Discrete math is the study of mathematical structures that are countable, distinct, and separable.
It is important to point out the difference between discrete and continuous data types. Continous data includes the full range of numbers that we are familiar with. For instance, the numbers 2.67323 and 2.312 both fall under the category of continuous data.
On the other hand, discrete data types have clear spaces between them. Discrete mathematics focuses on discrete structures such as integers, combinations, graphs, and logical statements.
In this article, we will go over the difficulty of discrete mathematics, strategies to overcome the challenges you may face in the course, and compare it with other math classes.
Is Discrete Math Hard?
Discrete math is hard. Discrete math is considered difficult because it demands strong analytical and problem-solving skills. Discrete math relies heavily on logic and proof. Most students find discrete math hard because they have not experienced anything like it before.
Discrete math is essentially logic and abstract math problems. Discrete math uses several tools including induction, logic, invariants, examples, and optimality. Discrete mathematicians use mathematical proofs to discover whether a statement is true or false.
A proof is a story that tells you whether a mathematical statement is true or not. This is done with the help of definitions, theorems, and postulates. Discrete math is the first introduction to mathematical proofs for most students which explains why so many students struggle with this course.
Proofs are challenging because they require creativity, strategy, and perseverance. There is no single correct way to approach a problem and find suitable mathematical proof for it. You will need to play around with the problem until you construct an appropriate proof for it.
A typical undergraduate discrete math course will cover the following topics:
- Formal Logic Notation
- Proof Methods
- Induction
- Well Ordering
- Relations
- Elementary Graph Theory
- Integer Congruences
- Asymptotic Notation
- Growth of Functions
- Permutations and Combinations
- Counting Principles
- Discrete Probaibility
As you can see for yourself you would probably be unfamiliar with most of these topics. This is another factor that contributes to the overall difficulty of discrete math. Knowing the rudiments makes it easier to learn the more advanced technicalities of any particular topic.
Most other maths courses you would have encountered until now place rely on memorization of the formulae and plugging in the values accordingly. They require minimal analysis and abstract thought.
Discrete maths is different. This is possibly why most students struggle with the course. Discrete maths demands strong critical thinking and problem-solving skills. The questions will require you to apply your knowledge to both familiar and unfamiliar contexts.
Discrete math is an integral course for many STEM disciplines including computer science, mathematics, and the various branches of engineering.
A computer is a discrete machine itself since computers work with 1s and 0s. Moreover, discrete math is applicable in several computers science domains such as big data, machine learning, and cryptography and remains central to game theory, automata theory, and graph theory.
Is Discrete Math The Hardest Math?
Discrete math is not the hardest math course for most STEM majors. Students find linear algebra, calculus II, and differential equations harder than discrete math. Discrete math is considered difficult since it is the first time students are introduced to mathematical reasoning and proofs.
Linear algebra is considered harder than discrete math since it has more complex material, the subject material is difficult to visualize, and the mathematical proofs are more difficult.
Calculus II is also harder than discrete math since it has more advanced concepts and ideas. However, the difficulty of calculus II is subjective since some courses are proof-based while others are not.
Finally, differential equations are also harder than discrete math since they are abstract and applied at the same time. Differential equations require a deep understanding of the underlying principles but also the knowledge to manipulate equations to fulfill the requirements of the questions.
Other math courses such as real analysis and topology are harder than all the courses we have mentioned but we are not discussing them in detail since most STEM majors do not have to take these classes. The courses are reserved for mathematicians and to a lesser extent physicists.
Do Programmers use Discrete Math?
Programmers used discrete math moderately. Discrete math is an important component of computer science theories and applications but most programmers are involved in surface-level work. However, discrete math concepts are used by programmers to solve more challenging tasks.
Many programmers today do not graduate with a college degree in computer science or software engineering. Instead, potential programmers join coding boot camps where they learn the basics of software development and get hired for programming-related jobs.
Similarly, students who study discrete math in college do not necessarily use it in their careers. However, to be eligible for all kinds of programming and technology-oriented jobs you should study discrete math since it is very useful in many fields.
Not studying discrete math will limit the number of programming jobs you can apply to. Hence, if you are being offered the chance to study discrete math you should go for it. Even if you don’t use it directly it will make you a better programmer since you will have a more thorough understanding of the underlying principles.
How Long Does It Take to Learn Discrete Mathematics?
You can learn the fundamentals of discrete mathematics in 6-12 weeks of consistent studying. Discrete math is a broad field and can take years to master. However, most students only take one or two introductory courses of discrete math and can easily study them over a semester.
Most universities do not have degrees that focus purely on discrete mathematics. Instead, discrete math is considered a subset of mathematics, and only one or two courses are allocated to learning it.
In STEM majors such as computer science and engineering, discrete math concepts are used to build on more complex ideas and theories. Hence, you can easily learn the level of discrete math required for your particular major in a few weeks.
The best strategies to learn discrete math include consistent studying, regular reinforcement of concepts, and mastering mathematical proofs. Knowing your way about mathematical proofs is invaluable since they are a core component for several STEM courses.
Do You Need Calculus to Learn Discrete Math?
You do not need college-level calculus to learn discrete math since calculus at high school is usually a sufficient prerequisite. Calculus is a form of continuous math whereas discrete math is the branch of mathematics that deals with distinct values.
Since calculus and discrete math are two different branches of mathematics you do not need either one to study the other.
However, you may find colleges requiring you to study calculus I before discrete math. Similarly, they may demand you to study discrete math before taking on more advanced forms of calculus.
This is because calculus I is often the first math course that STEM majors take and it serves the purpose of introducing students to college-level mathematics. Discrete math is the first course where students get accustomed to a variety of mathematical techniques such as proofs which are useful for more advanced math courses including calculus.
Hence, it is important to take discrete math before proceeding with more advanced forms of calculus. This is to ensure you have a more thorough understanding of calculus when you get a chance to study it.
Is Discrete Math Used In Physics?
Discrete math is used sparingly in physics. The core principles of physics are based on continuous math such as linear algebra, differential equations, and calculus. This explains why discrete math is usually not a requirement for physics majors.
The few areas where physicists use discrete math include computational physics. Physics is the branch of science that deals with the nature and properties of matter and energy. Physics focuses on the real world where numbers are continuous.
A computer on the other hand is a discrete machine which explains why discrete math is a core course in computer science curriculums.
Conclusion
Discrete math is an essential course for computer science and to a lesser extent for engineering majors. It is a difficult course since it focuses on problem solving and analysis. It is also the first real introduction to mathematical reasoning including proofs which further exacerbates the difficulty of the course.
However, with consistent studying and regular revision, you can easily master the course. Good Luck!
