What prerequisites are needed for studying linear algebra?

In summary, one can learn linear algebra without prior knowledge of calculus, however it may be easier if one has a basic understanding of integration and differentiation.
  • #1
lax1113
179
0
Hey guys,
I have recently decided that i want to try to self-learn some more math along with what I am doing in high school. I am really interested in math and want to do it sort of as a hobby. Obviously, I know i can't learn calculus 2 because i finish calc 1, but what other maths could i try to pick up before finishing calc? or does a lot of it rely ona foundation of calculus...
One i was looking into would be linear algebra. I got a book recommended to me from someone on PF, but a lot of college sites claim that a prereq. of calc one is required for linear algebra. Is this because you need to know all of the basics of calc to take it, or just because calc is sort of more needed for math, well not more needed, just more widely used i guess, so they want you to take a more 'relevant math' before taking linear.
 
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  • #2
There are some parts of linear algebra where you need calculus--for example taking the norm of a vector in L2 you need to know integration which you learn for the most part in calculus 2--but for the most part I think you can learn linear algebra without a previous knowledge of calculus.
 
  • #3
I think for most universities, linear algebra is recommended right after calculus 2 or calculus 3. I'm in a class called Math for Engineering Analysis right now, which is calc 3 and linear algebra merged into one class. From what I can remember right now (it's hard for me to separate the two subjects in my head because we're learning them simultaneously), there hasn't been any calculus involved in the linear algebra portion of the class.
 
  • #4
That requirement is because some people find Linear algebra hard and maybe taking calculus first will either make it easier or cause the person to stop taking matm classes, calculus provides a few convienent examples and exercises in linear algebra, and the two are sometimes integrated at some point. If one has a basic idea of what integration and differntiation are and how calculus is used that is plenty. More important preparation for linear algebra would be some familarity with abstration, algebra and proofs.
 

1. What is linear algebra?

Linear algebra is a branch of mathematics that deals with linear equations and their representations in a vector space. It involves the study of vector spaces, linear transformations, and matrices, and their applications in various fields such as physics, engineering, and computer science.

2. What are the prerequisites for learning linear algebra?

The main prerequisites for learning linear algebra include a strong foundation in algebra, including knowledge of basic operations with matrices and systems of linear equations. Knowledge of calculus is also helpful, as it involves the use of derivatives and integrals in matrix operations.

3. Why is linear algebra important?

Linear algebra is important because it provides a powerful tool for solving systems of linear equations and studying linear transformations. It also has applications in various fields such as computer graphics, data analysis, and machine learning.

4. Can I learn linear algebra without prior knowledge of calculus?

While a basic understanding of calculus can be helpful in learning linear algebra, it is not necessary. Many introductory linear algebra courses do not require prior knowledge of calculus, and it is possible to learn the fundamentals of linear algebra without it.

5. What are some good resources for learning linear algebra?

There are many resources available for learning linear algebra, including textbooks, online courses, and video lectures. Some popular textbooks include "Linear Algebra and Its Applications" by David C. Lay and "Introduction to Linear Algebra" by Gilbert Strang. Online resources like Khan Academy and Coursera also offer free courses on linear algebra.

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