Advice for a high schooler in mathematics


by shezi1995
Tags: maths, olympiad
shezi1995
shezi1995 is offline
#1
Nov19-12, 06:12 AM
P: 8
I am doing A levels and in my first year (equivalent to a junior in american system). I am very passionate about mathematics and physics but I get bored in my a level studies especially maths though I am a topper of my class. I therefore watch online university lectures like those of mit and other open courseware sites to quench my thirst of maths. My plan is to study mathematics at university and then research(I know how different maths is at university) So I want advice on how to study maths keeping in my mind my future goal.
  • What are the high school maths topics that I should master and how do I do that? The normal school books are not interesting and are rather easy.
  • What should I study? I am also participating in my country's national level math olympiad which leads to participation in the IMO. So should I work hard studying olympiad level maths like number theory and geometry? How much will it benefit me in mathematical career?
  • I am finding combinatorics hard. I am more comfortable in algebra and geometry. Is that okay? How do I improve my understanding of combinatorics?
  • I also have a copy of calculus by apostol and I like it a lot as I have some experience in proofs due to the olympiad. I have studied few topics and absolutely loved those. Should I continue to study it? Some people here suggest that it is better to approach calculus after one has mastery of algebra and other topics.
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
espen180
espen180 is offline
#2
Nov19-12, 09:52 AM
P: 836
I would say that coming out of high school you should at least have no problems manipulating algebraic expressions, and should be familiar with trigonometric, exponential and logarithmic functions.

Number theory and geometry will definitely benefit you (especially the latter!) I suggest you learn as much geometry as you can. (Euclid's Elements are freely available online).

Improving your combinatorics would also help, mostly for number theory and abstract algebra. Speaking of which, you can probably pick up a copy of "Visual group theory" immediately and start studying from it to get a head start in abstract algebra.
mathwonk
mathwonk is offline
#3
Nov19-12, 09:57 AM
Sci Advisor
HW Helper
mathwonk's Avatar
P: 9,428
maybe try euclid elements, euler's elements of algebra, and apostol's calculus.

phospho
phospho is offline
#4
Nov19-12, 10:38 AM
P: 251

Advice for a high schooler in mathematics


Quote Quote by shezi1995 View Post
I am doing A levels and in my first year (equivalent to a junior in american system). I am very passionate about mathematics and physics but I get bored in my a level studies especially maths though I am a topper of my class. I therefore watch online university lectures like those of mit and other open courseware sites to quench my thirst of maths. My plan is to study mathematics at university and then research(I know how different maths is at university) So I want advice on how to study maths keeping in my mind my future goal.
  • What are the high school maths topics that I should master and how do I do that? The normal school books are not interesting and are rather easy.
  • What should I study? I am also participating in my country's national level math olympiad which leads to participation in the IMO. So should I work hard studying olympiad level maths like number theory and geometry? How much will it benefit me in mathematical career?
  • I am finding combinatorics hard. I am more comfortable in algebra and geometry. Is that okay? How do I improve my understanding of combinatorics?
  • I also have a copy of calculus by apostol and I like it a lot as I have some experience in proofs due to the olympiad. I have studied few topics and absolutely loved those. Should I continue to study it? Some people here suggest that it is better to approach calculus after one has mastery of algebra and other topics.
If you go through C3 and C4 now, and enter for STEP I this year then you'll be in good stead for at least a cambridge interview. Studying for STEP itself improves your mathematical maturity.
shezi1995
shezi1995 is offline
#5
Nov19-12, 12:13 PM
P: 8
Thank you everyone. I would certainly try Euclid's elements. And perhaps would check out the STEP I questions as well since its also more directly related to A level.
I do have my question regarding the olympiad maths. Should I work hard in that? Will it be of great help?
phospho
phospho is offline
#6
Nov19-12, 02:18 PM
P: 251
Quote Quote by shezi1995 View Post
Thank you everyone. I would certainly try Euclid's elements. And perhaps would check out the STEP I questions as well since its also more directly related to A level.
I do have my question regarding the olympiad maths. Should I work hard in that? Will it be of great help?
I would, but remember that higher UMS during your AS levels is more beneficial than a competition. But definitely compete and see how far you can get.


Register to reply

Related Discussions
Advice for a first year high schooler who wishes to be a theoretical physicist Academic Guidance 4
Awesome! I'm as smart as a high schooler! General Discussion 8
Interview with a High Schooler Academic Guidance 1
Questions about fusion (from a high-schooler)... Nuclear Engineering 31
Little Advice for a High Schooler? Academic Guidance 11