Is College Matrix Algebra Worth It for Physics?

[complexPHILOSOPHY]

I want to eventually do quantum physics (or some aspect of theoretical physics), so naturally I will be doing linear algebra after I finish my calc sequence, however, my school offers a course called 'College Matrix Algebra' and the only pre-req is Intermediate Algebra. Would this benefit me at all later on in any maths and physics classes, or is this class not very rigorous? I am at a community college by the way, if that has anything to do with the cirriculum. I always get an alternate text and do my own math courses anyways since I don't trust the courses they offer (or the professors for that matter).

They seem to dumb things down for all of the lazy kids in my classes.

Here is a description from the website:

116 College and Matrix Algebra
3 hours, 3 units
Prerequisite: Mathematics 96 with a grade of "C" or better, or equivalent, or Assessment Skill Level M50.

One of the aids which might be used to determine readiness for this course is a qualifying score on the Intermediate Algebra Diagnostic Test. This course is designed to strengthen the algebra skills of business or life science students in preparation for calculus. Matrix algebra and linear programming will also be included. Analytical reading and problem solving are required for success in this course. Transfer Credit: CSU and/or private coll/univ. UC Transfer Credit: Mathematics (MATH) 116 and 141 combined: maximum credit, four units.

 

[Mororvia]

Ehhh, I don't think that would be the one that you'd be looking for just based on the info posted. It sounds like matrices are just a certain part of the course and not the full course. The linear algebra course I took wasn't the one math majors take with full proofs or anything... but I also think the one I took is a few steps above this one listed.

It it would be beneficial to you or not, well I don't know. If you get a week or so into the semester before your schedule is set, you might just want to enroll and see what its like.

Good luck!

 

[mr_coffee]

Linear algebra is pretty basic, nothing too intense mathematically. I'm not sure if physics majors have to take that course but Engineering do, I havn't used any matrices in any of my other courses, well a little in Differential Equations.

 

[complexPHILOSOPHY]

Linear algebra is pretty basic, nothing too intense mathematically. I'm not sure if physics majors have to take that course but Engineering do, I havn't used any matrices in any of my other courses, well a little in Differential Equations.

I want to do theoretical quantum physics and from talking with a few friends doing their PhDs in high energy, they have stressed the importance of linear algebra as being one of the fundamental fields of maths that they use. A friend of mine doing his phd in high energy (he recently graduated from cambridge) said he didn't pay as much attention in his linear algebra class as he had wished, so he had to go back through it when he started doing higher physics.

That is one of the main reasons I wanted to take the class but it looks like it might be for non-math majors?

I haven't completed my calculus sequence yet, so I am not prepared for a linear algebra class (nor will they let me take one until I complete ODE).

 

[mr_coffee]

Thats odd...
why do you need calculus or ODE to do linear algebra?
You could do linear algebra with just basic understanding of vectors and algebra

 

[dontdisturbmycircles]

Yea complexPHILOSOPHY I don't think they would let you take an ODE course without Linear Algebra. (I don't know for sure but I am pretty sure that Diff EQ's are very linear algebra dependent, aren't they?) Linear Algebra is fairly basic as Mr.Coffee said. I haven't read through the entire lin algebra book that I got from the Library but I have got a far way though. It's nothing to worry about, you definitely don't need Calculus. In fact I think that Linear Algebra before calculus is maybe a good idea.

 

[mr_coffee]

I agree with circles,

infact in pre-calc you should have been introduced to some basic matrices and how to row-reduce them and do multiplication of 2-3 matrices, etc.

 

[complexPHILOSOPHY]

I reversed the order. I can't take linear algebra until I complete Calc II and I can't take Diff Eq. until after Linear Algebra.

My fault, mixed them up. So I can work through linear algebra without knowing much past calc I?

 

[dontdisturbmycircles]

Yup, absolutely.

 

[gravenewworld]

I want to do theoretical quantum physics and from talking with a few friends doing their PhDs in high energy, they have stressed the importance of linear algebra as being one of the fundamental fields of maths that they use.

