Programs Mathematics degree not going too well advice needed.

[Rello]

Hello PF,

I would be grateful for some advice regarding my study situation.
I have lived in the UK for a while and now have moved to back to Europe to start there a mathematics degree.

I did not have a particularly mathematical education, so I did a year long access course to higher mathematics at university level, I did ok, but not great, partly because I tried to learn too much at once, but I did my best to prepare myself well for the maths degree.
I have received encouragement from my tutors there, who said that my kind of thinking is what I need to study maths.

Compared to the people from the country I am in at the moment I probably have some lacks from the secondary school level; the access course I did was a bit weirdly structured, it covered partial differential equations for example, but did not really cover limits, and now I am feeling the lack of that practise in my current Analysis course.

I have read up on studying maths as such, if it is possible to do it with my background, and the answer was "yes if you are prepared to work really hard", and I thought since I am considered highly intelligent I should be able to manage it.

The feeling I got from reading this forum as well, was that people who do mathematics are usually open and helpful to people who want to learn it.

My motivation for studying it is that I think it is a necessary subject to know, and want to train my thinking.

This term I am taking Linear Algebra 1 and Analysis 1.
I am doing ok in Linear Algebra, but so far Analysis is going rather horribly: the level is really high, which is good, I can follow the concepts, but when it comes to proofs I tend to deliver results with low marks.

We need to hand in our weekly assignments in groups of two, and it does not help that my partner has been really "flaky" and does not want to work on them together, I always did the harder questions, and messed them up, and he even messed up the easier ones (we get graded together).

I have talked to my tutor about this, and he told me to come to him to ask for help with course work etc, but he also told me "directly" (because here everyone is very "direct") that my work lacks "a sense (flair) for mathematics", even though he knew I did a rushed job before class and was not able to talk to the other person from the group before, and we talked only about 2 pieces of my work. It is my first term...is that not too soon to pass a judgement like this?

Overall the feeling I get from the course is that the atmosphere is very harsh and competitive. The first 2 terms are meant to be as hard as possible to "weed out the bad students", which I understand, but I struggle with the atmosphere (and of course I feel homesick..)
At British universities, the culture was different: you received critique for your work, but also encouragement. I knew tutors who were extremely intelligent and knowledgeable, but who never, ever appeared arrogant or "superior" to the students, even the ones who were asking very silly questions, here I see "put downs" happening a lot, in very subtle ways.
I know it all takes place to make us "good mathematicians" but I miss the sense of encouragement and human warmth I felt in the UK.
Now I am facing the prospect of repeating Analysis 1 (which is apparently considered "normal") and 3 more years studying in this cold atmosphere. I am wondering if I have done the right thing.
I don't aspire to be "real" mathematician, I only want to understand mathematics better and be good at it. I don't think this is an unreasonable aspiration.

I am wondering if I have made the right choice, if maybe I don't fit into this degree, I study less and worry more, this is a vicious cycle.
I don't know if the doubts I have are because of the subject itself, or of the university and the atmosphere there.
I would be grateful for some advice.

Thank you

 

[micromass]

What kind of things are you seeing in analysis?? What book are you using. If you never did calculus before (limits for example), then an analysis course will be very tough for you.

Here are some things I suggest for you to do:
1) Pick up a good calculus book (the calculus book of Spivak for example) and a proof book (for example, by Velleman).

2) Take about all the aid you can get: go to office hours! Present your proofs here on PF and let us give criticism. Ask help if you need it!

3) I know the atmosphere isn't good, and that's not fun. But I'm sure there are people who want to cooperate with you. Find some like minded people and form study groups. Ask around a bit.

Repeating the analysis course is no shame. But be sure not to make the same mistakes again. Be well prepared next time. And try your hardest now to succeed.

 

[Rello]

Thank you for the recommendation Micromass!

To answer your questions:

I'd say I have some experience of calculus: differentiation, integration, sequences and series and so on, the major difference was that almost all the topics were approached with the attitude "calculate the interest on a mortgage after 20 years", or the "first terms of a sum", or "integrate by parts the following...", so we were taught techniques from the calculus syllabus, but totally avoiding treating the essence of the topics: their connections to limits, which were only briefly introduced.

The content of the 6 weeks of the first term (that I can remember, there was more I think), was: field and order axioms for reals, definition of the natural numbers as the intersection of all inductive subsets of any inductive set, the Axiom of Archimedes, Bernoulli inequality, definition of square roots, convergence of sequences, limes superior and limes inferior, maxima and minima of bounded sets, Bolzano-Weierstrass theorem, Completeness Axiom, Cauchy-sequences, all the different criteria for convergence of series (Leibnitz, comparison test, etc.), definition of e as a limit of a series, Cantors theorems about the countability of sets, and last week we started introducing theorems about continuity of functions, (but I have not read that yet).

The course follows these books: Barner/Flohr Analysis I and Otto Forster Analysis I.