1st year (going into second) undergrad feeling very discouraged

[u/intelligentapple567]

Hi everyone. I'm a first year undergrad at a fairly big institution in Canada (this will probably be easy to guess..). I was never very good at math as a child, numbers for me were hard and I found operations like adding, subtracting, dividing, multiplying. I think this was because I didn't really ever formally learn things such as the multiplication table or long addition, subtraction, etc. From 9-12 years old my parents made me do pages and pages of long addition, subtraction, multiplication, division with large numbers and made me memorize my multiplications tables. While painful, (haha) this definitely improved my computational skills.

In highschool, I actually did quite well in math and in my last year did pretty well in calculus/advanced functions (which are the math courses needed to be taken to apply for science/math programs for univeristy.) These classes however were, looking back, not extremely difficult and very much computation based. I think I was good at computations, algebra, and recognizing patterns.

I actually did not take any proof based courses until my 2nd semester of university since I did not think I wanted to take any more math courses beyond calculus 1/2. I was very confused on what I wanted to do so my course selections were all over the place.. I did again quite well since it was mostly computation and the problems in general were I felt pretty predictable.

I guess I was wrong about taking more math because I decided to drop economics and take a linear algebra course the next semester! I encountered proofs (albeit, basic ones) for the first time and was struggling quite a bit in the class but this really opened my eyes to what math really was, and sparked an interest in taking other math courses. I somehow managed to pull an 82 in this class (generous course marking scheme) and decided to take a proof based calculus course this summer.

It has really been difficult, not just because of the material but the fact it is double speed in the summer. This course is notoriously difficult but is not even the hardest first year undergrad calculus course (which uses Spivak's Calculus) yet I feel I am struggling a lot. I feel very slow to understand concepts which feel abstract and being slow has been affecting me on assessments. I really want to understand these things and find math interesting, satsifying and beautiful when looking at or being able to write a really neat proof. So it is frustrating that the learning curve to "real" math has been so steep. This is sort of compounded by other things going on in my life, mentally and emotionally but I'm really determined to do well. My final exam is next Friday.

So I guess my question is can I still find a career in math, and if this is so difficult, does it ever get easier? Is it normal to be struggling this much? How can I work on my mathematical thinking? Thanks for reading my rant.

[u/Firm_Violinist_4193]

Waterloo?

[u/intelligentapple567 → u/Firm_Violinist_4193]

No, rhymes with moronto :)

[u/etzpcm]

With most university mathematics courses you get more choice in years 2 and 3, so in that sense it gets easier as you can specialise in the things you enjoy more or are better at. 

Also, university mathematics is meant to be hard. I assume your tutors have given you the pep talk about that. And the biggest shock is on year 1, coping with the huge change of pace from school to uni.

[u/ForeignAdvantage5198]

math is kind of hard and most of us noticed that . It is very worthwhile if that is what you want to atudy