[Mahratta]

This is the final course in the linear algebra sequence (1B-2R-2S) and is meant to be a transition towards the sort of math one would encounter in upper-years, particularly towards abstract algebra.

The course starts with definitions of basic algebraic structures, leading to a slightly more in-depth study of groups, rings, and fields. None of these concepts were studied in much detail, which made learning about them rather more difficult if you're interested in the bigger mathematical picture (you have to fill in a whole lot of gaps, or wait until 3rd year). Emphasis was placed on the study of (basic) polynomial rings over finite fields.

We then covered standard linear algebra from an abstract perspective - basically, the material you would have seen in 1B and 2R, except done properly. One can compare earlier linear algebra courses to this one in the same sense as one compares the abstract algebra aspects of this course to math 3E and 3EE. We also covered dual spaces, generalized eigenspaces, and the Jordan Canonical Form (kind of like 'generalized diagonalization').

The primary aim of the course was to be an introduction to proofwork in algebra. I found the proofs we had to do quite easy, but I'm more 'proof-oriented' than 'computation-oriented', so this particular note shouldn't be taken for granted. Generally, the proofs were 'definition-chasing' and nothing more, requiring symbolic manipulations and not much thought to go along with them.

Overall, this course was very interesting, and very enjoyable. The professor, Dr. Boden, was a good lecturer, although he tended to emphasize definitions over intuition in this course.
This is not an easy course, however, and I wouldn't recommend it to anyone who is taking math electives because they're good at, say, calculus, or computation-style linear algebra. I would recommend it to any math major, especially 'pure' math majors.

The assignments were interesting, but time-consuming. The tests were fair, and a lot easier than the assignments. The final was pretty easy.

If I may add to this for any students who do end up taking 2S:

Dr Boden tends to mark the assignments and tests quite strictly. However, we found that he was a lot more generous than explicated - there was a 100% final option, and I think he may have curved the grades as well.

That review pretty much covered this course pretty well, if you're not for the abstract mathematics and formulation of theories and definitions do not take this course. If you are then you're in the right place!

Have you taken 2T03? For math specialization...ther e is the option of 2S and 2T...what one would you recommend?

I highly doubt anyone will answer this question any time soon, but would it be pointless to take this course after taking 3E03?

Originally Posted by oranges

I highly doubt anyone will answer this question any time soon, but would it be pointless to take this course after taking 3E03?

I wouldn't say so. Even with both 3E03 and 3EE3, 2S has a lot of independent material. In fact, it would be nice to have a more rigorous version of 2S after 3EE3 (maybe module theory?), instead of having it before.

Originally Posted by Mahratta

I wouldn't say so. Even with both 3E03 and 3EE3, 2S has a lot of independent material. In fact, it would be nice to have a more rigorous version of 2S after 3EE3 (maybe module theory?), instead of having it before.

Ah, Mahratta, you're back! Thank goodness.

And thank you for the advice. Unfortunately 2S03 conflicts with 3EE3 this upcoming year, but I might take it next year so long as it doesn't conflict with another course again. It sounds very interesting.

Originally Posted by oranges

Ah, Mahratta, you're back! Thank goodness.

Couldn't stay away forever -- that early timetable release is like crack.

And thank you for the advice. Unfortunately 2S03 conflicts with 3EE3 this upcoming year, but I might take it next year so long as it doesn't conflict with another course again. It sounds very interesting.

In that case, you may want to check out what the curriculum is (the book by Valenza is excellent); if you take 3EE3 you can sort of self-teach 2S03 from an even better standpoint, since you'll have all the connections with field theory. Basically, in 3EE3 you'll learn something about modules, which are generalizations of vector spaces and allow you to consider them over rings instead of fields. If start with that module-theoretic background and then specify, you should find it much more interesting.

In other words, it's not that important to take 2S, but the theory of finite-dimensional vector spaces is very important and will show up everywhere in pure mathematics, from functional analysis to algebraic geometry to model theory, and, in many cases, in greater generality. So it's a nice subject to have a good grasp of.

If you're interested in self-study, I can recommend some books, or perhaps we can meet in person and talk math.

Originally Posted by Mahratta

In that case, you may want to check out what the curriculum is (the book by Valenza is excellent); if you take 3EE3 you can sort of self-teach 2S03 from an even better standpoint, since you'll have all the connections with field theory. Basically, in 3EE3 you'll learn something about modules, which are generalizations of vector spaces and allow you to consider them over rings instead of fields. If start with that module-theoretic background and then specify, you should find it much more interesting.

In other words, it's not that important to take 2S, but the theory of finite-dimensional vector spaces is very important and will show up everywhere in pure mathematics, from functional analysis to algebraic geometry to model theory, and, in many cases, in greater generality. So it's a nice subject to have a good grasp of.

If you're interested in self-study, I can recommend some books, or perhaps we can meet in person and talk math.

Ah, interesting... I'll consider taking it if I don't get around to self-studying it. I actually plan on self-studying real analysis (primarily using Rudin) later this summer, so unfortunately my self-study plans are somewhat booked for now. But I'll see how it goes and I'll let you know if I need some book recommendations. Thanks again for the advice!

Originally Posted by oranges

Ah, interesting... I'll consider taking it if I don't get around to self-studying it. I actually plan on self-studying real analysis (primarily using Rudin) later this summer, so unfortunately my self-study plans are somewhat booked for now. But I'll see how it goes and I'll let you know if I need some book recommendations. Thanks again for the advice!

Rudin's good, but may I suggest reading Carothers book alongside (if this is "baby Rudin" you're referring to, not "Real and Complex Analysis" or "Functional Analysis") -- Rudin is known for being dry, while Carothers is both rigorous and intuitive.

Rudin is a good reference book -- not a great learning book, in my opinion.

Originally Posted by Mahratta

Rudin's good, but may I suggest reading Carothers book alongside (if this is "baby Rudin" you're referring to, not "Real and Complex Analysis" or "Functional Analysis") -- Rudin is known for being dry, while Carothers is both rigorous and intuitive.

Rudin is a good reference book -- not a great learning book, in my opinion.

Yeah, I was referring to Baby Rudin. I should have specified. I took a look at Carothers' book and it does seem much less dry than Rudin's, which should make it easier to self-study from. I'll definitely go ahead and use it. Thanks for the suggestion!