What I Wish I Knew at the Beginning of my Math Degree

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SirDucky
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What I Wish I Knew at the Beginning of my Math Degree

Postby SirDucky » Mon Jun 20, 2011 7:39 pm UTC

So I'm in the final year of my undergraduate degree, and really quite happy with my grades and experience. However, looking back on things, any success I had was due to egotistical exuberance more than anything, and there are a few things I wish someone told me at the beginning of my course. It would have made life so much easier. All of these statements come with the disclaimer "if your course is anything like mine", which means fairly rigorous, with an 80% exam at the end of semester. I'm also in Australia, so it might be different in other countries.

- Every class has roughly 100 techniques, theorems, etc that you will have to learn. Plan for this and know what they are. Don't let yourself wait until a week before exams to figure out which parts of the course were important. Keep your own list, and just f*cking *know* them. Roughly 25 of them are things that are your bread and butter, and will use again and again for questions in the course. Know them inside and out, until you dream about them in your sleep. These are the things that you're paying your expensive-ass tuition for, and you're only cheating yourself if you don't know them.

- Show up to the damn lectures and practice classes. It doesn't matter how sharp you are: catching up on lectures is an uphill battle, and can guarantee you a mediocre to low grade. Practice classes are even more important, and directly correlate to knowing how to answer exam problems. Sooner or later though you'll miss something, and it's way better to miss a lecture than a practice class. Practice classes help you, well, practice, and are generally far more efficient at increasing your proficiency.

- In first year, pay attention every time you hear the word "proof". That sh*t's gonna take off in a big way in the next few years. You'll want to be comfortable reading and writing proofs, and will save a lot of trouble if that happens early.

- Don't let your eyes glaze over when lecturers show their work on lecture slides. It's easy to "skip to the end" and get the result of the theorem, but you will learn *so* much more when you take an extra two seconds and understand what they're actually saying and why it works. It's up there for a reason.

I think that's it. Hope it helps some fellow struggling undergrads.

Ankit1010
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby Ankit1010 » Mon Jun 20, 2011 8:55 pm UTC

Just wanna say, I think all of this applies to all undergrad courses. Sound advice.

achan1058
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby achan1058 » Mon Jun 20, 2011 9:07 pm UTC

I think my advice is:

Join the Putnam club/practice ASAP, even if you aren't going to get anything better than 0. They will have proofs drilled into your head in mere months.

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby mike-l » Mon Jun 20, 2011 9:16 pm UTC

Don't write off any areas just because the intro course was bad. All intro courses are a sliver of the real stuff, and often not a very good one.

Build relationships with your professors as much as possible

Almost everything in a course is relevant. If you don't see why, spend some time trying to figure it out.
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mdyrud
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby mdyrud » Mon Jun 20, 2011 9:40 pm UTC

mike-l wrote:Build relationships with your professors as much as possible
This. Other tips are great for making sure that you know what is going on the class, but this is how you open up doors for research and other stuff outside of the classroom. Plus math professors are usually pretty cool people.

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby ConMan » Tue Jun 21, 2011 12:35 am UTC

Any time something is proven in lectures, your best way to study is to try and replicate the proof - don't look at what the professor did unless you get stuck, try to understand what you're doing at every step.
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby gorcee » Tue Jun 21, 2011 3:59 am UTC

My $0.02:

Know your curriculum. Don't just follow the formula blindly. Understand why, when, and by whom all the courses are taught. Re-structure to suit your individual talents.

Use your advisor.

Learn the difference between a bad professor and your own stubbornness. Suffer neither.

If you're studying math, it's probably a safe bet to say you were always in the top 10% of your class in secondary school. Learn humility. Learn the difference between confidence and arrogance.

Embrace stress. Learn to manage it. Learn what to sacrifice and when. Your life will never be as easy and clear cut, with well defined temporal boundaries and a synthetic measure of intellectual progression. Once you are out of school, the world is an amorphic, unorganized mess, and you're left to make it up as you go along.

