Since all of upper year math course reviews aren't quite up-to-date, I was wondering if someone could provide feedback/mini-review to following courses:

Math 3A03 Math 3X03
Math 3E03 Math 3T03
Math 3F03 Math 2T03
Math 3Q03 Math 4TA3
Math 3B03 Math 3FF3

Thanks

I can't comment for sure on any of those courses (as I have yet to take any of them) but I do know that 4AT3 is a topic course, meaning that its content varies from year to year based on the prof who teaches it. So a review for it would probably be somewhat empty, unless the topic were to be repeated in a following year.

But with that said, I'd also appreciate it if someone could give us some feedback on any of those courses. Hopefully some upper year math majors see this thread.

I've taken 3A (wrote up a course review already), 3X, 3E, 3EE, and 3T from that list, and know people who have taken 3F, 3FF, and 4AT.

3A03: fairly straightforward, a typical intro real analysis course. Lots of somewhat unmotivated proofs, and lots of examples -- this is the first introduction to actual mathematical proofs for many, so it goes pretty slow.

You'll basically make calculus in one variable rigorous by the end of the course. A note on analysis: it's one of the widest branches of mathematics. You can treat it very concretely in differential equations or the calculus of variations (what 4AT was about), or treat it from various "pure math" standpoints. Here's a note on "hard" v. "soft" analysis: http://terrytao.wordpress.co m/2007...nce-principle/

3X03: again straightforward, a typical intro to complex variables. Less proof oriented, there's plenty of computation here.

3E03: intro to group theory; an area of abstract algebra. Groups are generalizations of the integers in additive terms; this structure is actually fundamental throughout mathematics. You mainly focus on finite group theory, starting with intuitive examples (permutation groups, dihedral groups, etc.) and then generalize. The "crown theorems" of the course are the fundamental theorem of finite abelian groups and the Sylow theorems.

3EE3: basic ring theory. This course is much more focused on generalizations of the entire multiplicative and additive structure of the integers (i.e. rings) as well as those of fields (like the rationals and reals). You will also look at rings of polynomials, the beginning of algebraic geometry.

3T03: topology. Probably the most difficult of the listed courses here, but very important in both pure and applied mathematics. This is about the shape of mathematical structures, which is fundamentally linked to the open (or closed) sets on the space. You'll do all sorts of cool stuff, topology is a very visual subject.

Also, if you're in math (pure or applied), you will need to take:

4A03: a real analysis course that should put things in perspective. In this course, you'll start doing real math. You'll cover a lot of stuff from 3A pretty quickly and in more detail / rigour / in greater generality before moving on to Fourier analysis and/or Lebesgue theory. Both of these are of great importance in mathematics; Lebesgue is probably more important for this course, simply because it's the foundation of all the analysis you'd see in the future. Definitely more difficult, but also far more interesting, than 3A03.

Also, I can say that classes get really small by 4th year; even 4A03, which pretty much every applied/pure math major takes, has around 20-25 students. Grades are correspondingly higher, but so is the workload.

If anyone could provide feedback on Math 4Q03, it would be very much appreciated!

Hey Mahratta!! thanks a lot!!

Can you tell us a little about 3f and 3ff based on your friends?? Also what about 3b?? Also do you know anyone who has taken the math history course??

Thanks!!

Originally Posted by Biochem47

Hey Mahratta!! thanks a lot!!

Can you tell us a little about 3f and 3ff based on your friends?? Also what about 3b?? Also do you know anyone who has taken the math history course??

Thanks!!

No problem.

I've heard good things about both 3F and 3FF.

3F03 is about the qualitative theory of ODEs, so you will learn about what you're actually doing when you solve ODEs (rather than simply learning techniques, like you did in 2C03).
You'll learn a bit of the mathematics behind systems of ODEs from a somewhat rigorous standpoint; there is actually some degree of connection between concepts in this course and the rest of mathematics (unlike 2C03, where all that really mattered was how to solve problems).

So 3F03 is a good course for pretty much anyone in math, and is more or less required if you want to go to grad school for applied mathematics (including finance, bio, etc.)

