Exploring a Mathematics Career - 1J

[l-1j-cho]

Greetings

I am an ordinary high school student who is enthusiastically interested in pure mathematics (especially the number theory) and philosophy. I am achevieing outstanding (I know this might sound ridiculous to you because I have heard that mathematics in university is quite different and challenging in relation to high school mathematics), 98% in IB HL Mathematics.

However, I have never considered myself as an innate genius. I might acheve decent marks in school materials, but I have never won a major contest. Or very few.

Also, I tend to think that my Asian heritage is the sole reason I am doing a good job in mathematics course. Although most topics I study in school are new to me.

But I try to understand the nature and principles of mathematics, not merely how to 'operate' mechanical calculations.

Could you give me an advice?

Cheers

1J

 

[wisvuze]

Books:
Calculus - Spivak
Principles of Mathematics - Allendoerfer
Mathematics: form and function - Saunders Mac Lane

( and wh y do you think having an asian heritage means anything? :S )

 

[chiro]

Hey l-1j-cho and welcome to the forums.

If you want to understand maths you need to do maths and think about maths.

When you do coursework in maths, if you have an experienced lecturer, they will introduce you to the major ideas that have shaped maths throughout its history often up to the present day.

You'll get exposure to all kinds of math and sooner or later you'll start to see connections between things.

Apart from the books recommended above, I recommend you reading the books that the original author of the theorem, framework, or area of study has written. People that create areas or discover results can often become "philosophers" with regard to their area and often add insight to what they have been doing with their life when they invented or contributed to an area of mathematics.

Also read books by people that apply mathematics, but that are not necessarily mathematicians. I have found that engineers can write better books on some areas of math that are essentially applied than a book by some pure mathematicians. Engineers need to calculate things and apply math so experienced engineers can show a different perspective of some area of math that is simpler and more intuitive than some pure mathematician that churns out proof after proof without really getting to the crux of what it all means.

If you want to do math or a job that makes heavy use of math from first principles (like say an engineer, physicist, scientist etc), then my advice is whenever you are introduced to a subject focus on the concepts that every area is focused on and ask why. Also when you get to new areas try to think "how does this new area build on that old area?" In other words, how does the new area generalize in a more broader way what the old area did.

If you like maths, are curious about maths, and do maths, you may even surprise yourself with how far you get and I think you will do well.

 

[Delong]

Wow I took IB HL mathematics and I never got a 98%. How do you do it?

 

[l-1j-cho]

Books:
Calculus - Spivak
Principles of Mathematics - Allendoerfer
Mathematics: form and function - Saunders Mac Lane

( and wh y do you think having an asian heritage means anything? :S )

thank you for replying me and recommending those books.
the reason I am worried about my race is because, I don't know about other countries but, it has been denounced by the public opinion that the education system is flawed. Teachers (not high school teachers but those who teach in after-school session or tutors) just 'inject
' subjects, without realizing the aesthetic process of mathematics. They just memorize proofs, without understanding it.

Also, I have been frequently told that those asians who dazzled in high school mathematics course struggle quite a lot in the universities, since the nature is quite different

I am not sure if I belong to these cases, but, anyhow

The stories above is based on what I have been told. So don't trust me 100%

 

[l-1j-cho]

Hi chiro and thank you for replying me

First few lines sounds quite abstract to me. I am not sure if I can handle this in the universities.

One thing I worry about my path is that, I am not a dazzling genious such as Leonhard Euler (my favorite). I am living in a small town, so I have not seen a true genious. However, as I move to big cities, I might be disappointed of my incompetence. How should I handle this? Should I be an innate genious?

 

[hadsed]

Should I be an innate genious?

No you don't have to be.