Computer science is one of the most popular degrees today, with applications in many fields. It’s a vast field that is separated into two categories, theoretical and practical. But the base of both these fields is mathematics.
Mathematics for computer science is also known as discrete mathematics. It is not the same as the mathematics you learn in school, which can make it more confusing to understand.
You will need to be proficient in mathematics to succeed in a career as a computer science engineer. So, before you start learning computer science, you must learn the mathematics of computer science.
Finding the right tutor or an online course can be a hassle. To help you out, we have compiled a complete guide containing all the information you’ll need to start learning.
What Is Mathematics for Computer Science?
Mathematics is often considered one of the most difficult core subjects. On the other hand, for many, computer science is considered exciting and easy to understand.
So, how are these two distinct subjects related? A house is stable only if its foundations are well constructed. Similarly, mathematics is the basis on which computer science is built. Computer science is the innovative application of mathematical algorithms.
These algorithms are specifically designed to be understood by machines. The branch of mathematics that deals with these equations is known as discrete mathematics.
Discrete mathematics is a little different from the general mathematics courses taught in schools. Math taught in schools is considered “pure mathematics,” and has no specific applications. Discrete mathematics is the math that computers use to formulate algorithms and manage data.
Machine learning, artificial intelligence, and data science all use discrete mathematics. To become proficient in any area within computer science, you must be highly knowledgeable in mathematics.
For example, to learn computer graphics, operating systems, and image processing, you will need to know linear algebra. For topics like artificial intelligence and machine learning, you must have an understanding of statistics, vector math, and probability.
What Is Mathematics for Computer Science Used For?
As we discussed earlier, mathematics is the foundation for all fields of computer science, and it is used in almost every computer application. The most common functions of discrete mathematics are:
- Studying a programming language. Mathematics can be used to analyze and understand problems. Solving problems is a vital skill for studying any programming language.
- Creating your own algorithm. To build advanced and complex computer applications, you need to create your own algorithms that meet the needs of your program.
- Solving real-life problems. We use many formulas and mathematical equations in our daily life without knowing it. The operating systems on our smartphones or laptops, as well as simple online search engines, are both based on mathematics.
Types of Mathematics for Computer Science
Discrete mathematics is a vast subject and you do not need to study every aspect of it. Different branches of computer science require different mathematical approaches.
To start, you should understand what sub-sector of discrete mathematics your branch of computer science will require you to know. The mathematical skills you will need depends entirely on the field you choose. There are three main fields.
Calculus
Calculus is very important if you want to pursue a career in image processing. It covers topics like Fourier transform, wavelets, and linear optimization.
Calculus can be applied to data mining, image processing, simulating 3D visuals, computer graphics, and the creation of physical engines. Calculus is also used in both basic and advanced computer software.
Algebra
Algebra is used in every aspect of computer science. From software development to creating algorithms that drive the software, algebra contributes to every field.
Matrix algebra and vector algebra are the two main sub-sectors. Algebra is used in various fields like web search, image processing, computer vision, and cryptography.
Elementary Statistics
You will come across software and programs every day that have been built using elementary statistics. It is used in a wide array of data mining and speech recognition software, as well as traffic modeling, data compression, and artificial intelligence. Elementary stats cover topics including probability and descriptive statistics.
Other Mathematical Skills Required for Computer Science
- Matrix algebra. This refers to a rectangular array of numbers.
- Probability. This is the branch of mathematics that deals with numerical descriptions.
- Information theory. This is the study of storage, communication, and quantification of information.
- Number theory. Number theory is simply the study of the properties of integers.
- Discrete mathematics. This is the study of countable mathematical structures.
- Linear algebra. Linear algebra is the study of linear equations through matrices and vectors.
Learning Mathematics for Computer Science
Learning mathematics for computer science is not as strenuous as it may seem. We have compiled several courses, books, and other resources to help you along the way.
Now, let’s see how long mathematics for computer science takes to learn and what other resources you can use to increase your knowledge.
How Long Does It Take to Learn Mathematics for Computer Science?
There is absolutely no fixed time period for learning mathematics for computer science because it depends on which major you choose. You can acquire a basic understanding of discrete mathematics in a few weeks. But it can take months to master mathematics for computer science.
This will vary from person to person. The time needed to learn discrete mathematics all depends on your ability to grasp the concepts and your ability to visualize while learning.
There is no end to how much you can learn, as mathematics and computer science are constantly evolving, with new algorithms created every day.
