How is math used in computer science
At their core, computers are number-crunchers. Just think about the word “computer” — something that computes. Even if you use your laptop to send emails more often than to balance your bank account, there’s math going on inside the machine.
If you aspire to a career in computer science, you may wonder how much math you need to know to succeed. The answer depends on what you want to do with your computing career, and how advanced you want to get.
Do You Need Math in Computer Science?
Because math is a foundational part of computer systems, every programmer and computer scientist needs to have basic mathematical knowledge. The type and level of math you need depends on what areas of computer science you want to work in.
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Some computer science career tracks require only minimal mathematical knowledge. For example, as long as you know basic programming languages and can do simple arithmetic, you can develop basic mobile apps.
But if you want to go further with your computer science career, perhaps exploring advanced fields like computer security or operating systems, you’ll need to understand some higher-level math concepts. No one expects computer scientists to be mathematicians, but studying high school and college level math can open doors.
"[In CS education] you learn more about data structures and algorithms. That's kind of the core, the math side of computer science."
“[In CS education] you learn more about data structures and algorithms,” said David Joyner, PhD and executive director of online education for the College of Computing at the Georgia Institute of Technology and instructor for edX’s Introduction to Python Programming Professional Certificate program.
“That's kind of the core, the math side of computer science. Those are very, very important because they give you a deeper knowledge of what developing with computers really is all about."
Math is fundamental to computer science, but an affinity towards math is not a prerequisite for success in the field. For example, the final course in the Python program Joyner is an instructor for, Computing in Python IV: Objects & Algorithms, covers object-oriented programming, a popular paradigm that Joyner likens to philosophy. “Object oriented programming speaks to my general desire to make people aware that computer science isn't just for the people who were really good at math in high school. It’s an area of programming that has a surprisingly deep conjunction with philosophy,” Joyner said. “I think that's one thing that people often underestimate about careers in computer science, is they are very creative kinds of areas.”
What Kind of Math Is Used in Computer Science?
Computer scientists use all different types of math. Those who work with advanced algorithms and matrices, like the kind involved in image recognition for medical diagnostics, need to understand higher-level concepts like differential equations.
But for aspiring and first year professionals, it’s more important to master number theory and basic equations. Here are some topics to explore.
Binary and Hexadecimal Counting
The binary number system uses only two digits, 0 and 1, to express all mathematical concepts. Computers use the binary system instead of the more common decimal system, so computer scientists need to know how it works.
Computers can read binary, but it can be inconvenient for humans to deal with. As an alternative, computer programming has turned to a system called hexadecimal, which uses all nine decimal digits and the letters A through F. It makes more sense to humans and converts electronically to binary.
Don’t let the unfamiliarity of these languages scare you away. Computer science programs tend to cover them early on, so you can start practicing right away.
Discrete math is tangible math. It analyzes the relationship between things that are distinct and separate. The concepts of discrete math include:
The problem-solving processes of discrete math are the basis of modern computer engineering. They power both simple and complex disciplines such as:
Machine learning and artificial intelligence
As a computer science professional, you might use discrete math to test out multiple algorithms and learn which is the most efficient. Meanwhile, the logical thinking you develop as a discrete math student will help you to approach programming and development tasks more methodically.
Data has become an increasingly important aspect of scientific computing in the past few years, from machine learning to personalized app performance. This increased reliance on data has made statistics an important topic of study for all computer science students.
Statistics allow computer programs to deliver accurate generalizations and predictions based on available information. Understanding statistics can make it easier to grasp concepts like:
Computer graphics analysis
The more you learn about statistics, the more adept you’ll become at managing and using complex data structures. This lets you write more advanced algorithms and push the envelope in software customization.
Computer science and software engineering rely on algorithms. An algorithm is a formula that takes you from a specific input to the correct output. If that sounds familiar, it may be reminding you of middle school or high school algebra.
Algebra includes concepts like:
Each of these concepts has real world computer science applications. Understanding exponential relationships can help you to adapt visuals so they appeal to the eye. Solving linear equations helps with analysis of algorithms because it helps you to spot inaccuracies.
You can get by in software development without knowing much algebra, but learning it can help you to reach greater heights.
If you plan to get a computer science degree, you’ll probably take a calculus course at some point.
There are two different types of calculus: integral calculus and differential calculus. Together, these disciplines help you to figure out rate of change, which is an important ingredient in many algorithms and programs.
Differential equations are particularly important. A differential equation calculates how something changes and how fast that happens, so a computer can predict future outputs. This helps with:
Improving problem-solving programs
Creating effective algorithms
Developing accurate graphs
The word “calculus” scares some computer science students, but it’s much less intimidating than most people think. The key is to find a course that will lead you through what you need to know to work in your field.