1. Algebra:

As you know Algebra generally includes the study of structures that are planned and then operated and then defined on these sets by initially satisfying people.

2. Calculus:

It basically studies the computation of the derivatives, integrals, limit of function for the real numbers and also particular studies immediate charge of change and Analysis is basically evolved from calculus

3. Geometry and topology:

As you know geometry is basically the study of spatial figures such as cubes and circles and is initially generalized. Topology is basically evolved from geometry and it includes properties that do not essentially change even if the figures are formed in order to stretch and bend just like a dimension.

4. Combinatory:

It is the study that basically concerns about the discrete objects in common. Some of the major aspects that it involve is that counting the objects and is considered to be one of the most satisfying criteria at the same time because it helps in deciding when the criteria are accomplished so that construction and analyzing of the objects can be taken place.

5. Logic:

It is considered to be that foundation that initially underlies the mathematical logic and also the rest of the mathematics too. It basically tries to honour all the valid reasoning. However, it basically defines what comprise a proof or evidence.

6. Number Theory:

It is considered to be that study which comprises whole and natural numbers. It is considered to be one of the most central concepts in terms of number theory just like a prime number.

7. Dynamical Systems & Differential Equations:

A differential equation is defined as that equation which duly involves an unknown function and also its derivatives. However, in a dynamical system, there is a fixed rule which is initially described by the time dependence in a geometrical manner. 

8. Mathematical Physics:

This is basically concerned with the main application of maths in order to solve problems related to physics as well and the development of the mathematical process and methods which are initially suitable and used in such applications and also used in formulating the physical theories at the same time.

9. Computation:

As you know the fields of mathematics and computing basically intersect both in computer science and it includes the study of the algorithms, scientific computing and also data structures because the study of algorithms includes the methods for problem-solving in the mathematics, engineering and science at the same time.

10. Information Theory and Signal Processing:

Information theory is considered to be a branch of the applied mathematics and also for the electrical engineering that duly involves the quantification of any particular information. Basically, the information theory is essentially developed in order to find the fundamental limits in order to compress and reliably communicating particular data. 

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