What do YOU think should be in the HSC exams in the next few years? (2 Viewers)

[mnmaa]

Is Peter Brown a Maths lecturer at UNSW?

Apparently so....
http://profiles.unsw.edu.au/maths/pbrown1

 

[Carrotsticks]

put vectors and vector calculus into the 4u course. Maybe even some hard vector proofs to sort the men from the boys

Note sure if Vector calculus is totally a good idea, because knowledge of Partial Derivatives and double/triple integrals is required. May be a bit much for Extension 2.

 

[mnmaa]

I was thinking more along the lines of applied vector calculus, such as that in the VCE specialist course which uses vector calculus to model rectilinear motion, projectile motion etc... good fun

 

[Carrotsticks]

I was thinking more along the lines of applied vector calculus, such as that in the VCE specialist course which uses vector calculus to model rectilinear motion, projectile motion etc... good fun

I'm curious... could you please upload one of the Specialist Maths papers if you have any?

 

[mnmaa]

Sorry I don't know how to upload but here is a link to one of the papers.
http://www.vcaa.vic.edu.au/vcaa/vce...specialist/pastexams/2011/2011specmath2-w.pdf

refer to Q2. section 2. Its pretty easy stuff.

 

[mnmaa]

Sorry I don't know how to upload but here is a link to one of the papers.
http://www.vcaa.vic.edu.au/vcaa/vce...specialist/pastexams/2011/2011specmath2-w.pdf

refer to Q2. section 2. Its pretty easy stuff.

 

[bleakarcher]

i wish they introduced differential equations into the course.

 

[cutemouse]

and double/triple integrals is required.

I loved double/triple integrals. My friends hated them though hahaha

Is Peter Brown a Maths lecturer at UNSW?

Yes. He was involved with the 2003, 2004 and 2005 hsc papers for mathematics. In fact, he wrote Q8b of the 2003 ext 2 paper.

 

[Carrotsticks]

i wish they introduced differential equations into the course.

Differential equations are already in the course =)

However, not so much methods of finding exact solutions using integrating factors etc.

I loved double/triple integrals. My friends hated them though hahaha

Currently studying them and it actually seems okay so far! However, determining the limits over non-rectangular domains can get a bit confusing. Going to try to source information from another textbook to see if it explains it a bit better.

Yes. He was involved with the 2003, 2004 and 2005 hsc papers for mathematics. In fact, he wrote Q8b of the 2003 ext 2 paper.

So he's the culprit for that irrationality of pi proof. Actually, I have seen a very similar proof (if not the same one) elsewhere.

 

[1xcv3we]

Carrotsticks, what text are you using for multi-variable calculus?

 

[Carrotsticks]

Advanced Calculus Demystified and Calculus: Early Transcendentals by Howard Anton

I also watch the MIT online lectures.

 

[nunaneomuyeppeo]

Currently, many exam questions are like this:

a) Consider XXXX

i. Show that XXX 2 marks

ii. Show that XXX 2 marks

iii. Hence deduce that XXX 1 mark

They lead you to the answer. Although I agree that there should be such questions (surely an exam can't consists of ONLY difficult questions), I think there should be a couple of questions like this:

a) Consider YYYYY. Show that YYY. 5 marks

My reason for this is because more often than not, there is more than 1 way of doing a question. Including such questions in the Extension 2 Examination would promote creativity of solutions (perhaps even elegance).

This is just regarding exam format.

Regarding actual topics, it would be nice to have questions on topics that are rarely/never been examined. A well rounded student should be able to apply their knowledge in order to do these questions, regardless of practice or not.

how would you do a marking criteria for that, if there are numerous ways of getting there?

 

[mnmaa]

Hey carrotsticks can you please give me a link to the MIT online lectures

 

[mnmaa]

Are the MIT online lectures useful for university maths?

 

[largarithmic]

So he's the culprit for that irrationality of pi proof. Actually, I have seen a very similar proof (if not the same one) elsewhere.

I don't think its any secret those proofs aren't actually written be the people who write the questions. Instead they just find the proof in academic literature and split it into the parts required for a school question.

And uh isn't vector calculus decently hard? like 2nd year uni

 

[mnmaa]

Applications of vector calculus isnt, refer to previous posts where I gave a link to a VCE specialist paper that had vector calculus questions

 

[cutemouse]

And uh isn't vector calculus decently hard? like 2nd year uni

Stoke's theorem and Gauss' Divergence theorem are interesting.

 

[largarithmic]

Applications of vector calculus isnt, refer to previous posts where I gave a link to a VCE specialist paper that had vector calculus questions

Thats not so much vector calculus as just normal one variable calculus done with mysterious constants attached (the unit vectors). Also at school we did "vecotr calculus" in the sense it appeared in VCE when doing circular motion, as a way to prove the eqns of motion.

 

[kaz1]

ODE's, multi dimensional vectors and matricies and maybe even some PDE's.

Definetly no stats stuff like ANOVA and hypothesis testing, that shit will turn people off maths.

 

[1xcv3we]

Advanced Calculus Demystified and Calculus: Early Transcendentals by Howard Anton

I also watch the MIT online lectures.

I have 9th edition of Howard Anton Calculus and I must say his section on limits is not as good (for single variable as well) but he has some great multi-integrals. James Stewart Calculus 6th or 7th edition cover these sections better (Stewart covers MV epsilon deltas too). I have started to read another text book called Calculus One & Several Variables 10th Edition. The latter has a more comprehensive coverage of epsilon deltas. When I did MV epsilon deltas it really comes largely down to trial and error at times unless there is an obvious solution/contradiction or you work out some insane substitution.

I never really found the MIT lectures useful when I did MVC, they have a very different take on it. I found my course notes and Stewart Calculus sufficient. If you want any more details on the above text books just PM me.