Informal and mathematical language

Hello students, in daily to daily life we use language to telling something to anyone not only we use but everyone use the language for the communication. The language may be anyone like English, Hindi, Latin and many more. But have you ever think about the language of Maths.  Here we are going to discuss the language of maths especially for the informal and mathematical language. In mathematics we use so many types of methods, theorems, expressions, symbols, proofs and many things, the all are comes in mathematical language. It is true that mathematics language is not used for the communication but without this we can nothing understand in math. Like algebra which is totally written in symbolic form.
We assumes math as a language and generally mathematical language is used for the better understanding, to represents the mathematical theorems more clearly, give their reason very logically so that everyone can easily understand. Mathematical language have own grammar, syntax, symbols and conventions. Like we use x for expressing theorems. The vocabulary words for the logic are ‘and’, ‘or’, ‘not’, ‘if…then’, ‘for all’, and ‘if and only if’. Symbols for operation are +, -, *, /, ∏, ∟, ∞, √, ∑, and ⌠ many more. Mathematical language is only used by the mathematicians for the communicating mathematical thoughts among themselves. (know more about cbse books for class 11, here)
Mathematical language also gives precise information for English like statements like we write a is equal to b in English language but the same statement in mathematical form will be a = b. The informal language in math is only used for understanding the concepts and proofs. Generally this language is not written; usually it is used for spoken and used according to the situations or conditions. In the next session we will discuss about Mathematical Reasoning. 

Tools to solve problems

In mathematics, we know that various types of tools are provided to solve the problem that is related to calculation. Problem solving is the logical process which includes the process of finding the problem and estimate there solution. In the process of solving problem, mathematics provides lots of tools like addition, subtraction, multiplication, division, various types of concept like equation and various types of formulas and theorems. Here we are going to discussing about the most popular Problem Solving Model that are used to solving problem.
Addition: addition is the most basic tool of the mathematics which is used to perform the sum of the different objects like total money in the account, total amount of bill etc.
Example: 4 + 3 = 7
Subtraction: this operation is also a most basic tool to perform the difference between two given objects like how money was left after spending in the market and so on.
Example 15 – 5 = 10
Multiplication and division: these are the most popular that helps in to overcome form the problem of repetitive calculation.
The above are the most basic tools that are used in our daily routine life without applying any concept or rule. But in mathematics, sometime we need to solve to solve those types of problem, where we need to find the value of the unknown variable. On the basis of unknown variable the solution of the problem depends. To solve that kind of problem we required the concept of mathematics that is known as algebra. Algebra is the mathematical concept, which is used to change the problem into equation then by finding the value of variable to solve the problem. (know more about cbse sample paper for class x, here)
Example: a + 5 = 9
In the above we can say that there is an example of equation, where we need to fill the value of a by the appropriate number which satisfy the given equation true. In the various field of science mathematical Tools To Solve Problems, are most widely. In the next session we will discuss about dependent.