a fundamental concept of mathematical notation. (See also some related concepts: Logical argument, Mathematical logic, and Model theory.)


A mathematical expression is a sequence of symbols which can be evaluated. For example, if the symbols represent numbers, the expressions are evaluated according to a conventional order of operations which provides for calculation, if possible, of any expressions within parentheses, followed by any exponents and roots, then multiplications and divisions and finally any additions or subtractions, all done from left to right. In a computer language, these rules are implemented by the compilers. For more on expression evaluation, see the computer science topics: eager evaluation, lazy evaluation, and evaluation operator.

Precise semantic meaning

Modern mathematics needs to be precise, because ambiguous notations do not allow formal proofs. Suppose that we have statements, denoted by some formal sequence of symbols, about some objects (for example, numbers, shapes, patterns). Until the statements can be shown to be valid, their meaning is not yet resolved. While reasoning, we might let the symbols refer to those denoted objects, perhaps in a model. The semantics of that object has a heuristic side and a deductive side. In either case, we might want to know the properties of that object, which we might then list in an intensional definition.

Those properties might then be expressed by some well-known and agreed-upon symbols from a table of mathematical symbols. This mathematical notation might include annotation such as

  • "All x", "No x", "There is an x" (or its equivalent, "Some x"), "A set", "A function"
  • "A mapping from the real numbers to the complex numbers"

In different contexts, the same symbol or notation can be used to represent different concepts. Therefore, to fully understand a piece of mathematical writing, it is important to first check the definitions that an author gives for the notations that are being used. This may be problematic if the author assumes the reader is already familiar with the notation in use.



It is believed that a mathematical notation to represent counting was first developed at least 50,000 years ago — early mathematical ideas such as finger counting have also been represented by collections of rocks, sticks, bone, clay, stone, wood carvings, and knotted ropes. The tally stick is a timeless way of counting. Perhaps the oldest known mathematical texts are those of ancient Sumer. The Census Quipu of the Andes and the Ishango Bone from Africa both used the tally mark method of accounting for numerical concepts.

The development of zero as a number is one of the most important developments in early mathematics. It was used as a placeholder by the Babylonians and Greek Egyptians, and then as an integer by the Mayans, Indians and Arabs. (See From Yahoo Answers

Question:I tend to forget formulas, so I require a full list of formulas for math. I am currently doing Advanced Functions & Calculus.

Answers:That's not very specific. But, hopefully this is helpful: http://www.xs4all.nl/~johanw/math.pdf

Question:My retest of maths is coming up, on the 15th and i need a list of o-level maths formulas! PLEASE! Anyone who can please put up most of the list, or suggest a website that has a list of all the formulas and stuff, i'd be extremely grateful! PLEASE HURRY!!! I need to memorize them as well as learn how to put them in use! O-Levels is like, this cambridge educational stream from classes 9 to 11 i think...yeah...and i just need all the basic math formulas, like, area of this and that...perimeter...volume...ratio...rate...time...interest....distance...all that kinda stuff...PLEASE!!! MAKE A LIST FOR ME! And i cant buy it, cuz i dont think its available where i live...=_=my darn luck.

Answers:your best option is to find the syllabus for the exam you are retaking - they will probably summarise that information there Alternatively you can buy a formula book - they tend to be for formulae that you don't need to memorise as you can often take that in to the exam - like trig relationships This site has a good list http://www.math.com/tables/index.html General math and geometry will cover most of what you need By the way - are you doing a GCSE resit? Ask your teacher for a formula list


Answers:a = 1/2(b*h) area of triangle l*W area of rectangle 2L+2W perimeter of rectangle A= pi r^2 area of circle x^2 + y^2 = r^2 Pythagorean theorem [-b +- Sqrt(b^2 -4 *A*c)]/( 2*A) Quadratic formula sin^2 x + cos^2 x = 1 trigonometric identity 1 + cot^2 x = csc^2 x trigonometric identity tan^2x + 1 = sec^2x trigonometric identity x^2 ( x represents side of square) area of a square

Question:I record statistics,eg., hrs worked per day ,products produced-per day,-per week,per month ,etc., these numbers are recorded in a vertical column onto a spread sheet .I then make a graph from just one column of numbers. The results are like a wave,leaving me to guess will the next number go up,down,stay the same ,what will it do? I'm looking for a simple formula based on a list of numbers that look random but aren't,there is a high max. and a low min.range different with each statistic.This would be a computer math formula for a spread sheet,my skills on working with formulas is very basic,so explaining step by step in laymans english would be most helpful. Here is a sample list of numbers -products produced- in cell 3c 23,in cell 4c 19,cell 5c 30,""21,""22,""29,""26,""26,""17,""20,""31,""33,""18,cell 16c 22,cell 17c(??????what is this logigal next number?)..... I hope i've explained this simple enough to be understood, can anyone out there help me with this problem????please?????

Answers:If I understood right, I think what you looking for is (IF). 1- click on INSERT (menu) 2- select fx (function) 3- select a function (IF) 4- office assistant with guide you through

From Youtube

Excel Basics #5: Formulas Operators and Math :The Excel Basics Series shows a systematic description of what Excel can do from beginning to end. #5 Video topics: 1)Excel operator symbols 2)Parenthesis is () 3)Exponent is ^ 4)Multiplication is * 5)Division is / 6)Adding is + 7)Subtracting is 8)Order of Operations 9)Complete list of how Excel Evaluates formulas 10)Excel 2003: Formula Evaluator: Tools, Formula Auditing, Formula Auditing 11)Excel 2007: Formula Evaluator: Formula Ribbon, Formula Auditing group, Formula Auditing icon

Basic Math: Lesson 7 - Units of Measurement :This lesson consists of providing you with a Self-Tutorial of the basic units used in measurement. These are the ones I discuss: Units of Time, Units of Length (Metric and US), Units of Area (Metric and US), Units of Volume (Metric and US), Units of Mass (Metric and US), Units of Liquid Capacity (Metric and US), Units of Dry Capacity (Metric and US), and other miscellaneous Units. Conversion Formulas and Abbreviations are also listed. This is a "must have" Lesson for those moving on to solving Word Problems in Algebra and other higher math.