Why is Mathematics important in Computer Science?
Imagine the Burj Khalifa (Tallest Building in the world). Now, what is the most important part of this building? No, not it’s not the height (well, that too!) but mainly its foundation. If the Burj Khalifa did not have a strong foundation, it would have been fairly wobbly and much more likely to fall than stand!!
Now, in case you are wondering about this off-topic story, Mathematics is the foundation on which Computer Science is built (Burj Khalifa…get it?!). In fact, it can even be said that Computer Science is the subset of Mathematical Sciences in general. How so? Well, some points that demonstrate this are given below:
1. Discrete Mathematics is the Foundation of Computer Science
Ever heard of Logic Notation, Set Theory, Combinatorics, Graph Theory, Probability, Number Theory, Algebra, etc.? Don’t be overwhelmed, these are all a part of Discrete Mathematics and also a basic foundation for Programming and Computer Science (And that means you need to study these for Computer Science!!!).
A prime example of this is Algebra. While Boolean Algebra is used in Logic Gates, Relational Algebra is used in Databases. In case you need another example, Number Theory has multiple applications in Cryptography and Cryptanalysis. (See the importance yet?!)
2. Mathematics Provides the Analytical Skills Required in Computer Science
Analytical skills are necessary for problem-solving and data analyzation. And guess where you first use these skills? Mathematics!!! Yeah, Mathematics always forces you to analyze your equations and understand the derivation flow in case a mistake is made. This mistake needs to be fixed in order to obtain the final solution.
This provides lots of analytical skills that can be used later in finding and fixing bugs!!! Even though there are modern tools that can do this job automatically, the experience and knowledge gained about the program flow and debugging is invaluable.
3. Mathematics Teaches the Usage of Algorithms
Algorithms are a fundamental part of Computer Science and all of you must have heard of them one way or another (If not…you need to study again!!!). They are basically a set of instructions that demonstrate the implementation of a program or an application.
Now, where did you first use an algorithm? It was not the Computer Science class but actually the Mathematics class! Don’t believe me?!! Well, “2 + 3 = 5” is a basic algorithm you learned in Mathematics class that demonstrates the sum of 2 and 3. Mathematics is actually very important in learning the basic usage of algorithms that are utilized in an advanced form in Computer Science.
4. Mathematical Concepts are Required in many Disciplines of Computer Science
Computer Science is an umbrella term that contains many disciplines like Operating Systems, Databases, Networking, Artificial intelligence, Embedded systems, Data analytics….need I go on?!!! And while there are some disciplines that you can handle with minimal knowledge of Mathematics, most of them require at least some level of competency.
For example, fields like Artificial Intelligence and Machine Learning require a thorough knowledge of Mathematical concepts like Linear algebra, Multivariable Calculus, Probability Theory, etc. (And that makes Maths pretty important!!!)
So What’s the Conclusion?
Is Mathematics really necessary Computer Science? Well, some would say that it depends on the job. For Example: Creating a blog on food does not necessarily require any knowledge of mathematics. But creating a successful blog is another thing entirely. It requires a focus on audience preferences, topic popularity, article ratings, etc. And guess what…Mathematics is required for all of this.
So yes…Mathematics is present in the foundation of Computer Science. And if you want to succeed in any discipline of Computer Science, it is much better to inculcate a love of Mathematics as that will help you tremendously.
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 Program tend to cover them early on, so you can start practicing right away.
Discrete Mathematics
Discrete Mathematics is tangible math. It analyzes the relationship between things that are distinct and separate. The concepts of discrete math include:
- Probability
- Combinatorics
- Logic
- Number theory
- Graph theory
The problem-solving processes of discrete math are the basis of modern computer engineering. They power both simple and complex disciplines such as:
- Computer architecture
- Functional programming
- Distributed systems
- 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.
Statistics
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:
- Data mining
- Machine learning
- Future modeling
- Speech recognition
- User responsiveness
- 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.
Linear Algebra
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:
- Exponents
- Polynomials
- Linear equations
- Quadratic equations
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.
Calculus
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:
- Designing simulations
- 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.
The Relationship between Mathematics and Computer Science
1. Mathematics is abstract in nature
Most concepts of maths are taught through abstract language. On
the other hand, one of the things that are covered in computer science is the
study of programming languages. Most of these languages are also abstract in
nature. They are characterized by syntax, well-defined processes, symbols,
single words, and even visuals.
Given the abstract nature of maths, you will have a smooth
sailing when learning programming languages. Mathematics will impart a student
with the art of reading, understanding and analyzing a problem before coming up
with a solution. All these skills are vital when it comes to programming and
computer science in general.
2.
Maths teaches on how to utilize algorithms
An algorithm is a commonly used term in the field of computer
science and technology in general. It provides a basis under which any program
or application should be created and implemented.
Although most people encounter this term for the first time in a
computer science class, the truth of the matter is they were introduced to it
in a math class. Do you know that a simple equation such as 7+3=10 is an
algorithm? From such simple equations, students are then introduced to complex
algorithms in computer science.
3.
Mathematics gives students analysis skills
Coding is not a one-way process. You have to keep coming back to
inspect what you have written and verified whether it is correct. This is
because you are bound to make one or several mistakes when coding.
In the field of mathematics, students are usually forced to
analyze their work. The answers that you might have given are not always
accurate. You need to come back and inspect the formula and the figures that
you have used. You will fix the mistake or errors before reaching out to your
final answer.
In other words, maths prepares students for the tasks of
identifying and fixing bugs. Even if there are tools that can do this job
automatically, students will still have the zeal of doing this job effortlessly.
4.
Computer science has lots of maths
Apart from the above skills, you will also encounter lots of
maths in computer science. Here you will be required to use mathematics
knowledge to solve real-life problems through a computer. Woe unto you if you never
took your math classes seriously.
For instance, there are lots of mathematical equations and
formulas that are used to design a program for controlling a self-driven car.
It will be very difficult if not impossible to write such programs if you are
completely green in the field of mathematics.
5.
Discrete maths is the background of computer science
It is not a secret that discrete mathematics forms a strong foundation for the study of programming and computer science. It will equip you with deep knowledge about algorithms, computability, and complexity which you will use in programming. Boolean algebra- a subject in discrete math is applied in creating control functions when programming. Once you master these mathematical theories, you will have an easy time putting them into practice in computer science.
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