Out of the various subdisciplines of mathematics, linear algebra has the most apparent use in multiple fields.
But its frequent presence in many industries does not mean that it is easy to master.
Linear algebra can be hard to learn because it demands logical and analytical skills when dealing with complicated topics like algebraic manipulations and function visualization. Unlike basic math, which relies heavily on calculation, you need to establish connections and write proofs to solve linear algebraic problems.
But there are ways to make studying linear algebra more painless.
In this article, we explore what makes linear algebra challenging and the strategies you can employ in your learning process.
Why Is Linear Algebra Hard to Learn?
Linear algebra can be difficult to learn because its abstract concepts require painstaking analysis for proof and connection.
In high school algebra, you are taught to visualize the functions through graphs.
However, with in-depth linear algebra, it will take more than charts to grasp the concept altogether, as you need to use techniques relative to vector geometry, matrices, and other mapping forms.
Some of the most challenging parts of linear algebra involve setting axioms for mathematical structures and digging into complex topics like abstract vector space, linear independence, orthogonal matrices, and singular value decomposition.
The topic names themselves can already be intimidating and get even more complicated as you get to later concepts.
For this reason and more, those who take linear algebra as a course are usually individuals who have an interest in becoming physicists, statisticians, research mathematicians, engineers, and economists.
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Can I Teach Myself Linear Algebra?
Given the complexity of linear algebra, it may not be the best idea to learn the subject independently if you’re not inclined to learn mathematics on your own.
Your best chance of mastering the subject is through enrolling in a course or having linear algebra as a major subject. This way, you get to learn from professors and experts in the field.
On the other hand, learning linear algebra concepts in the classroom or lecture hall may not be enough to comprehend the topics completely.
In this sense, you will need to supplement the class lectures by self-studying resources and techniques that best suit your learning style.
How Can I Be Better in Linear Algebra?
Like any other challenging subject, getting better in linear algebra combines grit, persistence, high motivation, and a smart approach. A critical foundation for this route is establishing your “big why.”
Pursuing linear algebra should be founded on clear goals.
It’s simply asking yourself, “What do I get from learning this subject?.” Once you’re set with this part, follow these steps to make your learning journey less difficult.
1. Understand the Real-life Application of Linear Algebra
It’s a known fact that when learners perceive the significance or use of a subject in real-life scenarios, it becomes easier to understand the topic and learn the concepts altogether.
Linear algebra shaped the evolution of artificial intelligence, information technology, imaging, modern physics, and even eCommerce.
So, it’s not too difficult to picture its real-life applications. Specifically, linear algebra is used in the following areas:
- Creating algorithms for search engines like Google
- Check energy levels at atomic and subatomic levels
- Used to analyze data for space study
- Machine learning using artificial intelligence
- Create accurate prediction levels for statistical data
- Natural language processing for chatbots, text analysis, and speech recognition
These are only a fraction of what linear algebra can do. However, it could be enough to make people understand how significant the subject is, especially for those who want to have a career in information technology, software development, and data science.
2. Take Notes During Lecture
Note-taking has been found to increase your engagement during lectures and allow you to pay attention.
In addition, it’s a good strategy to keep your mind from wandering off when the professor presents a topic – a habit that can be common when you lack focus.
However, taking notes during class is not simply copying what’s on the board or the presentation.
To do this strategy effectively, you must isolate key concepts, formulas, and ideas.
Write them down and the vital details that come with them. If they seemed vague, write a comment on the side stating you need more clarifications on the topic.
Then, you can consult your professor or highlight the concept during your review.
3. Ask Any Questions You Have During and After Class
Any confusion during the lecture should be addressed sooner than later.
For example, if you neglect your questions regarding a certain topic, the less likely you’ll understand it and move forward to the next concept.
Unfortunately, many students tend to shove their questions at the back in fear of getting humiliated in class for asking surface-level questions.
But for those lucky to have great teachers, you can ask them questions even after the lecture.
Otherwise, you can count on your peers or learning resources.
4. Use Free Learning Resources Online
Having multiple resources for studying is always an advantage when dealing with a complex subject.
Although your textbook and notes will keep you on the same page as your professor, you could also use other free learning resources downloaded or searchable online.
To start with, check out these websites and resource materials when studying linear algebra concepts:
- Khan Academy
- Better Explained
- Fundamentals of linear algebra
- UC Davis Math
- Linear algebra for beginners
You can also watch video tutorials on Youtube, such as the ones presented by Professor Dave Explains.
He has an entire playlist of linear algebra tutorials you can repeatedly use until the concepts become easier to understand.
It’s also a great learning resource for auditory learners.
5. Join a Study Group
Study groups can be influential if everyone maintains the same level of enthusiasm and get on a similar goal.
Being with your classmates allows you to learn from them and provides an equal opportunity to teach the concepts.
You can learn more when you teach. By relaying the information you gathered from the lectures and your learning materials, you can encapsulate the vital details and translate them into your own understanding.
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Frequently Asked Questions
What Level of Maths Is Linear Algebra?
Despite being already challenging, linear algebra is generally considered intermediate-level math.
This means it’s not as simple as pre-algebra and basic mathematics but not as complex as abstract algebra, modern statistics, or topology.
Nonetheless, the various terms you have to be familiar with, along with the multi-faceted analysis requirement, make linear algebra appear more difficult than it actually is.
Is Linear Algebra Worth Taking?
Yes, taking linear algebra is advantageous, given its many applications in technology, aeronautics, engineering, and research.
Those who have mastered linear algebra continue to contribute positively to the advancement of many fields.
Moreover, a solid background in the subject increases your appeal for employment with companies such as those involved in creating algorithms and signal codes.
Plus, you can also teach the subject to schools and universities.
Is Linear Algebra Harder Than Calculus?
Comparing the difficulty level between linear algebra and calculus can be subjective. While most find calculus harder than linear algebra, others believe it’s the other way around.
Nonetheless, looking into the depths of topics and skills required, calculus appears to be more difficult as it involves constant fact analysis.
Additionally, the subject advances to more varied and complex problems.
However, many find that taking linear algebra before calculus allows you to break down and understand concepts more easily.
This is because both subjects employ similar skills but at different levels and cases.
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Mathematics is already a daunting subject, to begin with. Bring up its more complex branches like linear algebra, and it may strike fear in your heart.
However, you shouldn’t be intimidated by linear algebra. Before going deep into its complex topics, know its significance in your future career and the industry you want to be a part of.
From that point, use various studying strategies along with multiple learning resources to help you understand linear algebra better.