# After Calculus I

1. Aug 5, 2007

### dtl42

I am finishing up a Calc. I course @ columbia university and I'm planning on taking Calc II back @ school (High school - 10th grade). I was wondering if it is possible to take Linear Algebra without having taken courses in Calc. II and Multi-Variable. In Calc I, I've done fairly well, averaging about a 97 and I understand all the topics and theories. My proof skills need some work but aren't god-awful. I just want to know if I'll even have a fighting chance in Linear Algebra. I guess I would be taking it alongside Calc. II just outside of regular school, probably at a community college. Thanks for all the help.

2. Aug 5, 2007

### ranger

Linear Algebra is a very fun (and easy) course to take. You should have no trouble with it. I took LA alongside calc II with absolutely no problems. Good luck!

3. Aug 5, 2007

### dtl42

Does anyone know why many schools make Calc. II a prereq. for linear algebra? It seems that the administration would be the only thing preventing me from taking a formal course in Introductory Linear Algebra, so I wouldn't mind seeing the argument from their side.

4. Aug 5, 2007

### huckmank

Because they're high school administrators with no clue about the content of the class. The only pre-requisite for linear algebra is algebra. I've known several people who took it before they took trig and it was still a breeze. I agree with ranger; linear algebra is a very easy and enjoyable subject.

5. Aug 6, 2007

### dtl42

Well a little while ago in Pre-Calc, we dealt with matrices briefly and I thoroughly enjoyed them, I was wondering if Linear Algebra is lots of matrices along the lines of pre-calc matrices, or if its different types of things. I am still wondering why the colleges have Calc. II as a prereq. for linear algebra as well, because it doesn't seem to make much sense.

6. Aug 7, 2007

### wildman

When I studied Eigenvalues and Eigenvectors (an important part of Linear Algebra), the main motivation was from Differential Equation solutions. Having Calc II under your belt would definately help in understanding that.

7. Aug 7, 2007

### malawi_glenn

I agree, and also it keeps you motivated. Algebra courses is almost always very abstract and it is sometimes hard to see the forest because of all the trees. Also linear algebra, such as vector spaces, Eigenfunctions and Eigenvectors of a matrix is used very much in quantum physics, scientific computing and so on. Sometimes Linear algebra II also covers "function spaces", so there is sometimes required pre-knowledge of one-dimensional analysis in those courses.

As the others says, you'll do fine. I also took Linear Algebra II at the same times as multivariable calculus.

Good luck!

8. Aug 7, 2007

### CPL.Luke

the standard reason for the calc 2 pre-req is that calc 2 tends to show people a bit of what abstract math is going to be like. However the requirement can easily be overridden.

9. Aug 7, 2007

### musicheck

I would also recommend you learn math that interests you in your spare time. Personally, I find your average "applied" linear algebra class useful and worthwhile but a little bit dull. More abstract linear algebra is much more interesting. If you have the time, I definitely suggest you work on "Linear Algebra Done Right" by Axler or "Linear Algebra" by Hoffman and Kunze at the same time as your linear algebra class. You certainly don't have to finish the book, but I think the more abstract approach will be a good introduction to proof-based math. I personally had a great time doing this with Axler's book, even though there are parts which I did not understand.

10. Aug 7, 2007

### dtl42

Is the "linear algebra done right" book for an intro. to linear algebra? It says on the amazon descriptions that it is "text for a second course in linear algebra". This confused me a little bit and I was merely seeking clarification.

11. Aug 7, 2007

### musicheck

Axler and Hoffman and Kunze are both books for second classes in Linear Algebra. I don't know Hoffman and Kunze so well, but Axler states in the intro to his book that the only essential prereq is a bit of mathematical maturity. The book does not assume you already know anything about LA. The only difference is that the book covers a lot of theory that is skipped in many linear algebra books, and the problem sets are almost always proofs instead of calculations.

12. Aug 7, 2007

### dtl42

Ok, but it would be ok for me to use it as an Intro to LA? Should I try something to help me with proofs before attempting LA?

13. Aug 7, 2007

### musicheck

I'm not saying that this is an essential thing to do. I'm just suggesting that while you take your linear algebra class, you also read a book of this sort (and maybe solve a problem or two) in your spare time. Its quite likely that some of it will seem incomprehensible to you (as it was for me) the first few times you read it. Nonetheless, I think its a good way to ease yourself into more abstract math. It might not even help you too much in terms of grades in your linear algebra class, but I think it would be both a fun and enlightening experience.

14. Aug 7, 2007

### mathwonk

as others have said. no there is no reason in the world logically for calc 1 or 2 either to be prerecquisite for linear algebra.

indeed linear algebra is a prerec for calc 2 done right.

linear algebra is easier than calc and should be taught in high school before and instead of calc, but high school teachers do not realize this mostly.

high schoolers and their teachers do have a chance of doing justice to linear algebra, but most high school calc courses are very poor substitutes for college ones.

if high schools taught linear algebra instead of calculus they would not do nearly so much harm as they presently do.

Last edited: Aug 7, 2007
15. Aug 8, 2007

### proton

For the most part, Lin Alg should be possible without calc II and III. The only reason I can think of that calc II is a prereq for most schools is that integrals and derivatives are linear. As others have said, knowing DEs before Lin Alg will be helpful for understanding eigenvalues/vectors

16. Aug 8, 2007

### dtl42

Alright, but knowing DE does require Calc. II and III right?

17. Aug 8, 2007

### morphism

Usually just Calc 2.

18. Aug 8, 2007

### z-component

At my school, Calc. II is required for DE but not Calc. III. In fact, one may take either Calc. III or ODE/PDE after Calc. II, then go back and take the other.

19. Aug 8, 2007

### Llama77

Its the same at most schools. many CSE and EE students will rush to take SE for Circuits.

I am going to be taking Calc 2 and Linear Algebra at the same time this upcoming semester. I had to ask specific professors and all but one said Calc 2 was a major wart of LA. I knew they were idiots, so I found the best teacher who said I would be fine taking it.

I really cant wait.

20. Aug 9, 2007

### dtl42

OK so I'm fairly sure I'm going to take linear algebra, I just need a textbook recommendation. Can anyone suggest a textbook in a A) Theoretical Approach (more proof oriented) and B) More applied, (computational).

Thanks, I just need the title and the author, so I can find a cheap copy used. Also is does Apostol's book have linear algebra in it, and if so, which volume of his?