April 24, 2024

Spandana Cheruvu

10th Grade

Williamsville East High School

Various branches of mathematics are required to problem-solve, analyze algorithms, and write efficient codes in computer science. A fundamental five, however, are most necessary in computer science: discrete mathematics, linear algebra, calculus, number theory, and statistics. All of these types of math serve as the backbone for computational thinking and can be applied in algorithm formulation, robotics, software development, and artificial intelligence.

Discrete mathematics is perhaps the most essential math in computer science. One subject that falls under discrete mathematics is binary math - the system that coding relies on. The binary number system, made up of only 0s and 1s, is easier for computers to process and in coding replaces the decimal system. Outside of binary math, discrete mathematics includes countable concepts, set theory, matrix theory, induction and recursion, and graph theory. Discrete math is used for computer architecture, computer systems (hence the binary system), databases, functional programming, machine learning, operating systems, and networks. 

Linear Algebra is the mathematics of vectors, matrices, and linear transformations. It is particularly influential in coding theory, the study of the properties of code and their fit for specific applications. Graphs, functions, and algebraic relationships are also instrumental in the development of algorithms and software for working with mathematical problems. Algebra can be used to design formulas for numerical programs and to complete scientific computations.

Calculus is the study of continuous change and the rates at which change occurs. It involves the findings and properties of integrals and derivatives of functions. There are two types of calculus: differential calculus and integral calculus. Isaac Newton and Gottfried Leibniz are credited with the invention of calculus in the 17th century. Closely related to physics and science, calculus involves the calculation of velocities and slopes. It has many practical uses in computer science, such as in creating graphs, visuals, and simulations. It also may be used in the design and analysis of algorithms. 

Number Theory is a type of pure mathematics, involving primarily positive integers and arithmetic functions. Before the mid-twentieth century, number theory was considered to have no real-world applications, at least not directly. However the development of computers and digital communication revealed number theory’s usefulness. In computer science, it is used for cryptography, the process of utilizing techniques for secure digital communication. In other words, cryptography is code made to be seen only by the intended receiver. Number theory is instrumental in this process; concepts from it such as totient functions and remainder theorems are used in encryption algorithms. Number theory also allows for random number generation in code along with computer organization and security.

Statistics is the last of the five mathematics necessary for computer science. Statistics is the collection, analysis, and interpretation of empirical data. It includes concepts such as probability, regression, variance, hypothesis testing, and correlation. In computer science, statistical models are greatly beneficial for computer scientists to improve the efficiency and accuracy of their algorithms. Statistics provides the principles to evaluate computational systems. Above all, statistics allows computer scientists to make informed decisions about their programs.

The involvement of math in computer science traces back to the earliest days of programming. The world’s first computer programmer, Ada Lovelace, was a mathematician. Her mathematical expertise allowed her to write the first computer program. In her own words, “Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able to fully appreciate, to feel, to seize the unseen, the unconscious”.