From what my professors have told me, QM can be summed up as linear operators in hilbert spaces i.e. it makes use of some rediculous LA and some hardcore analysis. I don't know how close this claim is, because I have never studied QM, but I have studied hilbert spaces.


On the contrary I think you definitely DO need Calculus and Diff eq. before taking LA. Some spaces use stuff like integrals to evaluate norms and inner products.

 

[mgiddy911]

At my institution, they recommend taking calc 3 before linear algebra, or concurrently, because here our calc 3 is vector calculus, so its beneficial in some ways to linear algebra, both as just a refresher of vectors but also getting used to thinking and viualising more than 2 dimensions

 

[dontdisturbmycircles]

I suppose that this may be true and I can't argue against it, but can't someone take an intro LA course without calc? Although I am guessing that most students of an intro LA course would have one semester of Calc before LA. I have seen a few textbooks and have only seen a couple with calculus prereq's, although I could be wrong. Maybe clarify with your math prof or something.

I know for a fact that many LA textbooks are very comprehensible to a student who just knows algebra and some stuff about vectors, but I guess in the end that is all I can base my opinion on.

I would definitely guess that mgiddy and gravenewworld are correct, but I am surprised.

 

[gravenewworld]

http://en.wikipedia.org/wiki/Operator

Read about operators. You will definitely come across operators in LA. The derivative and integral are introduced as operators when you study LA. You definitely need to know calc for a lot of theory in LA. You could probably understand a few chapters in intro LA without ever having Calc, but some where along the line you will definitely need to know some calc while studying LA.

 

[cristo]

http://en.wikipedia.org/wiki/Operator

Read about operators. You will definitely come across operators in LA. The derivative and integral are introduced as operators when you study LA. You definitely need to know calc for a lot of theory in LA. You could probably understand a few chapters in intro LA without ever having Calc, but some where along the line you will definitely need to know some calc while studying LA.

Whilst this may be true, I think the OP is asking about an introductory course to Linear Algebra. In order to learn the basics, one does not need to know any calculus.

 

[gravenewworld]

Whilst this may be true, I think the OP is asking about an introductory course to Linear Algebra. In order to learn the basics, one does not need to know any calculus.

Catalog description of intro to LA at my school:

Vector spaces linear transformations, self-adjoint and normal operators, bilinear and Jordan forms.


Operators are the basics. I feel that most schools require Calc I and II before taking LA. And this is because it is for a good reason.

 

[dontdisturbmycircles]

Intro to LA without an introduction to matrices and eigenvalues/eigenvectors? Do you go to MIT or something?

 

[cristo]

Hmm, that seems a weird introductory Linear Algebra course! My intro course was complex numbers, vector & matrix algebra, vector spaces, linear transformations, inner product spaces (ok, I admit one would probably need to know calculus for the latter!) I'm from the UK though, so I don't know whether the courses will be different.

 

[gravenewworld]

Intro to LA without an introduction to matrices and eigenvalues/eigenvectors? Do you go to MIT or something?

No I didn't go to MIT, but learning about linear spaces includes linear transformations which matrices are. Learning about eigenvalues/vectors at my school was in a math class entitled Diff eq. & LA which was a lower level course. In a formal LA course they general try to ween you off of working with matrices/doing matrix algebra and make you start learning about linear transformations in a more abstract sense.

 

[Chris Hillman]

Hi, complexPHILOSOPHY,

It sounds like you are rather ambitious, and I presume you did very well in at least one previous math course at your school. If so, you might want to find a friendly faculty member and ask if they would be willing to supervise a reading course so that you can learn much more at your (presumably much faster) pace, ideally combining some solid theory with some computational work with matrices.

I'd suggest you see if your college library has the textbook by Paul Halmos, Finite Dimensional Vector Spaces and the textbook by Gilbert Strang, Linear Algebra and its Applications.

The first is a wonderful book by a legendary mathematical expositor, which corresponds to the kind of "linear algebra for math students" course mentioned by gravenewworld. Halmos was a leading expert in mathematical subjects which involve infinite dimensional vector spaces, and as the title of the book suggests, his intent here was to lay a solid foundation for a book on "functional analysis".

