calculus vs. linear algebra

[mikeczyz]

I am currently taking both classes for my own enjoyment. However, linear algebra is clearly more difficult than calc, imo.

Anyone else have a similar experience?

[rja87]

No, I've never experienced enjoying a class.

[Wyman]

What level calculus and what book? What book for linear algebra? What's your math background?

I don't think linear alg. is much more difficult than calc, but I think it requires you to think about things that you're not used to thinking about (if this is your first linear alg. course). Also some places teach it proof-based, which makes it seem more difficult than calc to students who haven't done proofs before.

[rwejr]

conceptualyl I think calc is more abstract and therefore harder. Linear algebra is just so boring and simple, that it was hard to stay focused and motivated in the class. they are basically the same thing except I think linear algebra is way easier to see on paper, but the class is harder because it sucks

[mikeczyz]

Calc 1--Single Variable Calculus Early Transcendentals by James Stewart.
Linear Algebra- Using Otto Bretscher's Linear Algebra with Applications.

Math background is basically nil...a few business math courses and pre-calc in college. This is my final year and I'm trying to take more math classes because 1. I kinda like math and 2. every grad program I am interested in is going to laugh at my (lack of)math background.

[Dan.]

Liner Algebra was "harder" simply because it was new to me at the time. That aside, I think there's a certain beauty in linear algebra, and it helps me feel like an elitist as nearly everyone has taken calculus.

[relativity_x]

An upper level linear algebra class is conceptually harder than calculus in my opinion.

Classes in differential equations are far more interesting/difficult than calculus and use advanced topics in linear algebra to solve them.

[Quicksilvre]

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An upper level linear algebra class is conceptually harder than calculus in my opinion.

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Yeah, I would agree. Elementary calculations in linear algebra are much easier; it's mostly just row reduction and calculator work. However, I think the theory behind linear algebra is a lot more difficult, because it's a lot more abstract than it is in calculus.

[tabako]

I am taking multivariable calculus (calc 3) and "Elementary Matrix and Linear Algebra" this semester. The texts are: "Thomas' Calculus" 11ed and "Elementary Linear Algebra /w applications" 9ed by kolman/hill.

So far, I am enjoying calc 3 much more than the linear algebra class. The classroom material in linear algebra has seemed a bit more difficult(most likely because it is proof based, as wyman suggested above), though the assignments and tests have been easier.

The calc prof is much, much better than the prof for LA, which might be why I am enjoying that class more. The LA prof just spends each class doing one long proof that involves an arbitrary sized matrix with lots of variables and is not very interesting. Most of proofs involve things that make sense to me, but I wouldn't know how to prove. The assignments (tests too) in LA, however, don't involve any proofs. They just involve doing very basic things like calculating determinants or solving a system of equations.... things I was doing in first year high school math.

I find the calculus class much more engaging on a theoretical level. I could care less about the formal definition of a determinant, or how to use that to prove that switching two rows in a determinant switches its sign.

These two classes are the first I have taken since high school calculus. Lately, I have been considering adding a math major (along with econ). If anybody has advice on whether this would be a good fit for me or not based on what I wrote above, please let me know.

[Wyman]

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I could care less about the formal definition of a determinant, or how to use that to prove that switching two rows in a determinant switches its sign.


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Lately, I have been considering adding a math major (along with econ). If anybody has advice on whether this would be a good fit for me or not based on what I wrote above, please let me know.

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I was just going to say no, based on your feelings about the determinant proof. But upon further thought, I think you should:

Take a real analysis class and an algebra class. Then decide if you want to be a math major. If you decide not, take a stats class and a combinatorics class. Then redecide. By this point, you're already a math major though. Hey, you learned a whole bunch of (interesting? applicable?) stuff, and you still did your econ major.

There is so much math that has nothing* to do with calculus and linear algebra that you really can't know how much you like "math". You can appreciate beautiful proofs in different areas, but usually you find some area of math that really appeals to you (even if you hate other areas), and you go with it.

If you enjoy calculus, why not take more? Maybe a few years down the road, after a serious algebra course, perhaps, you'll think back on this proof that switching rows of the matrix negates the determinant and think "wow, that's kinda nice." Or, maybe not.

*Obviously, I don't mean "nothing", but I mean that upon a cursory glance, the courses seem to have nothing to do with each other.