There is no such thing as summer. Love the illusion while it still is there.

And most importantly: your undergraduate degree is not the last step in your schooling. It is the first step in your career.

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby Adam Preston » Tue Jun 21, 2011 2:25 pm UTC

This is great advice for me on how to structure myself if I were to go to university for whatever course. I'm sure University will keep me busy, so thank you for making me aware of what I would need to look out for.
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Game_boy
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby Game_boy » Wed Jun 22, 2011 9:20 am UTC

(Undergraduate Physics at highly regarded school, just finished first year)

If you go into a tutorial/supervision not knowing something, and in that session you figure out how to do something you were stuck on, write down in your OWN words how you now understand it. Otherwise when it comes to revision you'll have forgotten again and your original notes alone won't help because they didn't before.

The easy stuff is still worth practising from the beginning because the volume of stuff you are required to learn for the exam means you will sideline what you think you already understand and the first time you may be doing that technique is in the exam itself.

Work from past papers and if possible their markschemes, not from the notes. Get your supervisor to mark all or part of a past paper so you can learn your weaknesses in exam technique (not writing enough, not using all the information in a question, time management, etc.)

Yes, that annoying 2-page proof will come up on the exam.

When you do revision, act like it's unrelated to the exam and you're just doing an hour's work on topic X because you have to, and in your mind don't associate that with actually getting more marks on the exam by doing that work. This is so it is in small manageable chunks. Otherwise you'll see how much work you have to do for the whole revision period every time you sit down to do it and consequently be under too much pressure.

In subject X that you're finding hard / a lost cause, it's because you didn't pick up on the few basic rules that simplify 100 cases to under 5. You should go to supervisors and, by getting them to walk you through questions, determine what those rules are and how to recognise when you need to use them. Half an hour with my Chemistry supervisor turned it from something I expected to fail to my best subject, by realising every mechanism was one of two cases.

If you are feeling stressed/upset enough that you're spending long periods of time thinking about it, or it is affecting your work, or you're not sleeping, you need to TALK to someone. Your parents, your academic supervisors or counselling. Not friends; they will be pretending they are fine and confident and it will make you feel worse.

And the kicker - YES, you were AMAZING at school and didn't need to revise at all. You do now. No, really. Even if you still think it doesn't apply to you, it does. And all that means is a few hours' extra commitment to revision a week for the whole school year, but if you don't do it you will realise about 2 weeks before the exam that you should have. (Learned the hard way. I was the kind of person who would read this comment and still think I didn't need to)
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gorcee
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby gorcee » Wed Jun 22, 2011 4:01 pm UTC

Oh, and one last thing:

SLEEP

An hour of sleep is worth two hours of studying. Fatigued minds make mistakes, and overlook things, and make your study hours worse. What might take you 5 minutes to understand while rested can take you an hour while fatigued, and it will frustrate you, and burn you out. All-nighters are fine to do on occasion, but don't do it because you need to study for an exam that you didn't prepare for.

Corollary: Crunching is stupid. In the US, semesters are 15-16 weeks long. You had 15 weeks to learn the materials. If you didn't learn it then, then you probably won't learn it sufficiently in the 2 hours prior to your test. Cut your losses. Focus on the things you have an actual chance of learning. Or, read a book and relax. Seriously. You might not get an A. But if you didn't do the work during the semester to prepare yourself, then you don't deserve the A.

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby Hendecatope » Wed Jun 22, 2011 11:04 pm UTC

Putnam / and other contests
Someone above mentioned that joining the local, friendly, problem solving, math contest class or club is a good idea. I have to second this! Half-way through my freshmen year a professor asked if I would be interested in a weekly contest class meeting; when I told him that I was only a freshmen he exclaimed "Perfect!", as it's best to start early while you don't know a damn thing.