3FF3 is pretty much just PDEs, and with rather less theory than 3F. You will learn a lot of techniques, but with more theoretical background than 2C.

So it seems that 3FF is not quite as good to take if you're interested in pure math as 3F, but is again more or less required if you're into applied math.

And an aside for pure math majors:

If you want to go to grad school, make sure you take 3E03, 3EE3, and 3T03.

Originally Posted by JessMo

If anyone could provide feedback on Math 4Q03, it would be very much appreciated!

I haven't heard much besides that it was full of engineers, and so went really slowly.

Just got a couple things to add:

Whether you're into applied math or not, hated 2C03 or not, but have a basic appreciation for math, 3F03 will pique your interest. You learn to analyze systems of differential equations via matrices (much like the standard linear equations in 1B03) and can produce crazy diagrams, dependent on your eigenvalues (Real and distinct, Real and singular, or both Complex are the possibilities).

3FF3 is about showing you the limitations of current mathematics in the fields of PDEs. As you may know, solving differential equations is tricky, and in fact, it's been proven that some (many) differential equations have no hope of ever being solved. 3FF3 attempts to show you some of the boundaries of research and proves a few key results which emphasize this fact. This is crucial for anyone who wishes to work in applied math, since differential equations are so darned useful in modelling real life.

3B03 is your crash course in differential geometry (it leads to 4B03 - Calculus on manifolds). You take the concepts learned in your first two years of calculus, particularly the calculus of 3-D shapes, and learn to analyze more complex structures. You can figure out many properties about parametrized surfaces (contrast this with parametrized curves in 1AA3...it works as you might expect), such as whether or not they have self intersections, or whether that surface can be embedded in |R^3 (if it can be "drawn" but the term is used loosely). It's a great course, and it's being taught by Andy Nicas next year, who is a great prof with very very (very) reasonable tests.

4TA3 - I'm not sure what this course is, did you mean 4AT3? The topics course? Anything with a "4T" indicates a course that changes topics and profs quite drastically every year (such as 4TT3, or 4TB3).

When I took 4AT3, the topic was Fourier Analysis with Dr. Walter Craig, but you likely won't cover this same material anyway so I won't bother going into it. I do just want to say that the topics courses I have taken were, hands down, the most interesting (note: and challenging, but hence rewarding) of my undergraduate career...with only a few exceptions. I also loved 3T03 and 4B03 like they were my grandchildren.

EDIT: I took 3Z03 and the course was a nice break, it was inquiry based and student driven. I got to learn a lot about the foundations of mathematics as well as current research. The course consisted of 2 presentations, accompanied by 2 written essays, over the entire semester. There's not much to be evaluated on, but if you put a decent amount of effort into the presentations/papers, you should end up with some sort of A. The two topics I had chosen were spherical trigonometry (and I had to present who/when it came into existence, how it was first proven, etc.) as well as the mathematics of music (the ratios between piano keys, and the mathematics of AI that can generate music).

And I too heard 4Q moves a bit slowly...but that's a bit outside of my area of expertise.

[quote=Mahratta;316145 ]No problem.


If you want to go to grad school, make sure you take 3E03, 3EE3, and 3T03.


[quote]

Do you mean grad school for Pure Math? Or grad school for any math subject?
I'm in Stats and steered away from Differential equations, but am considering a Masters in Stats

Originally Posted by Melanieee

Do you mean grad school for Pure Math? Or grad school for any math subject?
I'm in Stats and steered away from Differential equations, but am considering a Masters in Stats

I thought I specified that...in any case, I meant pure math. It may be very helpful for applied math too; surely, it couldn't hurt. Stats is probably a different story, I don't know anything about what's required for stats, sorry.

Originally Posted by Incognitus

4TA3 - I'm not sure what this course is, did you mean 4AT3? The topics course? Anything with a "4T" indicates a course that changes topics and profs quite drastically every year (such as 4TT3, or 4TB3).

When I took 4AT3, the topic was Fourier Analysis with Dr. Walter Craig, but you likely won't cover this same material anyway so I won't bother going into it. I do just want to say that the topics courses I have taken were, hands down, the most interesting (note: and challenging, but hence rewarding) of my undergraduate career...with only a few exceptions. I also loved 3T03 and 4B03 like they were my grandchildren.

