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I'm in need of advice with my life/studies. This will probably turn out to be a long post so here goes.

My background

I did very well in high school mathematics achieving an average 97.5% over 6 math classes I took and achieved a 99% in 3 of those. It was during Gr.10 that I realized I wanted to study math and tried to purchase books to get ahead but unfortunately my family couldn't afford them. I participated in a few Canadian math competitions and did okay - placing in the 25th percentile in the Fermat Competition and making the cut for the bronze section for the Galois Competition. So I realized I had some skill (talent) at mathematics but never got a chance to nourish it. Nonetheless, I did well and applied to the University of Toronto for the Mathematics program to which I was accepted. At this point I honestly had no clue what I was getting myself into because I didn't really know what pure mathematics entailed. We started off Analysis with Spivak's Calculus and Linear Algebra with Friedberg et al. I honestly sort of hit my face because the level of abstraction was high and I had no prior exposure to it but that's how things are done at UofT. I also had bad working habits as high school was a breeze for me so my expectation was that university was going to be the same. It clearly wasn't and I started to do poorly. I also had this fear of not understanding what I read and being afraid of not being able to live up to my parents' expectations. So I lost motivation and started to trail behind. I ended up achieving a 70% in Analysis and a 78% in Linear Algebra I. When I did Linear Algebra II during the second term I had completely lost motivation and didn't do a single assignment and only read my text before the day of the midterm and got a 58% and so I needed a relatively good grade on my final to pass the course. I read the sections required for the final the night before and got the 50% I needed in the course to not fail. So I completed my programs first year courses and I was "happy". Summer came a long and I did useless courses because I had dropped physics and Economics during the year and the same trend continued. At the end of the summer, I had been placed on academic probation due to poor grades. As a matter of fact, I hadn't realized this so I started 2nd year with the same habits. Analysis II was being taught from Spivak's Calculus on Manifolds and once again I didn't have the motivation for anything and didn't do anything. I was also taking a course on ODE's and at the end of the year I had failed both because I hadn't done any course work. So as a result of my poor grades I was suspended for a year. During my year off I worked and before going back to school I studied Spivak's Calculus in a month doing a chapter a day and doing problems, but linear Algebra was left untouched. I entered 2nd year again and this time Analysis II was being taught using Munkres' Analysis on Manifolds and I was doing very well, but at the start of the second term my brother went through an operation and I had to take care of him and I had to be away from school for about 3 weeks. During this time we had started Multilinear algebra and differential forms and I wasn't able to keep up and fell behind and never managed to catch up. So at the end of the year I had basically only completed half of the course material and I walked into the exam unprepared and my final grade turned out to be a 56%. So once again I got the course but didn't know the material well. I started 3rd year and was taking Complex Analysis I (taught from Stein and Shakarchi), Real Analysis taugh from Pugh, Abstract Algebra taught by Dummit and Foote and Topology taught from Munkres. Sadly I entered with the same mentality as in previous years and I didn't do work. This time I was smarter and dropped these courses and only kept a class on Sociology. However, I ended up failing this course and I got suspended for 3 years. I'm just finishing the first year of my suspension and during this time I've had a lot of time to think about my life and what to do with it and I need advice.

Currently, I'm doing self study and I'm reading up on the mathematics I should have done during my first two years in school and plan on reading further. I feel my motivation is back and I'm once again enjoying math as I used to when I was in high school. I plan on going back to school at the end of my suspension in 2 years finish my degree. If any of you bother calculating I'll be 26 years old. I know I'll be older then and it can honestly be depressing thinking about heading back to school at that age and not having accomplished anything, but I really want to and if everything goes as planned I will.

Advice

I need advice considering my situation on what I should do. My dream has always been to work in academia, but I don't know (and I should probably be saying it isn't) if its possible to achieve something like that at this stage. I don't know if any graduate schools would be willing to accept me considering my course record and I believe the last time I checked my GPA was a 1.2 if not even less so to raise it to something respectable seems to be nearly impossible. I have also always had an interest in number theory so I've considered going nto industry. Forgetting it all and becoming a high school teacher has also crossed my mind, but I'm not sure which dreams I should let go and which ones to hold on to.

I've tried speaking to academic counsellors but they haven't been much help so I thought I'd seek some advice/help here. I would really appreciate any advice and words of wisdom or even a slap on the wrist.

Thank-you.

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Even though you didn't say that your age is an issue, I'd like to mention that it's a common opinion that it probably isn't. This and this should help you out with somethings. Don't just look at the answers. The comments have some really useful links. –  Git Gud May 3 '13 at 23:36
    
Thanks for those links. I'll read them through. –  user75838 May 4 '13 at 0:04
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@user75838 : your post was awfully long and I didn't read every word, but I think I read enough. High school teachers make peanuts for salary and you must take this into consideration. They have to follow nonsense rules by administrators who know nothing about mathematics or much else. There is very little demand for theoretical mathematicians unless you go to a top-tier grad school, meet the right people, and publish papers that people will want to read. I think the academic job market is better than it used to be but it is still awfully competitive, and you would be competing against ... –  Stefan Smith May 4 '13 at 1:22
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... many people who breezed through all their undergrad and grad classes in math and everything else. I think you are more probably likely to find a rewarding career outside of academia. However, you must get some credentials in computing, or business, or actuary science, etc. Employers do not care about how smart you are, only your credentials. Although there are jobs that use a lot of mathematics, you are probably not going to get an academic job if your education is solely in math... –  Stefan Smith May 4 '13 at 1:27
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If you work outside of academia and decide you want to teach, colleges will probably consider your nonacademic experience a plus. The reverse is not true. By the way, I don't think 26 is too old. Sorry for the long comments. I probably should have made this an answer. Hope I didn't break some MSE rule. –  Stefan Smith May 4 '13 at 1:29

1 Answer 1

I'd like to address the age issue, which I think has you worried unnecessarily.

Where I'm from, people enter mandatory military service for three years, and sometimes even extend that. Then, they might take a couple of months to a year to travel and work before college, and during college, they generally work, lengthening their degree period. All in all, it's not at all uncommon to see people finishing their undergrad degree at 26. So, I wouldn't let the age issue deter you.

The age issue also makes a difference on your study habits, I think those extra couple of years will definitely help you be more focused on your studies next time around.

With regards to future carrer planning, I think it might be worth while learning some practical (a.k.a computer science) tools while you're waiting, since although there are many math graduates, there are far fewer positions for theoretical mathematicians. This reality isn't as harsh as it sounds - there are many interesting positions available for algorithm developers (to name but one application).

In any case, good luck with what ever path you choose.

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