 # What is Mathematics?

Posted at: 08 Sep 2020
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Should you be interested in majoring mathematics, you might find mathematics unique and beautiful, or, perhaps, you simply love dealing with numbers. However, what is mathematics? Math is the study of numbers, shapes, and space using reason and usually a special system of symbols and rules for organizing them. Before getting to know branches of mathematics, you should know what pure mathematics, applied mathematics, and general mathematics are.

Pure Mathematics: Pure mathematics is the study of the basic concepts and structures that underlie mathematics. Its purpose is to search for a deeper understanding and an expanded knowledge of mathematics itself. Traditionally, pure mathematics has been classified into three general fields: analysis, which deals with continuous aspects of mathematics; algebra, which deals with discrete aspects; and geometry. Some people would like to include combinatorics as well. For example, pure mathematics exercises would look like “Show that the triangle formed by the points (-2,5), (1, 3) and (5, 9) is right-angled.” or “An arithmetic progression has first term a and common difference -1. The sum of the first n terms is equal to the sum of the first 3n terms. Express an in terms of n.” However, as you study further into it, the exercises tend to get more difficult.

Applied Mathematics: Applied mathematics is the mathematical study of general scientific concepts, principles, and phenomena that, because of their widespread occurrence and application, relate or unify various disciplines. It includes probability, statistics, numerical analysis, and symbolic computing. The learning goal of applied mathematics is 1. Master theoretical foundations based on mathematical rigor through proofs 2. Apply mathematical theory to model and solve problems dealing with physical, natural, and societal problems 3. Use technology to solve computational problems, including simulation and visualization of mathematical models 4. Provide clear and effective written and oral communication to diverse audiences 5. Develop content knowledge in a related discipline

General Mathematics: General Mathematics is the study of pure mathematics and applied mathematics together. The study is not in-depth and its aim is to provide students to gain a basic understanding of math. To simply put it, think of the high school math as general mathematics.

What are the branches of mathematics?
There are many branches and sub-branches in mathematics. Most of them connect to one another in many ways, so there's no definite answer to that question. Here are some branches of mathematics
Analysis: It is the branch that deals with the study of the rate of change of different quantities, which also includes the study of functions, calculus, differential equations, etc. To get in detail, it focuses on measure theory, complex analysis, geometric analysis, harmonic analysis, stochastic analysis, calculus of variation, functional analysis, and multivariate & vector analysis. It is perhaps the branch of mathematics that has the most obvious and direct applications to other sciences. In the analysis, you study the ways in which a certain quantity behaves when it depends on one or several parameters, like the position of a ball thrown by a football player depending on time and on how he launched it. I'd say it takes its origins in Descartes' work and was developed a lot by Newton and Leibniz, and those who came after them.
Algebra: It is a kind of arithmetic where we use unknown quantities along with numbers. These unknown quantities are represented with letters of the English alphabet such as X, Y, A, B, etc. or symbols. The use of letters helps us to generalize the formulas and rules that you write and also helps you to find the unknown missing values in the algebraic expressions and equations. It includes linear algebra, abstract algebra, and number theory.
Geometry: It is the most practical branch of mathematics that deals with shapes and sizes of figures and their properties. The basic elements of geometry are points, lines, angles, surfaces, and solids. It focuses on topology, discrete geometry (or combinatorial geometry), manifold, differential geometry, convex geometry and etc.
- Discrete mathematics: It is of direct importance to the fields of Computer Science and Information Technology. This branch of mathematics includes studying areas such as set theory, logic, relations, graph theory, and analysis of algorithms.
Combinatorics: the branch of mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those of graph theory. It includes graph theory, external combinatorics, and enumerative combinatorics.

What are the job opportunities?
Usually, people often think majoring in mathematics means being a math teacher. It is not true. Mathematics is versatile since every field needs math. For example, math graduates can calculate the probability for business companies such as insurance companies to maximize the profits, or they simply work in the engineering field, or even working with information technology. So, the job includes actuarial analyst, chartered certified accountant, data analyst, investment analyst, statistician, systems developer, insurance underwriter, software tester, financial manager, operational researcher, or even financial trader.

Should you be interested in majoring in mathematics, the Royal University of Phnom Penh (RUPP) is the best choice for you.

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