I think the topic last year was calculus of variations. They did some measure theory too. (...Mowicz?)

Originally Posted by Mahratta

I thought I specified that...in any case, I meant pure math. It may be very helpful for applied math too; surely, it couldn't hurt. Stats is probably a different story, I don't know anything about what's required for stats, sorry.

Im an idiot. Yes you specified that but thanks for answering anyway! Your description of 3F sounds really interesting, but I BOMBED 2C03, it was like a slap in the face, my lowest mark yet. And so I have a bad taste in my mouth

Originally Posted by Melanieee

Im an idiot. Yes you specified that but thanks for answering anyway! Your description of 3F sounds really interesting, but I BOMBED 2C03, it was like a slap in the face, my lowest mark yet. And so I have a bad taste in my mouth

I haven't taken 3F yet, but I'm seriously considering taking it and the topics in DEs course next year...I just don't know what the topic will be. And yeah, I really didn't like 2C at all; probably the worst math course I've taken (not marks-wise, but in terms of interest) -- didn't leave me with a good impression of DEs either!

Thanks for replies. If you don't mind, can you please specify what textbook was used for each course so we can get rough idea about rigour. Thanks

Originally Posted by Differential

Thanks for replies. If you don't mind, can you please specify what textbook was used for each course so we can get rough idea about rigour. Thanks

Good question, here's all the textbooks for the courses I've taken (relative to those you want to take). I can't say anything about the ones I haven't taken, I don't know what they used.

3A03: I don't remember, sorry. I borrowed this book, it wasn't great, but the questions were pretty much all on a test-level of difficulty. Whatever it is, it's less rigorous than, say, Baby Rudin. About the same as Rosenlicht, although not quite as nicely and concisely explained.

3E03 & 3EE3: Free book! By Judson, here's the link: http://abstract.ups.edu/download/aata-20110810.pdf
It wasn't great, once again, but is a good introduction to those who haven't seen much proofwork or abstract algebra before. A good supplementary book is Dummit & Foote's "Abstract Algebra", or Artin's book of the same name.

3T03: Munkres. Classic, and for good reason. Probably the best book out of the ones from 3rd year. I'm pretty sure it will be valuable for years to come.

3X03: "Basic Complex Analysis" (the pun gets old fast) by Marsden. Boring book, I found it takes all the fun -- i.e. the visualization -- out of complex analysis, and it's not even that rigorous...

3B03 - We used Elementary Differential Geometry by Andrew Pressley (http://www.math.sjsu.edu/~simic/Pics/Pressley.jpg)

3F03 - Hirsch Smale and Devaney (http://img2.imagesbn.com/images/155280000/155286874.JPG)

3E/3EE3/4E/702 (Same book) - Abstract Algebra by Dummit and Foote is essentially the bible of Abstract Algebra(http://www.cems.uvm.edu/~foote/book_cover.gif), with alternate resource (which I liked a bit more, and found it more 'learner friendly') A first course in Abstract Algebra by Fraleigh (http://www.math.umb.edu/images/books...0-Fraleigh.jpg)

4AT3 - Stein and Shakarchi's Fourier Analysis (I highly recommend any books by these two gentlemen... they were part of the Princeton Lecture Series in Analysis and are so crystal clear it's ridiculous! Fantastic lecturers these guys). (http://press.princeton.edu/images/k7562.gif)

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I also noticed you mentioned 2T03. 2T03 is the "applied math" counterpart to 2S03. Both are an extension of the material covered in 2R03. I'd recommend 2S personally, unless you're considering doing something in computational mathematics, and would like to learn how to use maple to solve 20x20 matrices and the like. (But then...I'm biased. :p)

I would say I'm interested in applied math with heavy emphasis on theoretical foundations(typical Soviet perspective on math) but then again I'm only 1st year entering 2nd year and the question I asked was basically my schedule for incoming year. I definitely favour analysis over geometry as I haven't developed good taste for it.