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Linear Algebra vs. Calculus


in2bat0r

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Linear algebra is more abstract than calculus so people often times find that harder. Linear algebra deals with the geometry of spaces and you will have to deal with matrices, vector spaces, etc. If you take the honors version you will also be exposed to a lot more advanced theoretical topics. I remember when I took linear algebra we did a lot of group theory, ring theory, etc. which are extremely abstract concepts that most people will have a lot of problems with. However, it was a solid foundation for upper level math courses in abstract algebra.

 

With that said, linear algebra is essential to mathematics and fields like physics, chemistry, engineering, statistics, etc. In fact, if you understand linear algebra, you'll have a good understanding of the basis of linear and logistic regression, two methods/models most often used in biomedical and public health research.

 

Both courses are integral if you are majoring in physics, math, etc. If you are a typical premed looking to avoid math, I'd probably go with calc II as it is more useful in the long-term.

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I'm currently doing the Linear Algebra course (and I had Cal II last semester). Personally, I find that Calculus is easier because what you do is more "mechanical". Once you know the formulas, you just apply them and solve for the answer.

 

However, this semester, our teacher keeps throwing a bunch of theorems at us and it seems like it will never stop :eek: . Yes, it is very abstract, but I guess that the calculations themselves are not very hard.

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I agree with what the others have said. However, Calculus II deals mainly with integration (at most universities, anyways) which can get tricky sometimes, but is also a basic technique that you should know how to do if you are a science student (imo). Also, from all of undergrad so far, any Calculus course has been one of my favorites.

 

Linear algebra is more computation based, which you must understand the theory in order to do correctly, but are not inherently complicated themselves.

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Engineering science major here so I'll pipe up.

 

Calculus II will probably be "easier" because it's a simple progression from Calculus I. Yes, some people have a little trouble with integration, but the major conceptual hurdles have already been addressed in Calculus I.

 

Linear Algebra, on the other hand, will probably introduce more foreign concepts to you and thus is often perceived as "harder". However, if you're someone who is able to grasp those concepts (Note: know the invertible matrix theorem! All of its points!), using and applying them is fairly straightforward. The concepts aren't hard--just more foreign to you ("newer") so they may seem harder.

 

In terms of usefulness, for a science student, I'd probably say Calculus II is more useful--unless you want to get into the mechanisms of calculation and informatics, where linear algebra becomes very useful.

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I actually found linear algebra easier and for what I did more practical - I use linear algebra in programming but really calculus never comes up. This is possibly one of those personal choices :)

 

One thing I would add though is that often schools in the US are specifically looking for calculus in the application process.

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I always loved math, and if you're like me, you'll find both courses pretty neat and not too difficult. Sooo, with that said, my question is, why not take both?

 

Take Calc II next term since it follows nicely after Calc I, and then later, when you need a course to fill a slot, and want a break from your typical bio/chem/biochem/lab-type course, take algebra! If you're a math nerd like me, might help your GPA!

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Linear algebra is easy, most of a standard linear 1 class is vectors and matrices. It gets very abstract at the end (vector spaces, eigenvalues, basis dimensions etc) but overall I found it easier than a cal 2 class (cal 2 starts with integrals and typically ends with series, more specifically power series and Taylor and Mclaurin theorems).

However, unlike moo, we didn't cover rings in our linear class. They were covered in ''algebra'', not ''linear algebra''. I would've liked to study those sweet jewlery theorems though but now it's too late.

 

Peace

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I took second year calc and now taking differential equations with first year linear algebra. Personally, I really dislike linear algebra. It's not hard, but I personally find calculus to be easier to understand and therefore less tedious.

 

However, if your calculus 2 is similar to the one I took, integration techniques and series can be a pain in the rear (they can throw a lot of curve ball equations and ask you to integrate, series is more memorizing and recognizing the pattern, which I personally dislike).

 

Expect quite some work in calc 2, but once you get it the marks will fly in. Linear algebra...I'm not so sure (since I'm taking it right now).

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Linear algebra was a pain in the ass for me. My teacher had super strong soporific powers... and she knew how to use them ! Furthermore, the exams were hard ! Still, the required workload to get a good mark was much less than in Calculus 2.

 

I remember long days doing integrals & series...

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Linear algebra is more abstract than calculus so people often times find that harder. Linear algebra deals with the geometry of spaces and you will have to deal with matrices, vector spaces, etc. If you take the honors version you will also be exposed to a lot more advanced theoretical topics. I remember when I took linear algebra we did a lot of group theory, ring theory, etc. which are extremely abstract concepts that most people will have a lot of problems with. However, it was a solid foundation for upper level math courses in abstract algebra.

 

Weird. Why would you cover groups and rings in a linear algebra class? In any case, you're quite right that linear is more abstract than (intro) calculus. I don't think you need to be particular adept at "spatial" thinking for linear, though.

 

With that said, linear algebra is essential to mathematics and fields like physics, chemistry, engineering, statistics, etc. In fact, if you understand linear algebra, you'll have a good understanding of the basis of linear and logistic regression, two methods/models most often used in biomedical and public health research.

 

Linear algebra is fundamental to all quantitative disciplines. It's fair to say that modern algebra beyond that point isn't terribly applicable outside of highly technical areas in physics and chemistry.

 

Both courses are integral if you are majoring in physics, math, etc. If you are a typical premed looking to avoid math, I'd probably go with calc II as it is more useful in the long-term.

 

"Integral" is the right word here. It's true that linear algebra is not, in itself, terribly useful without further study in statistics. As for calc II, everyone who aspires to a career in a field filled with dynamic processes should have at least a basic understanding of rates of change and integrals. You don't really need to "do" calculus in medicine, but being familiar with the concepts is key.

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