Discrete math deals with counting, probability, logic, and algorithms and is one of the branches of mathematics.
Discrete math is used in many different fields of study, including computer science, engineering, physics, chemistry, biology, economics, and finance.
But is discrete math hard? It might sound difficult just by the name, ‘discrete’, as-if there’s something secretive about it. There are those who say discrete math is hard, but there are others who say that it’s much easier.
In this article, I’ll cover how discrete math can be hard and easy at the same time to different people.
- Related article: What are the Hard Majors in College?
What Is Discrete Mathematics?
Discrete mathematics is the study of discrete (countable), as opposed to continuous, mathematical objects (uncountable). Discrete mathematics is widely used in many disciplines, including engineering, physics, computer science, and others. Sets, sequences, functions, graphs, and number counting are a few examples.
Discrete mathematics is frequently compared to other branches of mathematics, such as analysis, algebra, geometry, calculus, probability, statistics, and topology.
Is Discrete Math Hard?
Yes, discrete math is hard. The difficulty of discrete mathematics comes from a need for high level of analytical and problem-solving skills. Discrete mathematics, which is largely concerned with abstract mathematical problems, depends heavily on logic and proofs.
Due to its abstract character, discrete mathematics may be difficult for students to understand. Logical and abstract math issues serve as the foundation for the majority of discrete math issues. For a variety of reasons, most college students find discrete mathematics challenging.
It may be more difficult for kids to think conceptually and then reason logically if they have never been introduced to abstract arithmetic. Since there might not be a solution, there is also a problem with not having to prove anything.
The use of proofs in mathematics classes is highly advantageous. They can be used to verify whether something is actually true or not. A proof, which is analogous to presenting a story to reach a conclusion, can be used to establish the truth or falsity of a mathematical proposition.
Proofs can be difficult because they need creativity, forethought, and perseverance. Students commonly get trapped when attempting to verify assertions. Since there is no one “correct” answer to a problem, finding a strong argument requires some trial and error.
Even though discrete mathematics is routinely taught at the introductory level, it is challenging to learn. The following are a few subjects that are typically covered in an undergraduate discrete math course:
- Formality notation
- Proof methods
- Induction
- Well ordering
- Relations
- Elementary graph theory
- Integer congruences
- Asymptotics
- Growth of functions
- Permutation and combination
- Counting principles
- Discrete probability
You have it, then. There are numerous subjects that you might have zero knowledge of. This is a crucial component that increases the difficulty of the topic overall. Learning difficult concepts is made simpler by gaining a strong foundation in the fundamentals.
The absence of any formula memorization requirements is one of the best things about discrete mathematics (DM). To use DM to address issues encountered in daily life is the goal. Discrete math can be used in a wide variety of everyday settings.
A discount code, for instance, may be provided when making an online purchase. You receive the discount if you properly enter the code. However, if the incorrect code is entered, the full amount is paid because the discount won’t apply. Therefore, you need to comprehend the idea of discounts before you go shopping.
Another situation is when you’re trying to figure out a puzzle. For instance, there may be some missing pieces in a photograph. You work hard to assemble the components. It’s not as cut-and-dry as you may think because certain portions might resemble others. The next step is to figure out how to combine the components while keeping an eye out for their differences.
The foundation of computer science is discrete mathematics. DM is a key component of several logic and programming disciplines, including graph theory, automata theory, game theory, cryptography, and others.
Only a handful of the topics addressed by the branch of mathematics known as discrete mathematics include counting, grouping, permutations, combinations, and other related mathematical concepts. In order to find solutions to problems combining computation, logic, and probability, these concepts are used.
Is Discrete Math The Hardest Math?
Yes and No. There’s no doubt that discrete math is hard, but whether it’s the hardest math course depends on who you ask. Some students say DM is the hardest math class, while other students will say that the most difficult math class is actually calculus. But one thing they all agree on is that DM is one of the most useful classes. They can use DM’s principles across other classes and in daily life.
Jay Collier, a Math Major from Carnegie Mellon, says “Discrete math uses a different part of your brain than calculus and algebra.” He adds that “it’s a great way to make sure that you’re thinking logically and mathematically as opposed to just memorizing things. If you are good at memorizing and applying formuals, you probably won’t like DM.”
The best thing about discrete mathematics is how it forces you to think creatively. Not all math is learned by memorization of facts. Instead, you learn how to use math in practical contexts. This implies that issues in virtually every discipline can be solved using discrete mathematics.
For the majority of STEM Majors, Discrete Math is not the hardest math course. Students find that Discrete Math is easier than Linear Algebra, Differential Equations, and Calculus II. Due to the fact that DM is your first exposure to mathematical reasoning and proofs, it might be said to be challenging.
