Advice for a high schooler in mathematics

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In summary, it is okay to be more comfortable in algebra and geometry, but you should study number theory and geometry as well. It is also beneficial to compete during your AS levels.
  • #1
shezi1995
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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.
 
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  • #2
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.
 
  • #3
maybe try euclid elements, euler's elements of algebra, and apostol's calculus.
 
  • #4
shezi1995 said:
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.
 
  • #5
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?
 
  • #6
shezi1995 said:
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.
 

What are the benefits of studying mathematics in high school?

Studying mathematics in high school can provide a strong foundation for future academic and career pursuits. It can help develop critical thinking and problem-solving skills, improve analytical abilities, and open up opportunities for higher education in fields such as engineering, finance, and computer science.

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To improve your math skills in high school, it is important to attend classes regularly, actively participate and ask questions, and practice regularly. You can also seek help from your teachers, peers, or online resources. Additionally, setting realistic goals and having a positive attitude towards math can also be beneficial.

What are some common challenges faced by high school students in mathematics?

Some common challenges faced by high school students in mathematics include difficulty in understanding concepts, lack of motivation or interest, and test anxiety. Time management and balancing multiple subjects can also be a challenge.

How can I prepare for standardized tests like SAT or ACT in mathematics?

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What are some resources that can help me with my math studies in high school?

There are many resources available to help with math studies in high school, such as textbooks, online videos and tutorials, study groups, and tutoring services. Your school may also have a math lab or offer after-school help. It is important to find a resource that suits your learning style and needs.

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