The second is a somewhat idiosyncratic book which offers lots of really fascinating applications. Strang teaches linear algebra at MIT, where of course many students will want to see such applications as soon as possible. When I taught linear algebra I used that as motivation for extra stuff I tried to sneak into the curriculum.

Another topic I snuck in was the application of eigenthings by Frobenius to the theory of Markov chains, which you can read about in various places, but one of the most readable accounts is by John G. Kemeny, J. Laurie Snell [and] Gerald L. Thompson, Introduction to finite mathematics, 3rd edition, Prentice-Hall, 1974. Kemeny was a notable figure in mathematical pedagogy, BTW; in the early days of computers, together with Thomas Kurtz, he designed BASIC as an instructional language; as you may know, BASIC is still in common use today. He was also Einstein's last assistant at Princeton, served as president of Dartmouth, and served as chair of the Three Mile Island commission, so probably has something to do with why Chernobyl did not (yet) happen in the U.S.

You might also look for the two volume book by Baumslag and Sternberg, A Course in Mathematics for Students of Physics, which has a more systematic introduction to Kirchoff's circuit theory, one of the most delightful applications of elementary linear algebra (which is secretly a homology theory!).

Back to theory: another interesting book is Fekete, Real Linear Algebra, where any budding young mathematician should be intrigued by his treatment of matrix exponentiation, which includes an introduction to the Steenrod twist algebra, a beautiful way to treat rotations (which also applies readily to the Lorentz group). This is secretly a foretaste of Lie theory; as you may know, Lie groups and Lie algebras lie at the heart of much of modern theoretical physics, e.g. gauge theories.

These books should offer plenty of food for thought! If you bring them along to show to your friendly professor, you have a greater chance of inveigling him/her into agreeing to supervise your study. Reading courses generally involve setting a time to meet in the professor's office once per week so you can ask questions, have him/her quiz you to assess your progress, and so on.

 

[dontdisturbmycircles]

No I didn't go to MIT, but learning about linear spaces includes linear transformations which matrices are. Learning about eigenvalues/vectors at my school was in a math class entitled Diff eq. & LA which was a lower level course. In a formal LA course they general try to ween you off of working with matrices/doing matrix algebra and make you start learning about linear transformations in a more abstract sense.

Ok, that makes sense I guess.

 

[mgiddy911]

I second the vote for Strang's LA book, I use it my class currently

 

[gravenewworld]

Axler's Linear Algebra Done Right is also a phenomenal book. It doesn't even make use of determinants until the very end of the book which is good.

 

[morphism]

I'd suggest you see if your college library has the textbook by Paul Halmos, Finite Dimensional Vector Spaces and the textbook by Gilbert Strang, Linear Algebra and its Applications.

I wouldn't recommend Halmos to a non-math major with no previous exposure to linear algebra. Everything is too condesed, and the notation is somewhat cumbersome. I find it more of a book to read over after you've learned linear algebra to gain deeper insight.

I personally would recommend Linear Algebra by Friedberg, et al.. It's a great, comprehensive text on undergraduate linear algebra. Another recommendation would be Hoffman and Kunze, but it gets slightly more difficult than Friedberg in its treatment of invariant subspace decompositions. It also lacks 'concrete' examples in general.

Finally, one more popular book seems to be Axler's Linear Algebra Done Right. I've only glossed through it, and I think it could serve as a supplement to one of the two aforementioned text. I do not think it can be used as a textbook by itself, however, as it covers relatively little material.

 

[mr_coffee]

My linear algebra class taught the same thing as yours graven and I didn't have calc III nor calc II, I had calc I and I did fine in that class.

He simply taught us right on the spot how to work with eigenvalues/eigenvectors, then when i took Diff Eq it was just a review.

Just because a subject is in an upper level math course doesn't mean it can't be introduced in a lower math course nor does it mean the students are going to be lost.

The professor simply has to present it in a way that the students realize that yes, this is more advance material but its still just as easy to understand with proper explanation.

a lot of classes have pre-req that don't even apply. I could have taken Discrete Math without any prior knowledge to calculus or any sense of programming at all and yet the pre-reqs are Intermediate Programming, Calc II.