For fun: favorite UG math course

[DanM]

Which course did you find most interesting/intellectually stimulating/fun/whatever criteria you use to determine your favorite undergraduate math course?

 

[NeedOPT]

Algebra 3 (group theory)

 

[DanM]

Algebra 3 (group theory)

I wish I could have added more choices - I would have added more pure math courses as options. However, with the max 10 restriction, I decided to go more with applied math courses, given that this is a FE forum. Although there is an 'other' option.

 

[Andy Nguyen]

Addictive number theory. So elementary and easy to understand yet some problems have been unsolved for centuries.

 

[AnoopRN]

Vector Calculus - used it extensively for antenna theory and wave propogation.

 

[elliot]

Talk by Gilbert Strang http://www-math.mit.edu/~gs/videos/index.html
He compares Linear Algebra vs Calculus

 

[DanM]

Talk by Gilbert Strang http://www-math.mit.edu/~gs/videos/index.html
He compares Linear Algebra vs Calculus

Interesting video. I actually enjoyed the part about the random triangle.

 

[elliot]

Interesting video. I actually enjoyed the part about the random triangle.

and he blames calculus(derivatites) for the current financial crisis.

 

[ramnik]

Well the list lacks courses on Optimization, both mathematical(read convex analysis) and numeric. I loved these courses, though primarily due to the professor.

 

[bigbadwolf]

Additive number theory. So elementary and easy to understand yet some problems have been unsolved for centuries.

Any number theory -- algebraic, analytic, geometric, transcendental. Great fun.

 

[IlyaKEightSix]

Optimization. Mainly because my professor was a hyper French redhead that could pass for an American supermodel.

 

[DanM]

and he blames calculus(derivatites) for the current financial crisis.

Heh - that was funny.

Anyways, he makes some good points in his Calculus vs Linear Algebra discussion. My first LA course was very abstract and proof-heavy - I found it pretty interesting actually. More challenging, but also more enjoyable than Calc I-II.

 

[victormora]

currently taking linear algebra in my undergrad... not too fond of it

 

[Dylan]

Do theoretical computer science courses count?*
If so, algorithms. I can't think of another applied math course that involved so much esoteric abstract math- you've got graph theory, number theory, lots of other discrete math, but its all used for very concrete problems.

*Of course they do!

 

[bigbadwolf]

currently taking linear algebra in my undergrad... not too fond of it

It's a beautiful subject in its own right. The spectral theorem for self-adjoint operators. The Jordan and rational canonical forms. Modules over a P.I.D. Dual spaces and tensor algebra.

 

[koupparis]

BBW, I agree! Too bad most of that isn't touched upon in an undergraduate linear algebra course. I would have to say algebra in general was one of my favorites, and algebraic topology and maybe complex analysis, and probability. Ok, I was a math major, would you expect me to only have one as a favorite?

 

[victormora]

It's a beautiful subject in its own right. The spectral theorem for self-adjoint operators. The Jordan and rational canonical forms. Modules over a P.I.D. Dual spaces and tensor algebra.

i think koupparis is correct on this because we have not touched on any of that just yet

 

[DanM]

i think koupparis is correct on this because we have not touched on any of that just yet

I haven't either.

What have you covered in your LA course?

 

[chaoticrambler]

As an engineering student, when I took undergrad real analysis (baby Rudin) in my first year in grad school, it was pretty great experience, and my first time taking a 'REAL' math course (i.e. theorem-lemma-proof). After that I was hooked, and took another real analysis course and then took a 2 semester sequence on functional analysis and another in basic topology.
In fact, the first time I encountered self adjoint operators, dual spaces etc was in the functional analysis course, where of course, finite dimensional case is taken as trivial

 

[bigbadwolf]

In fact, the first time I encountered self adjoint operators, dual spaces etc was in the functional analysis course, where of course, finite dimensional case is taken as trivial.

In my humble opinion, it's useful to see it in the finite-dimensional case first, to understand what it says, and the method of proof. Usually a first undergrad course in the subject has the spectral theorem as its high point. The spectral theorem for compact (infinite-dimensional) linear operators needs to use more complex tools from topology for its proof, and this applies to the even more recalcitrant bounded linear operators. The spectral theorems in these cases are generalisations of the finite-dimensional case, which falls out as a corollary. But I reiterate that the f-d case should have been seen first -- it's useful pedagogically. The same applies to dual spaces and annihilators. The Schaum series book on the subject (by Murray Spiegel?) is quite good on the subject and there are a couple of Springer undergrad texts (Curtis? Smith?) that are also sound.

---------- Post added at 03:33 AM ---------- Previous post was at 03:27 AM ----------

I would have to say algebra in general was one of my favorites, and algebraic topology and maybe complex analysis, and probability.

In my humble opinion, complex analysis is satisfying in a way that real analysis can't come close to. The theorems are stronger, more far-reaching, and the ideas more profound (analytic continuation, Casorati-Weierstrass theorem, Liouville's theorem, Rouche's theorem, infinite-product representation, residue theorem, etc.)

Algebraic topology is also great fun -- after the standard first course.