Let's hear it!

[Sidoh]

Linear was easy :\

You probably took linear algebra for engineers, though.  Engineering math is not to be confused with real math.

Mathematical linear algebra is far more abstract.  90% of my linear algebra course was proofs.  If you've never had exposure to mathematical proofs, it can be rather difficult.

Linear algebra is probably the course that convinced me to major in math.  I really enjoyed the abstractness/proofy stuff.  All of the courses I had before were for engineers, which were comparatively mundane.  It's "here's how to do this calculation, now do it a bunch of times."  Proof courses are "here are some theorems," then you're given some seemingly unrelated problems and told "prove: ...".

Admittedly, linear algebra was quite a bit more straightforward than some of the other math courses I've taken (algebra, analysis, etc.), but it was still quite a bit more rigorous than, for example, engineering calculus.

[dark_drake]

You probably took linear algebra for engineers, though.  Engineering math is not to be confused with real math.

Mathematical linear algebra is far more abstract.  90% of my linear algebra course was proofs.  If you've never had exposure to mathematical proofs, it can be rather difficult.

Linear algebra is probably the course that convinced me to major in math.  I really enjoyed the abstractness/proofy stuff.  All of the courses I had before were for engineers, which were comparatively mundane.  It's "here's how to do this calculation, now do it a bunch of times."  Proof courses are "here are some theorems," then you're given some seemingly unrelated problems and told "prove: ...".

Admittedly, linear algebra was quite a bit more straightforward than some of the other math courses I've taken (algebra, analysis, etc.), but it was still quite a bit more rigorous than, for example, engineering calculus.

Bu.. .bu... bu... I R engineer! I can do maths.

[Sidoh]

You probably took linear algebra for engineers, though.  Engineering math is not to be confused with real math.

Mathematical linear algebra is far more abstract.  90% of my linear algebra course was proofs.  If you've never had exposure to mathematical proofs, it can be rather difficult.

Linear algebra is probably the course that convinced me to major in math.  I really enjoyed the abstractness/proofy stuff.  All of the courses I had before were for engineers, which were comparatively mundane.  It's "here's how to do this calculation, now do it a bunch of times."  Proof courses are "here are some theorems," then you're given some seemingly unrelated problems and told "prove: ...".

Admittedly, linear algebra was quite a bit more straightforward than some of the other math courses I've taken (algebra, analysis, etc.), but it was still quite a bit more rigorous than, for example, engineering calculus.

Bu.. .bu... bu... I R engineer! I can do maths.

I'm sure you're perfectly capable of doing real math, but that doesn't change the fact that engineering math isn't real math.

I'm also not saying you haven't succeeded at doing real math.  I'm unfamiliar with what math courses you've taken over the years, but I wouldn't be surprised if you'd snuck a few 'real' math courses into your schedule.

[truste1]

Sidoh is more qualified to talk about math than God.

[Sidoh]

Sidoh is more qualified to talk about math than God.

This is vacuously true.

[iago]

Sidoh is more qualified to talk about math than God.

This is vacuously true.

That's the best kind of true!

[zorm]

Why on the subject of math, maybe someone can recommend me a good course to take next semester? I've done a lot of engineering math courses, enough for a math minor (I'd have a B.A. in math but I need ~13 hours of foreign language).

Looking at what courses I can pick from I see these:
Modern Geometry - An introduction to geometry including axiomatics, finite geometry, convexity, and classicalEuclidean and non-Euclidean geometry.
Introduction to Functions of a Complex Variable - Complex analytic functions, conformal mappings, complex integrals. Taylor and Laurent series, integration by the method of residues, complex analytic functions and potential theory.
Introduction to Abstract Algebra I - Concepts from set theory; the system of natural numbers, extension from the natural numbers to the integers; semigroups and groups; rings, integral domain and fields
Applied Modern Algebra - Topics from the theory of error correcting codes, including Shannon's theorem, finite fields, families of linear codes such as Hamming, Golay, BCH, and Reed-Solomon codes. Other topics such as Goppa codes, group codes, and cryptography as time permits
Introduction to Analysis I - Review of real number system. Sequences of real numbers. Topology of the real line. Continuity and differentiation of functions of a single variable.
Introduction to Topology - Metric spaces and topological spaces, continuity, connectedness, compactness and related topics.
Partial Differential Equations - First order equations, Cauchy problem for higher order equations, second order equations with constant coefficients, linear hyperbolic equations (Grad. Class)
Wavelets - Fourier analysis on a finite cyclic group, the group of integers, and the real line. The matching pursuit algorithm. The Poisson summation formula and sampling. Multi-resolution analysis, various wavelet constructions (including those of Daubechies and Meyer) and filter banks. An introduction to the MATLAB wavelet toolbox. (Grad. Class)

Are any of these really enlightening classes or cover subjects that are neat? I'm eyeballing the Wavelets class...

[Sidoh]

Of course it depends on what you want.  If you like pure math, then of course something like topology would be ideal.

I'm really enjoying analysis, and I think I would've liked algebra more had I had a different professor.  Still lots of fun, though.  Those are both rather akin to "pure math" too.

DiffEQ and Wavelets are both kind of applied subjects.  Useful, but not the kind of math I like.

The fact that any of them are graduate classes is mostly irrelevant.  We did more in my second semester of undergraduate algebra than the graduate algebra course does.

[d&q]

Modern Geometry - An introduction to geometry including axiomatics, finite geometry, convexity, and classicalEuclidean and non-Euclidean geometry.
Introduction to Functions of a Complex Variable - Complex analytic functions, conformal mappings, complex integrals. Taylor and Laurent series, integration by the method of residues, complex analytic functions and potential theory.
Introduction to Abstract Algebra I - Concepts from set theory; the system of natural numbers, extension from the natural numbers to the integers; semigroups and groups; rings, integral domain and fields
Introduction to Analysis I - Review of real number system. Sequences of real numbers. Topology of the real line. Continuity and differentiation of functions of a single variable.
Introduction to Topology - Metric spaces and topological spaces, continuity, connectedness, compactness and related topics.

Unless you need some grad courses atm, I would take one of these. Topology, Algebra, Real Analysis, Complex Analysis, Geometry (in order from most desired to desired).

[d&q]

The fact that any of them are graduate classes is mostly irrelevant.  We did more in my second semester of undergraduate algebra than the graduate algebra course does.

I would have to say that largely depends on the school...

[Sidoh]

The fact that any of them are graduate classes is mostly irrelevant.  We did more in my second semester of undergraduate algebra than the graduate algebra course does.

I would have to say that largely depends on the school...

and the class.  I mostly said that because people tend to think it means it's an insane amount of extra work.  Sometimes that's true, but it's usually manageable.

[Rule]

The complex variable course was my favourite of those listed.  The topics in 'intro to topology' and 'analysis I' were covered in one course, where I went.  You can even see in the descriptions that there is overlap... it seems strange that they have separated out the material into two different courses.

Of those, complex variables would be my first choice, and analysis I would be my second (presuming I did not have much math background).  Analysis I, without topology, looks really bare though. I consider things like compact sets, connectedness, metric spaces, etc., important parts of an introductory analysis course.

[rabbit]

I'm gonna have to agree with everyone else.  Complex seems most interesting, then topology after that.

[while1]

It sucks that 1/3 of my paycheck goes to taxes.  I wish overtime pay didn't get taxed .

[BigAznDaddy]

It sucks that 1/3 of my paycheck goes to taxes.  I wish overtime pay didn't get taxed .

or commissions.