What prerequisites are needed for studying linear algebra?

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Discussion Overview

The discussion centers on the prerequisites for studying linear algebra, particularly in the context of self-learning and the relationship between linear algebra and calculus. Participants explore whether prior knowledge of calculus is essential for understanding linear algebra concepts and what other mathematical foundations might be beneficial.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses interest in self-learning math and questions the necessity of calculus before studying linear algebra, noting that some college sites list calculus as a prerequisite.
  • Another participant suggests that while some aspects of linear algebra may require calculus, it is generally possible to learn linear algebra without prior calculus knowledge.
  • A third participant mentions that linear algebra is often recommended after completing calculus 2 or 3, sharing their experience in a combined course where calculus and linear algebra are taught together, but noting a lack of calculus in the linear algebra portion.
  • One participant argues that the calculus prerequisite may be intended to help students who find linear algebra challenging, as calculus provides useful examples and exercises, but emphasizes that familiarity with abstraction, algebra, and proofs may be more critical for success in linear algebra.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of calculus as a prerequisite for linear algebra. Some believe it is helpful or recommended, while others argue that linear algebra can be learned independently of calculus.

Contextual Notes

Participants mention varying experiences with the integration of calculus and linear algebra in courses, indicating that the relationship between the two subjects may depend on the specific curriculum or teaching approach.

Who May Find This Useful

Individuals interested in self-learning mathematics, particularly those considering studying linear algebra and seeking guidance on prerequisite knowledge.

lax1113
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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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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.
 
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.
 
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.
 

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