The first step you should take is to make up your mind about which area of computer science you would like to specialize in. Your choice of major will determine which field of math you need to learn. Remember that having a strong base is a must when it comes to studying mathematics.
How to Learn Mathematics for Computer Science: Step by Step
The steps listed below will help you to learn mathematics for computer science effectively.
- Choose your major. Choose your area of interest. Decide whether you want to become an expert in machine learning, artificial intelligence, cryptography, or another area.
- Analyze the major. The major you choose will have its own set of requirements. Make a list of all the mathematical topics you will be required to learn for that major.
- Get enrolled in courses. There are mathematics for computer science courses available online. Find the best ones and review books to support your studies.
- Earn certification. Certification will add prestige to your resume and confirm your expertise in a particular subject. Choose a course that will allow you to earn a certificate.
- Work experience. Do some project work to increase your practical knowledge. You can even try to find a computer science internship to enhance your skills.
Best Mathematics for Computer Science Courses and Training
There are a vast number of mathematics-related courses available online. Picking the one that is most worth your time can be challenging. To solve that problem, we have made a list of the best courses.
Discrete Math for Computer Science
- Provider: Udemy
- Time: 2 hours
- Prerequisites: None
- Price: $10
This certified course is provided by Luke’s Programming School via the massive open online course provider Udemy. It offers 23 lectures totaling 1 hour and 47 minutes. Once you complete the course, you will also receive a certificate of completion.
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MIT OpenCourseWare
- Provider: Massachusetts Institute of Technology
- Time: 2 to 3 weeks
- Prerequisites: None
- Price: Free
This course is offered by one of the top education institutions in the world. It covers elementary knowledge in discrete mathematics for computer science. The course is roughly divided into three parts: fundamental mathematics, discrete structures, and discrete probability.
You will be provided with a series of free video lectures and study material in this prestigious course. There are also several assignments followed by exams.
Mathematics for Computer Science
- Provider: Coursera
- Time: 38 hours
- Prerequisites: Basic mathematical concepts
- Price: $38
Coursera offers this course in partnership with the University of London. The lessons are designed to give you a background in the mathematical foundations necessary in computer science.
You will learn about transform numbers, identification of sequences, and more. Upon completing this course, you will be provided with certification.
Discrete Mathematics
- Provider: EdX
- Time: 1 to 2 weeks
- Prerequisites: Basic mathematical concepts
- Price: Free
EdX is a massive open online course provider that collaborates on courses with prestigious institutions like Harvard and MIT.
This course on discrete mathematics deals with graph theory, logic statements, finite and infinite numbers, and other basics.
These concepts are used to design all kinds of programs and apps. With the help of this course, you will gain practical knowledge of how mathematics is used in the real world.
These are the top three courses for learning mathematics for computer science online. But if you plan to focus on another area, you can search for other courses related to a specific topic. Taking any number of these courses will help you expand your knowledge and skill set.
Best Books for Mathematics for Computer Science
Reading is one of the best ways to explore a new topic. These days, we are surrounded by resources to help us meet our learning goals.
Apart from the courses mentioned above, there are lots of books available to help you excel in mathematics for computer science. We have narrowed down the options so you can learn from the best.
Mathematics for Computer Science
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes practical uses and helps you understand mathematical definitions and proofs.
Concrete Mathematics
This textbook was first published in 1989 and is based on a computer science course offered at Stanford University. It concentrates on mathematical knowledge and skills for computer science, especially algorithm analysis.
Concrete Mathematics: A Foundation Mathematics for Computer Science
The second edition of this book by John Vince features new chapters on probability and modular arithmetic. This textbook also includes examples of real-world applications of math in computer science. There are also many sample equations you can use to practice.
Best Online Resources for Mathematics for Computer Science
Mathematics for Computer Science
This free e-book is written by a group of mathematics, computer science, engineering, and AI professors from MIT. It includes university-level notes handwritten by the professors themselves. It is sure to help you gain a better understanding of the key concepts behind discrete mathematics, and will advise you of the best problem-solving methods.
Lectures and Notes
This course includes numerous video lectures, notes, and assignments. Several exam papers are also provided to help you find out any problematic areas in your studies.
Should You Study Mathematics for Computer Science?
Computer science is used in every industry, from healthcare to communication to natural disaster prediction. Its applications are endless.
In the fast-growing world of technology, we are constantly surrounded by machines and equipment. There are many branches of computer science, so there is also a high demand for computer science engineers. Computer science engineers are well paid, with average salaries in the US reaching $94,480.
So, if you are interested in computer science and want a stable income, then this is the right career for you.
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