# What is Mathematics?

The study of mathematics is a popular subject in the U.S. International students interested in studying math might want to know which subjects are covered in most programs in the U.S. Typical areas include algebra, calculus, and geometry among others.

Mathematics is a popular and vibrant area of study in the U.S. But it is difficult to say precisely what is math. That is in part because mathematics is used for so many different ends. A rough general definition is that mathematics is the study of the relationships between numbers, quantities, magnitudes, and other aspects of abstract reality. If you are an international student interested in studying math in the U.S., you might be particularly interested in which subjects within mathematics are typically covered in university courses.

### Algebra

Along the way to earning a math degree, every student will be expected to have a thorough understanding of algebra. In studying algebra, international students will learn about numerical operations and functions. Many times this will involve executing operations in the correct order to find a solution or solve an equation. Many students will be exposed to algebra in elementary and secondary education. In university courses, more complex and difficult branches of algebra are covered, including linear and abstract algebra.

### Calculus

Virtually all programs require that students be well versed in calculus to earn a math degree, as well. Calculus is useful for studying processes under variable time changes (such as in studying acceleration), complex slopes, and more complex functions than are dealt with in algebra.

There are two broad types of calculus: differential and integral calculus. Differential calculus involves determining the rate in which quantities change over time with respect to independent variables. The newer function is called the derivative function and the process of determining what that function is known as differentiating. That is how differential calculus gets its name.

Integral calculus is the study of two sorts of integrals, indefinite and definite. The indefinite integral is the antiderivative and involves finding a function from a derived function, as described in the previous paragraph. The definite integral is called the limit which, roughly, is equivalent to the area under a curve on a Cartesian plane.

### Geometry, Trigonometry, Topology

Geometrical shapes such as circles, triangles, and prisms also have interesting mathematical properties. Thus, many international students will need to take classes in geometry, trigonometry, and/or topology. Geometry is the general study of the mathematical properties of shapes, trigonometry focuses on the mathematical properties of triangles, and topology is study of the properties of continuity and contiguity. The knowledge international students gain in algebra and calculus classes is essential for understanding the subjects in this group.

### Coursework

In answering the question "what is math?," we can talk about the subjects that are covered within the discipline, but we can also talk about what it is to practice doing math. As you progress through courses in mathematics, you will find a change in the work expected of you. In the earlier classes, you will often be assigned exercises and directed to solve for a solution following a mechanical set of rules. These exercises are good for developing the ability to use mathematical principles in problem-solving, and to test that one has improved on this ability. However, as you move into more advanced classes toward your math degree, your understanding of mathematics needs to be tested more thoroughly than merely following mechanical rules. Instead of rote exercises, students will be expected to develop proofs for their homework assignments and exams. Proofs involve deriving conclusions from a set of assumptions called axioms. Deriving proofs are often challenging and provide different set of challenges than completing exercises, but to be an expert in mathematics, one must master the ability to derive proofs.

So that is the brief answer to the question "what is math?" If these topics sound interesting, then you might like to study math in the U.S.