So, every week I would get a problem that I often didn't know how to accomplish with the usual tools. This happened so much that when someone presented a non-standard proof of a number theory fact that didn't use the usual machinery someone would exclaim, "Oh, you will learn that in the first 2 weeks of NT". This joke was so common you might believe that our NT course was only 2 weeks long!

My point is, it's always best to approach something fresh without the knowledge of the slick machinery at first. This way you are forced to discover at least a portion of that interesting tool that you will learn about formally later.

Lastly, these kinds of problems vary heavily but the are your earliest exposure to proof techniques and in the end that's what matters.

Networking
It's good to know the faculty since it's usually better to take a course because the professor is good than to take a course in a subject you are interested in but taught by one that's not optimal for some reason.

You will never know what you are missing by not being at least "on their radar". One of my professors had some mysterious time blocked away on his schedule. When I asked him what it was it turned out he was filling in as the second coach for a High School contest team. I inquired further and eventually asked if I could be an assistant coach. In fact, no one else had this opportunity because I'm the only person who ever asked!

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby Dopefish » Thu Jun 23, 2011 3:41 am UTC

gorcee wrote:SLEEP


This. No one seems to believe me when I give that advice, often responding along the lines of "Pfft, not everyone is as smart as you, some of us need to study and can't afford the luxury of sleep.", but really, sleep is really really important.

The biggest dip in my grades occured during a period when I had formal lab reports (big 20+ page things full of by-hand error propagation and graphs and other time consuming things) due the day after the lab, basicly forcing me to sleep deprive myself on a weekly basis. It was terrible, as not only did I feel tired and blah, my marks were very average for that period, primarily due to stupid stuff.

Some people might be inclined to call me a baby and that I should just power through things when I say I need sleep, but really, whenever I'm properly rested I tend to do at least as good, if not better than, the people who stayed up the night before studying, and I'm confident a number of those people could easily outperform me if only they would let themselves sleep.

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby somebody already took it » Thu Jun 23, 2011 2:38 pm UTC

You can't comb a hairy ball flat without creating a cowlick.

Darryl
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby Darryl » Sat Jun 25, 2011 3:26 pm UTC

gorcee wrote:Use your advisor.

This one cannot be emphasized enough for any college program. At my CC, my advisor helped me jam two classes into my schedule to get done on time, even though one was a pre-req for the other. Unfortunately, I did fail that class (due to not doing the work), but it doesn't affect my transfer too much.

More advice:

Don't be afraid to change majors. If you change in your Junior year or later, it may cost you an extra semester, or maybe just an extra workload. But don't change at the drop of a hat. Most colleges require additional advisement before switching majors a second time for good reason.
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby Kurushimi » Sat Jun 25, 2011 6:39 pm UTC


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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby lu6cifer » Sun Jun 26, 2011 5:13 am UTC



Everything's a REPOST*!!!
Actually, I saw this post and had the exact same thought you did.



*Well, not technically, since it's by the same person.
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby teacupthesauceror » Thu Jun 30, 2011 5:21 am UTC

Having completed my first year, I can say:

- There is a limit to correcting lecturers. Don't make the class lose respect for them, or nobody will learn.

- Sleep is a glorious thing.

- Even those who "don't work" work. We just don't like to admit it.

- Making the most of my doss year was the best thing I could have done, real work is for second years. A social life is an excellent thing to have.

I'm amazed at the amount of contact you guys have with your supervisors. Maybe it's the stiff upper lips getting in the way, but there seems to be a general agreement that a five-minute meeting a few times a year is more than enough contact for someone not applying for mitigating circumstances. They have research to be getting on with, and friends are generally easier to understand when asked for help, if less equipped with blackboard.

