Coding is all about dealing with numbers and building logic around them. Mathematics is one of the most important tools for programmers to develop sophisticated applications. Without the knowledge of mathematics, a programmer is basically handicapped.
Therefore, it is important for all programmers to be well versed with certain topics in mathematics that are central to programming.
As a complicated field, there are various types of math in computer science. Computer science examines the principles and use of computers in processing information, designing hardware and software, and using applications. Possessing a strong foundational knowledge of mathematics is vital to gaining an understanding of how computers work. Mathematics is a fundamental scholarly tool in computing.
What Kind of Math is Used in Coding?
There are five major types of math used in computer programming. Let’s take a look at each:
1. Binary Mathematics
Binary math is the heart of computer operation and among the most essential types of math used in computer science. Binary is used to symbolize every number within the computer. The binary number system is an alternative to the decimal system. Using this system simplifies computer design. Reading and simple mathematical operations are vital for hardware low-level programming.
Knowing how to work with a hexadecimal number system is necessary for various programming functions, including setting the color of an item. Standard arithmetic is utilized in numerous functions of computer programming. In nearly every written program, addition, subtraction, multiplication, and division are used.
Learning binary code can be abstract and difficult and sometimes people might think that it is unnecessary to learn such a difficult concept. When you code and program for any application, you never dealing with the binary numbers directly. However, you write and read text, create and see images and work with all other things and hence you should know that the base of all is 0 and 1.
Also, the knowledge of binary code and the binary systems and their working can help you understand the working of a computer and everything your computer does like receiving input, storing and processing information, and producing outputs. It would not be wrong to say that all complex and sophisticated tools and technologies come down to just 1’s and 0’s.
2. Linear Algebra
Algebra is one of the foundational fields of mathematics and something students need to master to move on to higher-level math. Linear algebra covers foundational concepts such as linear equations, quadratic equations, exponents, factoring, polynomials, rational expressions, operations, radicals, ratios, proportions, and rectangular coordinates. Algebra is one of the oldest bodies of mathematical knowledge beyond basic arithmetical functions. It focuses on graphs and equations and the ability to solve equations for unknown variables. Linear Algebra is used in computer programming to develop algorithms and software for working with math functions. It is also involved in design programs for numerical programs.
Statistics is a field of math that deploys quantified models, representations, and synopses to conclude from data sets. In many different fields, statistical analysis is used for a variety of purposes, and this is the same in the computer science field. Statistics allow researchers to analyze data to derive conclusions about underlying trends and to make predictions about future behavior and trends.
Some measures used in statistics include regression analysis, mean, variance, analysis of variance, skewness, and kurtosis. Statistics are used in regression analysis within computer science, as well as data mining, data compression, traffic modeling, speech recognition, vision and image analysis, and artificial intelligence.
Statistics have been especially useful in speech recognition software with the advent of Apple’s Siri. Statistics also back programs such as Google Translate, which uses data to perform online translations. Statistics are used in both of these instances by using the spoken or typed word and changing it into a sequence of numbers that matches it with known dictionaries.
Data mining is performed with the help of statistics by using functions to find irregularities or inconsistencies within data. Data compression uses statistical algorithms to compress data. Statistics are also used in network traffic modeling, whereby available bandwidth is exploited to be usable while the use of statistical programs avoids network congestion. Artificial intelligence tries to simulate human thought using algorithms that are similar to voice recognition or translation software.
Other statistical uses in computer science include quality management, software engineering, storage and retrieval processes, and software and hardware engineering and manufacturing. Algorithms have become necessary in many facets of computer programming and data mining.
Calculus is the examination of continuous change and the rates change occurs. It handles the finding and properties of integrals and derivatives of functions. There are two types of calculus, differential calculus, and integral calculus. Differential calculus deals with the rate of change of a quantity. Integral calculus determines the quantity where the change rate is known. Calculus is used in an array of computer science areas, including creating graphs or visuals, simulations, problem-solving applications, coding in applications, creating statistic solvers, and the design and analysis of algorithms.
Calculus is primarily used in the following areas:
Graphing and Visuals: Calculus is used in creating visuals or graphs. Often these visuals/graphs are 3D. It is used often for video games, especially physics engines. The physics engine defines the physics in the games such as gravity, friction, etc.
Applications to Solve Problems: Calculus is used for general problem-solving applications, simulations, and physics engines. Physics engines create realistic situations in video games and probability simulations. In simulations, it is used to calculate probability.
5. Discrete Mathematics
Discrete math is the heavyweight math field in the realm of computer science and an essential study for a computer science degree. Discrete math examines objects that can be represented finitely using such methods as logic, number theory, graph theory, probability, counting, and recurrences.
Discrete mathematics is fundamental to every aspect of computer science and can be found underlying most areas of programming and computer science, including algorithms, computer systems, computer architecture, computer security, databases, distributed systems, functional programming, operating systems, machine learning, and networks.
The mathematics of modern computer science is built almost entirely on discrete mathematics, in particular combinatorics and graph theory. This means that in order to learn the fundamental algorithms used by computer programmers, students will need a solid background in these subjects.
Concepts of discrete mathematics are used in the following areas:
The field of cryptography, which is the study of how to create security structures and passwords for computers and other electronic systems, is based entirely on discrete mathematics. This is partly because computers send information in discrete — or separate and distinct — bits.
Number theory, one important part of discrete math, allows cryptographers to create and break numerical passwords. Because of the quantity of money and the amount of confidential information involved, cryptographers must first have a solid background in number theory to show they can provide secure passwords and encryption methods.
Relational databases play a part in almost every organization that must keep track of employees, clients, or resources. A relational database connects the traits of a certain piece of information. For example, in a database containing client information, the relational aspect of this database allows the computer system to know how to link the client’s name, address, phone number, and other pertinent information.
This is all done through the discrete math concept of sets. Sets allow information to be grouped and put in order. Since each piece of information and each trait belonging to that piece of information is discrete, the organization of such information in a database requires discrete mathematical methods.
Logistics is the study of organizing the flow of information, goods, and services. Without discrete mathematics, logistics would not exist. This is because logistics makes heavy use of graphs and graph theory, a sub-field of discrete math. Graph theory allows complex logistical problems to simplify into graphs consisting of nodes and lines. A mathematician can analyze these graphs according to the methods of graph theory to determine the best routes for shipping or solving other logistical problems.
Algorithms are the rules by which a computer operates. These rules are created through the laws of discrete mathematics. A computer programmer uses discrete math to design efficient algorithms. This design includes applying discrete math to determine the number of steps an algorithm needs to complete, which implies the speed of the algorithm. Because of discrete mathematical applications in algorithms, today’s computers run faster than ever before.
Programming and mathematics go hand-in-hand. Eventually, every programming problem is an underlying mathematics problem where programming has been used simply as a tool to perform computation and obtain the output. Therefore, all programmers who aim to be successful should be well-versed in the mathematics-related topics mentioned above.