Because it contains more sophisticated information than discrete math, linear algebra is regarded as being more difficult. Calculus II has more complex ideas and concepts than DM, making it harder. Calculus II’s complexity, however, varies depending on which courses use proofs and which don’t.
Because you must comprehend the underlying concepts and then use them to solve problems, differential equations are challenging.
You could believe that memorizing formulas is the simplest option, but if you try to use a formula to solve an issue, you will surely run into trouble. You will never arrive to a solution if you try to understand what happens when you enter numbers.
Understanding the fundamental idea that enables us to answer any problem is a superior strategy. Once you fully grasp the idea, you can begin using it in other contexts.
How Long Does It Take to Learn Discrete Mathematics?
It depends on your preferred method of learning and how challenging each topic is. Learn discrete mathematics in a variety of methods. In roughly 12–16 weeks, or a college semester, you can probably lay a strong foundation. Though DM will take years to master.
Universities hardly ever offer DM degrees. Instead, DM is a branch of mathematics that you study as part of degrees in computer science, engineering, and mathematics.
The greatest approaches to study DM, besides than attending discrete math classes in school, are:
- Online Courses and Resources – Khan Academy, MIT Open Courseware, Coursera, Udemy, and EdX are very helpful in learning Discrete Maths. These online courses are free and offer a wide variety of topics.
- Practice Problems – Try solving problems with no solution. Solve them again until you get the right answer.
- Textbooks – Books are another excellent resource for learning Discrete Maths because they provide detailed explanations of concepts. Some books include examples and solutions to problems.
- Online Videos – Videos are also a great way to learn DM. It can be similar to lecutre videos. They explain concepts in easy to understand language.
- Join a Community – There are several communities online that discuss Discrete Maths. For example, there are forums dedicated to Discrete Maths on Quora, Reddit, and StackExchange.
How Much Studying Is Needed for Discrete Math?
Your weekly time commitment for a discrete mathematics course will typically be between 10 and 15 hours. However, that may change based on the institution you are attending, your prior math experience, and your lecturer.
Depending on how much you already know, studying takes a variety of different amounts of time. Finding out where you are deficient in knowledge is the first step. You can then choose what to concentrate on.
Do Software Developers Use Discrete Math?
Yes. Every day, discrete math is used by software developers and engineers. To tackle challenging issues, they write code. Writing algorithms is a significant part of software development. In essence, algorithms are only collections of rules used to solve issues.
For many different kinds of software engineers, discrete mathematics is a crucial tool. It aids them in developing a deeper understanding of how programs operate and in logically considering alternative solutions.
If they haven’t studied discrete mathematics previously or if they wish to brush up, some programmers may enroll in an online course.
You can learn discrete math online through a variety of courses.
What Are Some Common Applications of Discrete Math?
Discrete math is used in all kinds of applications. Here are some common ones:
- Computer Science – Algorithms, Data Structures, Graph Theory, Logic, Probability, Set Theory, Topology, etc.
- Engineering – Algorithms, Formal Languages, Programming Languages, Robotics, Signal Processing, Systems Analysis, etc.
- Mathematics – Geometry, Linear Algebra, Number Theory, Polynomials, Statistics, etc.
- Statistics – Bayesian Inference, Decision Theory, Estimation, Hypothesis Testing, Mathematical Programming, Markov Chains, Monte Carlo Simulation, Optimization, Sampling Distributions, Statistical Modeling, Time Series Analysis, etc.
Do You Need Calculus to Learn Discrete Math?
No, calculus is not necessary to learn discrete mathematics. One doesn’t really build on the other because they are two distinct areas of mathematics. You should however be familiar with the fundamentals of calculus.
Calculus is crucial because it helps us comprehend continuous functions. Functions that change continually are said to be continuous. This implies that they are subject to both spatial and temporal change.
More discrete things are the topic of discrete math. These are things that remain the same across both time and place. Permutations, combinations, sequences, graphs, and trees are a few examples.
The majority of colleges will insist that you take Calculus I before DM. After that, you study discrete mathematics before moving on to more difficult calculus. This is because calculus I, which introduces pupils to college-level mathematics, is sometimes the very first math course STEM graduates attend.
Prior to studying more complex types of calculus, it is crucial to grasp discrete mathematics since it clarifies what calculus does and its purposes. Calculus will make discrete mathematics easier to understand for you, and vice versa.
Is Discrete Math Hard? Final Thoughts
Even though discrete math is hard, it is still important to learn. Learning discrete mathematics will be helpful if you have an interest in computer science, engineering, statistics, or any other area of programming.
For more on how hard other majors and topics are, check out these articles:
