How to study mathematics, that is in which order must a student or a graduate study maths?

Mathematics a big subject but for the ease of the understanding of the students it is divided in many sub divisions which are distinctly different from each other but are used together when solving a scientific or technical problem of a larger dimension. There are different ways the syllabus in schools or colleges can be structured which makes a base for advanced studies during graduation and post graduation. There could be some differences between the sequences of topics or subdivisions that are being taught in schools or colleges or in graduation and post graduation but essentially basic concepts in Mathematics are supposed to be taught before we enter into the advanced Mathematical principles and their application in engineering and technology. Another important thing in this matter is that at some level there is a good overlap between the Physics and Mathematics because understanding many Physics derivations is not possible without a robust understanding of the Mathematics. With this background now let us see what could be the best sequence of learning Mathematics. I would put it in the following manner.

1. Number system and basic Mathematics.
2. Algebra.
3. Trigonometry.
4. Vector and matrices.
5. Probability and Statistics.
6. Logic, set theory and boolean Algebra.
7. Differential and Integral calculus.
8. Dynamics and Statics.
9. Hydrodynamics.
10. Applied Mathematics in Engineering and Physics.

Mathematics is really an interesting subject and it has got its wide penetration in the different science subjects such solving the problems of Physics, Chemistry, Computers and also in the different areas of Engineering, Astronomy etc. Without having the sound concept of Mathematics, it would be difficult to understand the most of the parts of aforesaid subjects.
While getting inputs in this subjects we start with the number theory in the initial classes of our schools. Arithmetic is the core subject in the initial phase and without having a sound command on this, we cannot solve many problems pertaining to work and time, interest calculation, percentage, profit or loss etc.
Geometry consisting of two dimensional system are taught in the school days having wide applications in the practical fields.
In nut shell, whatever is taught to us right from our primary classes to post graduate level in Mathematics, each component is essential so as be used in the practical dimensions in the different areas. Hence every component be it number system or logic and foundation, we cannot ignore their roles.
All the branches in Mathematics are interrelated, so while solving the problems of trigonometry, we have to apply the theory of quadratic equations to find its value. Many of the arithmetical problems can be solved by means of algebra. Hence one should focus on all the different parts of Mathematics so as to have the conceptual clarity in Mathematics.
Though Hydrodynamics, Magnetism, Nuclear Physics,,Electrostatics, Current Electricity constitute the essential topics of Physics but without the application of Mathematics involving Differential Calculus, Integral Calculus, Differential Equation etc , we cannot arrive at the end result.
Here a sequence of learning of Mathematics is indicated below for the better comprehension of this subject -
1) Number System and Basic Mathematics.
2) Algebra.
3) Trigonometry.
4) Geometry related to two dimensions.
5) Solid Geometry.
6) Co- ordinate Geometry and three dimensional Geometry.
7) Vector Agebra.
8) Differential and Integral Calculus.
9) Differential Equations.
10) Probablity and Statistics.
11) Logic and Set theory.
12) Statistics and Dynamics
13) Hydrostatics.
14) Hydrodynamics.
15) Application of Mathematics in both Engineering and Physics.

Students have little difficulty in understanding the mathematics subject because they do not have the basic knowledge of the subject and that is why this topic causes them a lot of trouble, due to which they start running away from it, solving the math questions try to understand those questions, it is very important to remember multiplication tables, through this, you will be very helpful in solving maths questions, you will get at least 25 It is compulsory to remember multiplication tables up to 25, after that you need to memorize the square root table by 20, memorizing them will take less time to solve the questions, questions related to multiplication, division, square, square root, LCM, There will be an immense help in HCF, etc.

To learn mathematics, we can solve the answers to further questions correctly by learning basic things, so the study of mathematics should start from a certain step. There is a whole process of reading mathematics, which is followed and learning mathematics while moving from one step to another step.

1 Number system - natural numbers, integers, rational numbers, real numbers, complex numbers
2 Algebra -. Polynomial, pair of linear equations with two variables. Quadratic equations, parallel ranges
3 Coordinate geometry - line (DIV)
4 Geometry -. Triangle, tangent to the circle, the tangent point
5 Trigonometry -. Trigonometric identities,. Height and distance,
6 Mensuration -. Area related to circles, surface area and volume,
7 Statistics and Probability - Statistics,
8 Structures - group theory, graph theory, sequence theory



To study mathematics, keep these important things in mind as well.

1 - Mathematics is a very difficult subject to think out of mind.

2 - Like every subject, mathematics can also be read easily, for this, keep the grip strong from the beginning.

3 - There are low numbers or failures in mathematics or we cannot read difficult topics like mathematics, ignore all these things for us.

4 - Focus should be on understanding.

5 - Formulas are the life of mathematics, remember them always.

6 - Keep practicing continuously.

7 - To understand mathematics, instead of talking to others, believe in yourself, and also decide that I can solve this question only.

8 - Instead of running away from mathematics, understand it, and make a habit of asking what is not understood.

9 - Continue to read mathematics questions regularly.

10 - Instead of stress in the mind about mathematics, think and solve it with a fresh mind.

Nice answers by experts. However I was of the opinion that logic must be taught along with number theory since it underpins the very structure of maths. Do you agree with my pov?

Logic enables the student to visualize the nature of problem in a better and more cohesive manner enabling them to solve the problem faster.

Mathematics is a very important and useful subject. It is very much needed for chemistry and physics learning also. Engineering students also should have good knowledge of this subject. The students who have a good understanding of this subject can excel in other subjects also.
A student should be strong in basics and fundamentals. Once the foundation is strong, he can improve his knowledge in the advanced areas also. So your high school and junior college lessons in mathematics are very important.
In high school, we study mathematics where we will be taught how to think and to solve a problem. This will make us think logically and solve the problems. So you should start with mathematics in high school. Then continue into the other subjects, The preferred sequence can be.
1, Basic Mathematics.
2. Basic Algebra
3, High School Geometry
4, Advanced Algebra
5, Algebra with Trigonometry
6, Calculus with Analytic Geometry
7. Vector Calculus
8, Basic Mathematical Proof Class
9. Linear Algebra
10, Introduction to Differential Equations
11. Mathematical Analysis
12. Complex Variables
12. Introduction to Abstract Algebra
13. Application s of mathematics in other fields.

Mathematics will make a person sharp and it will make a person think in a systematic way. So one should concentrate on mathematics from high school itself and understand the subject and try to apply the same in other fields.