# What is Mathematics?

In the USA, it has become popular to study mathematics. Besides, more and more international students express particular interest in obtaining education in mathematics specifically in the USA. Therefore, many of them are eager to know which disciplines are included in the course of studying, which of them are compulsory and which are voluntary. As a rule, mandatory courses are calculus, algebra, and geometry among others. These comprise the basic knowledge that one should obtain before moving on to study something more advanced and complex.

It is hard to define what mathematics is, but it should be admitted that it is a versatile discipline. Students with excellent knowledge and skills in mathematics can work in different fields even if they are not directly related to math. Often, these fields can be just adjacent to math, in other words, interdisciplinary areas, such as business, accounting, finance, computer studies, etc. Mathematics studies the relationship between quantities, numbers, magnitudes, and other issues. So, if you are an overseas student showing particular interest in math, you might be really interested to get some more details regarding the main courses that belong to university math courses.

## Calculus

Almost all studying programs require from students to have excellent knowledge of calculus if they aim to earn a math degree. Calculus is applicable for studying acceleration, complex algebraic functions, and complex slopes among others.

Calculus is divided into two types: differential and integral. The first type involves determining the rate at which certain quantities undergo alterations with time in relation to independent variables. The whole process of determination is referred to as “differentiation,” whereas the newer function is entitled “derivative function.” In short, this is how differential calculus has obtained its name. The second type studies two kinds of integrals – definite and indefinite. The former integral is referred to as the limit, which actually equals to the area under the curve on a Cartesian plane. The latter is called the antiderivative, and it involves finding a function from a derived one.

### Algebra

Throughout the long and tiresome process of obtaining a degree in mathematics, every student will be required to have profound understanding of algebra. International students studying algebra in the USA will learn about functions and numerical operations. In particular, they will develop skills in executing algebraic operation in the right order in order to work out a solution or solve an equation. What is even more important, many students will apply algebra even in elementary and secondary education. Further, when students want to study math at university, they will learn more complex and advanced algebraic principles, namely learn the principles of abstract and linear algebra.

### Geometry, Trigonometry, and Topology

The studying of the properties of triangles, circles, and prisms is also interesting for many students. In such case, they enroll on courses in trigonometry, geometry, and topology. Trigonometry is focused on studying mathematical properties of triangles. Concerning geometry, it is the general study of shapes and their mathematical properties. Topology, on the other hand, studies the properties of contiguity and continuity. To successfully perform in geometry, trigonometry, and topology, students need to be well versed in algebra.

### Coursework

When seeking an answer to the question, “What is mathematics?” it is possible to talk about general subjects that the discipline covers. It is equally important to find out what it is like to apply math in practice. As you make progress in the math courses, you will see that you are expected to change something in your work. For example, in the first classes, you will have to do exercises aimed at finding a solution to some mathematical problems. Such exercises will help you improve your practical skills. During more advanced classes, however, your mathematical skills will be tested in some other ways rather than merely testing your knowledge of mechanical rules. In particular, you will be given home tasks to develop some proofs and you will pass more exams than before. When developing proofs, you will learn how to derive conclusions from axioms, which are a set of assumptions. Such task is always rather challenging, but it helps one to become an expert in mathematics.

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