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby AMathematician » Thu Jun 30, 2011 5:39 am UTC

teacupthesauceror wrote:- There is a limit to correcting lecturers. Don't make the class lose respect for them, or nobody will learn.
And that limit is only if they have a mistake in a proof that isn't necessarily obvious. Seriously. Nothing is more irritating than someone interrupting lectures to point out that in an intermediate step the professor wrote a 2 instead of a 4. If they carry this mistake on to the next step, mention it. If it appears to be a pretty subtle mistake, mention it. But if they accidentally wrote the formula for the area of a circle as [imath]2\pi r^2[/imath] but still computed the area correctly, don't worry about it.

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby Game_boy » Thu Jun 30, 2011 9:58 am UTC

teacupthesauceror wrote:
I'm amazed at the amount of contact you guys have with your supervisors. Maybe it's the stiff upper lips getting in the way, but there seems to be a general agreement that a five-minute meeting a few times a year is more than enough contact for someone not applying for mitigating circumstances. They have research to be getting on with, and friends are generally easier to understand when asked for help, if less equipped with blackboard.


Maybe "supervisor" means a different thing here, because we have 4 hours a week of time with them in groups of 2.

I would have something similar that to be common at US universities since the fees are so high.
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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby gorcee » Thu Jun 30, 2011 1:24 pm UTC

Game_boy wrote:
teacupthesauceror wrote:
I'm amazed at the amount of contact you guys have with your supervisors. Maybe it's the stiff upper lips getting in the way, but there seems to be a general agreement that a five-minute meeting a few times a year is more than enough contact for someone not applying for mitigating circumstances. They have research to be getting on with, and friends are generally easier to understand when asked for help, if less equipped with blackboard.


Maybe "supervisor" means a different thing here, because we have 4 hours a week of time with them in groups of 2.

I would have something similar that to be common at US universities since the fees are so high.


Yeah.

Where I went to school, the financial breakdown when including room and board, was that I was paying $50 per hour spent in class. I don't care if the professors have other obligations and don't like to deal with students. Guess what? I don't like having to write mathematical reports in Microsoft Word, but I still have to do it for my job. Professionals have things they don't like. They just have to suck it up and deal.

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby teacupthesauceror » Thu Jun 30, 2011 3:14 pm UTC

gorcee wrote:
Game_boy wrote:
teacupthesauceror wrote:
I'm amazed at the amount of contact you guys have with your supervisors. Maybe it's the stiff upper lips getting in the way, but there seems to be a general agreement that a five-minute meeting a few times a year is more than enough contact for someone not applying for mitigating circumstances. They have research to be getting on with, and friends are generally easier to understand when asked for help, if less equipped with blackboard.


Maybe "supervisor" means a different thing here, because we have 4 hours a week of time with them in groups of 2.

I would have something similar that to be common at US universities since the fees are so high.


Yeah.

Where I went to school, the financial breakdown when including room and board, was that I was paying $50 per hour spent in class. I don't care if the professors have other obligations and don't like to deal with students. Guess what? I don't like having to write mathematical reports in Microsoft Word, but I still have to do it for my job. Professionals have things they don't like. They just have to suck it up and deal.


Ahhhh, that's the Cambridge-style system where you get almost-individual tutoring. Not so in the other universities of the UK, where it's 10-on-1 at best, but that's cause the uni doesn't pay them for that kind of teaching with the £3000 ($4,500) they get per student. And to be honest, independent learning is a skill that needs to be learned.

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Re: What I Wish I Knew at the Beginning of my Math Degree

Postby Game_boy » Sat Jul 16, 2011 2:15 pm UTC

teacupthesauceror wrote:
Ahhhh, that's the Cambridge-style system where you get almost-individual tutoring. Not so in the other universities of the UK, where it's 10-on-1 at best, but that's cause the uni doesn't pay them for that kind of teaching with the £3000 ($4,500) they get per student. And to be honest, independent learning is a skill that needs to be learned.


I don't want to make this thread into the other thread about this, but that should be £9000 or £10,000, because unis say that the new £9000 fees actually represent a decrease per student; I believe the extra government contribution before was £7000/student on top of that £3000.
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