Questions about an Honours Year in Maths

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I'm considering taking honours next year in statistics with a project in financial mathematics. I'm really looking forward to taking more classes in this area, but I have a couple of worries I'd like to air...

1. How smart do you really have to be? I think I'm above the curve, I can get high distinctions (around 90) when I put in the work, but... the other people I know considering honours are like emerging geniuses... the uni has them running tutorial classes while they're still doing their undergraduate degree... today one of them helped me with an assignment for a subject he's not even taking! I am simply not on this level, and it worries me.

2. How well-rounded in maths do you have to be? I decided a little late that I loved maths, probability & statistics is really the only area I've excelled in and feel like I'm really good at...

3. Bit nervous about taking on the project... am I expected to come up with new ideas or proofs and stuff? I really wouldn't even know where to start... I want to do the honours year because I want to learn more, I don't feel like I'm at a stage where I can do new work...


Thanks in advance for any replies

 

[tmc]

1. Smartness is an odd thing to define, really. If you can understand the material after doing the work, then that's all you need. There will be other students who will understand the material much faster and will have to do less work than you, and there will be students who understand slower than you. You're taking the class for yourself, because you want to learn the material. You're not here to win a prize or beat the competition; you want to learn material. So take the class. And if you really can't handle it, then drop it and read the textbook at your own pace.

2. That really depends on your teacher. Most profs are pretty good at not assuming that their students know unrelated material, so the courses should be pretty much self-contained (especially in pure math courses, where terms will absolutely be redefined anyways to prevent any ambiguities with regards to what means what). If you have a poor teacher who assumes you know a lot of material that you don't, and who doesn't care to explain when you ask, then you might be in trouble.

3. Your supervisor will be doing most of the hard thinking, really. You will probably be required to come up with new ideas and proofs (that's the whole point, really), but the hardest part of research projects is often coming up with the problems to solve, not actually solving them. Coming up with new ideas is the fun part that you should be looking forward to; it's what you'll be doing daily once you get your degree. And if you get stuck, you have access to a supervisor who probably already has a good intuition for how to solve it.