Is Linear Algebra Harder Than Calculus? (Yes, let’s find out why!)

Is Linear Algebra Harder Than Calculus
A high Student Studying Mathematics

If, like most of my serious students, you are a student wondering which math course to choose; you may be debating between linear algebra and calculus. The truth is that both of these courses involve complex mathematical concepts, so, understandably, many students are curious to know which one is more difficult.

So, is linear algebra harder than calculus? Most of my students have a more challenging time with linear algebra. One of the reasons is that linear algebra forces you to think abstractly and in multiple dimensions. Even though mathematics is relatively simple and repetitive in linear algebra, the concepts are more abstract than in single-variable calculus. It also all depends on the student’s individual strengths and weaknesses.

I realized that most of my students taking linear algebra find the applied part relatively easy but struggle with the proofs part. Generally, proving a new concept in linear algebra is easy; it just requires a new way of thinking.

In this blog post, I will provide an overview of the major differences between linear algebra and calculus to help you make the decision easier.

If you are looking for ways to improve your grades in calculus, I encourage you to read this article about the best ways to learn calculus online with free resources to Ace calculus.

What Is Linear Algebra?

Linear algebra is a mathematics branch focusing on linear equations and functions. It involves manipulating matrices and vectors in order to solve problems. Linear algebra has many applications, including mathematical physics, modern algebra, and coding theory.

Linear algebra is the study of vectors and linear functions (Source: University of California, Davis)

Linear algebra is a mathematical discipline that deals with vectors, matrices, and, more generally, vector spaces and linear transformations. If you want to learn linear algebra, I suggest you start with Khan Academy.

You can also watch the video below to learn more about linear algebra.

What Is Calculus?

On the other hand, calculus deals with derivatives, integrals, and limits to understand how changes in one variable affect another.

The fundamental idea of calculus is to study change by studying “instantaneous ” change, which means changes over small intervals. In real life, calculus helps solve problems related to geography, photography, computer vision (such as for autonomous driving of cars), artificial intelligence, video games, robotics, and even movies.

Calculus is defined as the study of how things change. With calculus, we can model systems with change and make predictions (Source: MIT Department of Mathematics)

Calculus is required if you want to study actuarial science, biology, physics, chemistry, economics, or finance.

Check the video below to learn more about calculus.

Differences Between Linear Algebra and Calculus

Linear algebra is more abstract than calculus because it involves manipulating symbols rather than numbers or graphs. I believe this is what makes linear algebra more challenging for some students to grasp the concepts because they are not used to thinking about math in this way.

In addition, linear algebra requires careful attention to detail since small mistakes can quickly lead to incorrect results.

Calculus, meanwhile, requires a more visual approach since much of its content is based on graphs and diagrams. I believe this makes it easier for some students who may not have an aptitude for abstract thought but struggle with visualizing mathematical concepts.

With calculus, it’s important that you understand the underlying principles before attempting any calculations; otherwise, you might end up getting lost in a sea of numbers without understanding what they mean or how they relate to each other.

NOTE: Calculus is the mathematical study of change. Geometry is the study of shape. Algebra is the study of operations and their application to solving equations (Source: ScienceDirect)

Is Calculus Or Linear Algebra More Difficult?

In terms of difficulty level, many students find linear algebra to be slightly more challenging than calculus because it involves more abstract concepts. In addition, linear algebra requires a deeper understanding of the fundamentals in order to solve problems effectively. On the other hand, calculus is considered easier because it has fewer concepts that need to be mastered before tackling more difficult problems.

Another thing to remember is also the quality of teaching might also play a role in how hard you find linear algebra or calculus.

Calculus Vs. Linear Algebra, Which One Should You Choose?

One important factor to consider when deciding between linear algebra and calculus is their application in real-world scenarios. Calculus is often used in engineering fields such as physics or electrical engineering, while linear algebra is used primarily in data science or computer science applications. So depending on your career goals or interests, one course may be more beneficial than the other for you personally.

So, should you learn calculus first or linear algebra? Most areas of mathematics, including statistics and calculus, require prior knowledge of linear algebra. At the college level, you will likely go into Calculus II, then Linear Algebra, followed by Calculus III. Or sometimes Calculus III followed by Linear Algebra, depending on your major and university you are studying at (Source: Johns Hopkins University)

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Wrapping up

In conclusion, whether linear algebra or calculus is harder depends entirely on the individual student’s strengths and weaknesses. If you are comfortable working with symbols and manipulating matrices, then linear algebra might be right for you; however, if your strength lies with analyzing graphs, then calculus could be a better fit for you.

Whichever path you choose, I suggest you make sure you take time to properly understand the underlying principles to get the most out of your studies.

I believe any student can succeed with proper preparation, hard work, and understanding of the material presented in either course.

Altiné

I am Altiné. I am the guy behind mathodics.com. When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting mathodics.com.

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