BASIC MATH SYMBOLS

Symbol	Symbol Name	Meaning / definition	Example
≠	not equal sign	inequality	5 ≠ 4
=	equals sign	equality	5 = 2+3
<	strict inequality	less than	4 < 5
>	strict inequality	greater than	5 > 4
≤	inequality	less than or equal to	4 ≤ 5
≥	inequality	greater than or equal to	5 ≥ 4
[ ]	brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
( )	parentheses	calculate expression inside first	2 × (3+5) = 16
−	minus sign	subtraction	2 − 1 = 1
+	plus sign	addition	1 + 1 = 2
∓	minus – plus	both minus and plus operations	3 ∓ 5 = -2 and 8
±	plus – minus	both plus and minus operations	3 ± 5 = 8 and -2
×	times sign	multiplication	2 × 3 = 6
*	asterisk	multiplication	2 * 3 = 6
÷	division sign / obelus	division	6 ÷ 2 = 3
∙	multiplication dot	multiplication	2 ∙ 3 = 6
–	horizontal line	division / fraction
/	division slash	division	6 / 2 = 3
mod	modulo	remainder calculation	7 mod 2 = 1
ab	power	exponent	23 = 8
.	period	decimal point, decimal separator	2.56 = 2+56/100
√a	square root	√a · √a = a	√9 = ±3
a^b	caret	exponent	2 ^ 3 = 8
4√a	fourth root	4√a · 4√a · 4√a · 4√a = a	4√16 = ±2
3√a	cube root	3√a · 3√a · 3√a = a	3√8 = 2
%	percent	1% = 1/100	10% × 30 = 3
n√a	n-th root (radical)		for n=3, n√8 = 2
ppm	per-million	1 ppm = 1/1000000	10ppm × 30 = 0.0003
‰	per-mille	1‰ = 1/1000 = 0.1%	10‰ × 30 = 0.3
ppt	per-trillion	1ppt = 10-12	10ppt × 30 = 3×10-10
ppb	per-billion	1 ppb = 1/1000000000	10 ppb × 30 = 3×10-7

Calculus & Analysis Symbols

Symbol	Symbol Name	Meaning / definition	Example
ε	epsilon	represents a very small number, near zero	ε → 0
$\underset{x\to a}{lim}$	limit	limit value of a function	$\underset{x\to a}{lim}(3x+1)=3\times a+1=3a+1$
y ‘	derivative	derivative – Lagrange’s notation	${\left(5x^3\right)}^{\prime }=15x^2$
e	e constant / Euler’s number	e = 2.718281828…	e = lim (1+1/x)x , x→∞
y(n)	nth derivative	n times derivation	nth derivative of $3x^n=3n(n-1)(n-2)\dots .\left(2\right)\left(1\right)=3n!$
y ”	second derivative	derivative of derivative	$\left(4x^3\right)”=24x$
$\frac{d^{2}y}{d{x}^2}$	second derivative	derivative of derivative	$\frac{d^2}{d{x}^2}(6x^3+x^2+3x+1)=36x+1$
dy/dx	derivative	derivative – Leibniz’s notation	$\frac{d}{dx}\left(5x\right)=5$
$\frac{d^{n}y}{d{x}^n}$	nth derivative	n times derivation
$\ddot{y}=\frac{d^{2}y}{d{t}^2}$	Second derivative of time	derivative of derivative
$\dot{y}$	Single derivative of time	derivative by time – Newton’s notation
$D^{2}x$	second derivative	derivative of derivative
Dx	derivative	derivative – Euler’s notation
∫	integral	opposite to derivation
$\frac{af(x,y)}{ax}$	partial derivative		∂(x2+y2)/∂x = 2x
∭	triple integral	integration of function of 3 variables
∬	double integral	integration of function of 2 variables
∯	closed surface integral
∮	closed contour / line integral
[a,b]	closed interval	[a,b] = {x | a ≤ x ≤ b}
∰	closed volume integral
(a,b)	open interval	(a,b) = {x | a < x < b}
z*	complex conjugate	z = a+bi → z*=a-bi	z* = 3 + 2i
i	imaginary unit	i ≡ √-1	z = 3 + 2i
∇	nabla / del	gradient / divergence operator	∇f (x,y,z)
z	complex conjugate	z = a+bi → z = a–bi	z = 3 + 2i
$\vec{x}$	vector	$\vec{V}=x\hat{i}+y\hat{j}+z\hat{k}$
x * y	convolution	y(t) = x(t) * h(t)
∞	lemniscate	infinity symbol
δ	delta function

5 FUN WAYS TO PRACTICE MATHS

1. Roll the dice
Dice can be used in so many different ways when it comes to math. Whether you’re practicing multiplication facts or fractions, try having students create their own math problems with the roll of the dice. They can create fractions, simple multiplication problems or even word problems using dice. This can also be a fun way to put together a homework assignment: Students roll the dice during class, then take the problems home to solve.

2. Play math bingo 

Bingo is always a class favorite, and you can play it with any number of students. You can buy math bingo kits online . You can also make up your own. The way it works is students have to solve math problems in order to know what number to mark off of their sheet.

3. Play war
The classic card game War is always a good way to reward students when they have a few extra minutes here and there. Have several decks of cards in your classroom and use this as an incentive, either when they finish assignments or just as “bonus” time that they can earn. Make sure they are solving math problems when they lay their cards out, though.

4.Borrow or buy an adding machine.Do you remember the simple joy you had when playing around with an adding machine? If not, go to your nearest thrift store to find one! Students will love being able to punch in numbers and have the math problems come out on real paper. It’s a simple yet awesome way to get them excited about practicing math.

5.Create a math Concentration game.You know the classic game Concentration? Create your own version using math problems or cutting up old flash cards. Here’s how: Have the math problem on one card and then the answer on another. So you might have 4 x 5 on one card, and then another card would have 20. Have the students find each answer for a correct match. You could even color-code the cards to make it easy to distinguish questions vs. answers.

IMPORTANCE OF MATHS LIBRARY AND LABORATORY

In any scheme of education, mathematics library plays a key role.Class room teaching has its limitations.It is difficult for teachers to go beyond the prescribed text book.Class room teachings may leave gaps and doubts.A good library provides opportunities for leaving the gaps.The curious students get facilities for quenching their first thirst of knowledge through library.A well organised library is a source of attraction for its students.A mathematics library is the birth place of future mathematicians.It inspires, stimulates ans equips them to follow the footprints of great mathematicians.

A mathematics library,besides being a source of learning and inspiration to pits students,also serves the interest and needs of teachers.Knowledge has no boundaries.A teacher has to keep himself abreast of the latest knowledge and skills in his subject.He has to learn most effective methods and devices for teaching. A good library in this sense,serves the role of a burning lamp.It sets burning the ambitions of learning more and more in teachers and inspires the students to imitate the ideals of their teachers.

In many schools laboratories are generally established for science subjects.Therefore for a number of persons the  idea of setting mathematics laboratory in the school sounds quiet unusual and unpractical. Laboratory is a place which serves two fold purposes.Firstly it provides safe and proper place for placing all the essential material and equipment's concerning the learning activities in a subject.Secondly it gives proper facilities and opportunities for  essential practical work and lively learning experiences.Apart from this, setting of mathematics library will prove useful to a mathematics  teacher in many different ways.The mathematics knowledge which cannot be translated into practice is a useless burden and therefore students of mathematics should be given proper opportunities for the integration of theory with practice.

NEED AND IMPORTANCE OF MATHEMATICS LIBRARY

Having realized the need and importance of library in teaching of mathematics it is now to be thought whether to have a separate mathematics library or not.Generally in schools,there happens to be ageneral library where all sorts of general books andbooks related to different subjects and activities are placed in different almirahs at different places.On big table or tables,newspapers,magazines,periodicals and journals are placed.This place also seves as areading room.

           There should be a period for library reading in the time table for enebling the students of every section and class to have an easy access to such library.The teacher may take the help of monitor or some interested student of the class in the management of the affairs.Thw establishment of mathematics library in separate room or as part of general library may be supported on the following grounds:

1.     The separate arrangement brings fficiency in the organization.

2.      Mathematics teacher remains in touch with the volumes and literature available in library.

3.     It gives a sense of separate identity and inculcates interest in the subject mathematics.

4.     The student get better facilities for reading the books and literature.

5.     It helps in the activities of mathematics club.

6.     It may help in nurturing gifted and potentials students in mathematics.

Therefore,in every school attempts should be made to have a mathematical library with the cooperation of authorities and the students.

WHAT IS TO BE KEPT IN MATHEMATICS LIBRARY

Mathematics library should be made an attractive place.It should have useful information on its walls in in the form of writings, charts and posters about mathematicians,their contributions, the facts and principles of mathematics and the historical development of the subject mathematics.A library is known through its contents, therefore there should be a wise collection of useful books and literature in the mathematics library.For this purpose a mathematics teacher should spare no efforts for the judicious selection of books and literature.This collection then needs a proper categorization or classification.

      NEED AND IMPORTANCE OF MATHEMATICS LABORATORY

Advantages:

Some of the advantages of a mathematics laboratory may summerised as follows:

1.    It will help in creating interest of the students in the learning of mathematicians.

2.    It will help in making use of all the progressive methods like inductive,analytic, laboratory,heuristic and project methods in the teaching and learning of mathematics.

3.    It will help in the inculcation of scientific,problem solving and heuristic attitude among the students.

4.    The theoretical  concepts may be easily clarified through practical demonstration.In this way the laboratory should would definitely save the time and energy of the teachers as well as students.

5.    It will help in training the students for the practical application of mathematical facts and principles in their life.

6.    It will help in satisfying the creative and constructive urges of the students

WHAT SHOULD BE THERE IN A MATHEMATICS LABORATORY?

A mathematics laboratory may contain the following types of material and equipments:

1.     Different types of pictures and charts: Pictures  and charts makes the learning of mathematics interesting and useful.A mathematics laboratory should contain different types of charts and pictures concerning various topics and sub-topics of mathematics.A few pictures and photographs of mathematicians may also be hung on on the walls of the laboratory to make it as mathematical as possible.

2.     Models: In mathematics education models prove a very effective source of teaching and learning.

3.     Weighing and measuring instruments: These are two important aspects of mathematics.A mathematics laboratory should, therefore, have all the essential equipment for weighing and measuring purposes like different types of balances,weights,measuring tapes and graduated cylinders.

4.     Drawing instruments: For drawing and sketching of various figures and diagrams there should bedrawing instruments in mathematics laboratory.

5.     The useful material concerning other subjects:modern teaching follows the principle of integration and correlation.In mathematics text concepts and problems are sometimes very much linked with the experience areas of other subjects.

6.     Surveying instruments: Surveying is an important phenomenon concerning mathematics.For surveying purposes besides various types of measuring tapes the following types of special instruments should be kept in a mathematics laboratory.

Ø Angle mirror: It is used for laying out right angles in the field.

Ø Hypsometer and clinometers: Used in combination, the apparatus a simple device for measuring distance and heights of objects.

Ø Sextent: It is a sophisticated instrument for measuring the angular distance.It is used to find out angles of elevation and depression.

Ø Plane table:It is used for elementary mapping and surveying.

Ø Level:It is used in leveling the surfaces by finding differences in elevation.

Ø Transit: It is used in the measurement of angular distance and leveling.

7.     Other useful materials: The useful concrete material like beads, balls, sticks, match boxes, pebbles, seeds, didactic apparatus, different types of coins, different types of wooden or card board pieces etc. may be kept in mathematics library.

8.     Some other modern equipment: Under this category the following types of instruments may be kept in the mathematics laboratory:

Ø Proportional Dividers: This apparatus is based on the principle of proportionality in similar triangles and used for enlarging or reducing the pictures, maps or diagrams.

Ø Slide Rule: In principle it consists of two or more logarithmic scales sliding on each other.

Ø Calculating Machines: It is a sophisticated device for making the computation work a joy.It can also do all sorts of calculations in no time with great precision and accuracy.