Linear algebra is one of the most important courses and is relevant to nearly all areas of mathematics. In this article, we will be discussing the overall difficulty of linear algebra and the strategies you can employ to do well in this relatively hard course.
Linear algebra is a branch of mathematics that is concerned with mathematical structures closed under the operations of addition and scalar multiplication and that includes the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations.
Is Linear Algebra Hard?
Linear algebra is hard. Linear algebra is one of the most difficult courses that most STEM majors will study in university. Linear algebra is not an easy class because it is a very abstract course and it requires strong analytical and logical skills.
Linear algebra is considered such a demanding course by STEM majors since it gets exponentially complex and perplexing as the term progresses. Unlike other math courses, linear algebra starts out quite easy but gets almost impossible by the end of the semester.
Most math courses you have taken prior to enrolling yourself in linear algebra are not very complex or abstract. Calculus courses for example are not very difficult conceptually and you can do quite well in them as long as you understand the mechanics of what you are doing. Linear algebra is the opposite; the mechanics are quite simple once you understand the challenging core concepts.
Linear algebra is a prerequisite for introduction to proofs in most colleges. In turn introduction to proofs is necessary before you can start taking upper-level math courses.
Even if you are not pursuing a math major linear algebra is one of the most applicable and relevant courses for engineering, computer science, economics, and many other subjects. Linear algebra has numerous real-life applications since it has the power to reduce a large number of math equations to simpler forms.
Your university and the department that teaches linear algebra have a big role in the overall difficulty of the class. Typically higher ranking universities make their courses harder as they have more talented students and it would be unwise to hand out an A grade to every student.
Moreover, if you were to take your linear algebra course from a maths department then you can expect it to be quite proof heavy. Regurgitating statements and doing a few practice questions will not be sufficient to pass the course. Instead, you will need to have an in-depth understanding of the subject content.
Other departments may make their linear algebra class very applied and practical. Instead of focussing your efforts on proving equations, you will need to divert your energies to finding solutions to problems that mimic the real world.
Either way, linear algebra will really test your limits. You will have to constantly practice to do well in the subject. Trying to visualize using online simulators can go a long way in furthering your understanding of the topic.
Linear algebra is fundamentally different from most of the math courses you would have taken until now. Linear algebra is not very intuitive and it is often the first real math course students take after enrolling in college.
Why is Linear Algebra So Hard?
Linear algebra is so hard because it is not very intuitive, it places a strong emphasis on rigorous proofs, and its concepts are very abstract and difficult to visualize. Linear algebra is difficult because it is fundamentally different from most high school and college courses you have taken until now.
Linear algebra is renowned for being the first “real” math course. Typically all the math taught before linear algebra can easily be graphed on a sheet of paper. Students have always been taught to visualize functions in terms of graphs.
Linear algebra, however, demands students to come to terms with less direct forms of visualization or rely heavily on algebraic manipulations. You must align and modify your thinking of maths to understand the relatively abstract and perplexing material in algebra.
What is the Hardest Part in Linear Algebra?
The hardest part in linear algebra is defining a mathematical structure via a set of axioms and understanding baffling concepts such as linear independence, eigenvectors, and abstract vector space. Students generally struggle with understanding abstract concepts in linear algebra.
Prior to taking linear algebra students are made to focus on calculation rather than understanding the terms and concepts and then carefully assessing which calculation to use.
Students are not very good with writing proofs which further enhances the difficulty of linear algebra. Initially, linear algebra is quite straightforward but rapidly becomes very complicated particularly in the second half of the course.
Is Linear Algebra a Difficult Class?
Linear algebra is certainly a difficult class. You can manage the difficulty you experience in linear algebra by repeatedly practicing the problem sets, furthering your understanding of the topics by reading the textbook, and using simulations to help visualize the ideas covered in class.
Is Linear Algebra the Hardest Math Class?
Linear algebra is not the hardest math class. Compared to other math courses linear algebra is harder than calculus I and discrete math but similar to calculus II in terms of difficulty. However, linear algebra is easier than most upper-level math courses such as abstract algebra and topology.
