Should I study stuff outside of syllabus for Mathematics Extension 2? (1 Viewer)

[ilovemangos]

I'm currently at Dr Du for mathematics and they love teaching us stuff that is clearly not in the syllabus. They claim that it will help me with the harder questions. Is this true? Thanks!

For example, in Dr Du 3 unit we're learning differential equations and for some reason we're learning bernoulli equations and solving second order differential equations, which are not in the syllabus.

 

[tywebb]

That sounds great. You should cover the syllabus, but there is nothing stopping you from going further. There have often been many questions in Extension 2 HSC papers as well as in some harder trial exams which go beyond the syllabus.

Wider reading on the history of maths and also current research would be good too.

 

[ilovemangos]

Oh I thought HSC couldn't ask questions outside of the syllabus. I suppose then its a good thing to do wider reading. I might start looking at some university textbooks I guess.

 

[tywebb]

Schaum's Outlines are great for undergrad uni.

For history of maths, David E. Smiths's History of Mathematics Vol. I and II are good start.

Most of these are available as ebooks.

For current research the American Mathematical Society's website ams.org is good, particualrly the Notices of the American Mathematical Society at https://www.ams.org/notices/ as well as The American Mathematical Monthly from the Mathematical Association of America.

The AMS Notices are free downloads, and access to the MAA American Mathematical Monthly is also free provided your education institution has access to JSTOR. Not all schools have this access but many do. Talk to your librarian about this if you are interested. Just be aware the the AMM has a 3 year moving wall on JSTOR, meaning if you have access to JSTOR, you can only access it up to 3 years ago. More current ones can be accessed by subscription or inter-library loan.

For more hard-core research you can use Mathematical Reviews but that's like throwing you in the deep end so I wouldn't start with this. Nevertheless you can come back to that later if you are so inclined: http://www.ams.org/publications/math-reviews/math-reviews

Another resource for NSW secondary students since 1964 is Parabola Magazine which now has a website https://www.parabola.unsw.edu.au

 

[yanujw]

Contrary to the opinion above, I think this is a very poor idea. The teachers should focus on covering the syllabus in greater depth rather than trying to force wider learning on students. Imagine if an english tutor made their students learn and examine books not within the prescribed texts list in order to force them to have a better attitude towards the subject, when in fact the opposite would happen.

Just to be clear, it is VERY helpful when students are curious and do further learning on their subjects. However, I would not recommend reading uni math textbooks unless you have the time, are very curious, or are planning to study math in the future.

 

[tywebb]

I don't think it is about forcing. More about thinking a bit differently about mathematics.

Another resource are the mathematics competitions like IMO and Australian Mathematics Competitions as well as the Art of Problem Solving website https://artofproblemsolving.com/community

 

[ilovemangos]

Schaum's Outlines are great for undergrad uni.

For history of maths, David E. Smiths's History of Mathematics Vol. I and II are good start.

Most of these are available as ebooks.

For current research the American Mathematical Society's website ams.org is good, particualrly the Notices of the American Mathematical Society aas well as The American Mathematical Monthly from the Mathematical Association of America.

The AMS Notices are free downloads, and access to the MAA American Mathematical Monthly is also free provided your education institution has access to JSTOR. Not all schools have this access but many do. Talk to your librarian about this if you are interested. Just be aware the the AMM has a 3 year moving wall on JSTOR, meaning if you have access to JSTOR, you can only access it up to 3 years ago. More current ones can be accessed by subscription or inter-library loan.

For more hard-core research you can use Mathematical Reviews but that's like throwing you in the deep end so I wouldn't start with this. Nevertheless you can come back to that later if you are so inclined:

Another resource for NSW secondary students since 1964 is Parabola Magazine which now has a website

thank you for those, I have access to JSTOR so I'll try and read it in my spare time.

Contrary to the opinion above, I think this is a very poor idea. The teachers should focus on covering the syllabus in greater depth rather than trying to force wider learning on students. Imagine if an english tutor made their students learn and examine books not within the prescribed texts list in order to force them to have a better attitude towards the subject, when in fact the opposite would happen.

Just to be clear, it is VERY helpful when students are curious and do further learning on their subjects. However, I would not recommend reading uni math textbooks unless you have the time, are very curious, or are planning to study math in the future.

Yeah this is what I've heard as well. I'll just try to do it when I have time

 

[Trebla]

Nice to have with luxury of time, but this should never be at the expense of learning the actual syllabus content. Anyway, all HSC questions should be doable using syllabus content only (what makes them hard is knowing how to apply syllabus content in unfamiliar contexts), and anything beyond is just for wider exposure (kinda like how wider reading could be beneficial for English in general).

Keep in mind that the value-add of doing this is really marginal compared to say actually focusing on your weaker topics or weaker subjects - definitely do not recommend unless you are topping your grade already and want to state rank. You only have a finite amount of time, use it wisely.