Is Linear Algebra Harder than Discrete Math?
Linear algebra is harder than discrete math. Discrete math is typically a first-year course and is not as abstract or complex as linear algebra. Linear algebra is usually taught in the second year of most STEM majors and requires strong analytical and reasoning skills which makes it harder than discrete math.
What level of Math is Linear Algebra?
Linear algebra is considered intermediate-level math. Linear algebra is one of the toughest courses along with calculus II that STEM most majors will encounter. However, linear algebra is not a very advanced course since there are several more advanced courses such as abstract algebra and topology.
Linear algebra is quite different from most math courses. Customarily you will be expected to study calculus I before embarking your journey of studying linear algebra.
Linear algebra is generally a prerequisite to introduction to proofs which in turn is a requirement to study upper level math courses. Thus it makes sense to call linear algebra an intermediate level math course.
How long does it take to learn Linear Algebra?
It typically takes one semester to learn the basics of linear algebra. If you want to study beyond your course curriculum than it can take much longer. Mastering the more advanced concepts in linear algebra can take years.
An undergraduate course in linear algebra will help you learn the basics. However, to learn the advanced concepts in linear algebra you can expect to spend many more semesters studying this wonderful branch of mathematics.
Is there Calculus in Linear Algebra?
There is almost no calculus in a basic linear algebra undergraduate course. However, as you progress into more advanced mathematics you may find linear algebra problems requiring calculus and vice versa.
This interconnection is not only common between linear algebra and calculus but in several other fields of mathematics. For instance you may find calculus concepts in statistics, physics, and economics. Similarly, trigonometry, numerical analysis, optimization, and topology have overlapping ideas.
Is Calculus needed for taking Linear Algebra?
Universities typically require calculus I before you can take linear algebra. Although linear algebra has almost no calculus concepts; universities want their students to be familiar with basic mathematics before they proceed to take intermediate courses.
Is Linear Algebra worth taking?
Linear algebra is absolutely worth taking. If you have to choose between linear algebra and any other math course then selecting linear algebra is a no brainer. Linear algebra is one of the most important undergraduate course for STEM majors.
Linear algebra is so essential to so many fields.
Here are some uses of linear algebra:
- Multidimensional Calculus
- Differential Geometry
- Functional Analysis
- Multivariable Statistics
- Control Theory and Dynamical Syestems
- Optimization Theory
- Linear Programming
- Computer Graphics
- Machine Learning
- Multidimensional Stress and Strain
- Cryptography
- Current and voltage in LCR circuits
- Flow in a network of pipes
Is Linear Algebra the Most Useful Math?
Linear algebra is the most useful math along with calculus when it comes to the math courses taught in college. However, arithmetic, basic algebra, and trigonometry taught in primary, middle, and high school are more useful than linear algebra.
Linear algebra is so useful because it has the power to reduce some very complex equations. This is extremely useful because the ideas from linear algebra are basic and easy to understand as compared to the extremely complicated equations it is used to simplify.
Is Linear Algebra Different than Algebra?
Algebra is a general term and it includes a variety of different forms including elementary algebra, linear algebra, and abstract algebra. Linear algebra focuses on structures that can be described by a system of linear equations.
Elementary algebra deals with concepts such as slope of a line, factoring quadratic equations, and solving for a variable. This form of algebra is usually introduced in middle school and taught all the way until high school.
Another form of algebra, abstract algebra is only taught to math majors and possibly physics majors. Abstract algebra emphasizes the study of groups, rings, fields, and partial structures such as semigroups and magmas. Abstract algebra involves the use of rules and properties that are not followed by ordinary numbers.
Conclusion
Linear algebra is a hard course for most students since it is abstract and counter intuitive. It is unlike most math courses and you must develop techniques to help you visualize what is going on. This adjustment is necessary since most of the math you have studied until now can easily be expressed in a 2-D graph.
Overall linear algebra is an extremely useful course and you should try to understand the underlying theory as fully as possible since it has countless practical applications.
Although linear algebra does not really require calculus; most colleges expect you to have completed at least one course of calculus so that you have a better understanding of college level mathematics.
