Favourite Mathematical Concept/trick? (1 Viewer)

[study-freak]

I was under the impression that you already did Second Year maths. Unless you are referring to 3rd Year vector calc equivalent?

IMO order of difficulty MATH1903 --> MATH1901 --> MATH1905 --> MATH1004 --> MATH1902, where Linear Algebra was the hardest.

I started on a bit of Vector Calculus, and it seems quite interesting. You're right about it not being much different from MATH1901 and 1902 combined.

Plus, it has double/triple integrals to evaluate surface areas and volumes of non-revolutionary solids.

I think it also has polar and spherical co-ordinates. Not quite sure, I've just been going through my massive blue Calculus: Early Transcendentals textbook (the fat $150 one from the Co-op bookshop).

Nah, I only did MATH2965 and didn't do MATH2961. Maths units are my for-fun type subjects I overload on top of my normal 24cp/sem load anyway. My main interests are stats and med chem.

and MATH1902! I completely forgot about it. It was indeed the hardest 1st year maths course and so the order for me now is MATH1004, MATH1903, MATH1905, MATH1901, MATH1902, it seems.

Yep it has all that, but I've been using Kopystop notes that I borrowed from a friend of mine who already did the course. I've just finished the 1st chapter on functions of several variables in the book, so haven't done double and triple integrals yet. but looking forward to it!

 

[largarithmic]

Are you talking about the one that involves induction or is this a different one? I know the induction method, but if it's another way I haven't seen it.

This method uses the fact that (k+1)C(r) = kCr + (k)C(r-1), just to save confusion in case there was another approach to using induction.

You can do it by just counting it.

So if you think about it, the nPk = n(n-1)(n-2)...(n-k+1) right? Thats pretty easy to justify; n possibilities for the first, n-1 for the second, ... n-k+1 for the kth. So thats nPk. Now the question is, whats the relationship between nPk and nCk?

Now if you have some combination of k elements from the original set of n, how many permutations of it are there? Well there are k! right? So each combination corresponds to exactly k! permutations, while each permutation corresponds to only one combination. It follows from this there are k! as many permutations as combinations, right? Because for each combination, there are exactly k! permutations "corresponding" to it.

So that means that (nCk) times k! = nPk = n(n-1)...(n-k+1) = n!/(n-k)!. Then divide both sides by k! to obtain nCk = n!/(n-k)!k!.

Also dunno if anyone this applies to will see this by tomorrow, but USYD enrolment day is tomorrow and me and a few other friends I know are using TSP to overload and take 2nd/3rd year maths units - definitely 2962 (real/complex analysis) and probably 2961 (vector calc), but what others are really worthwhile? I was looking at 2967 (discrete maths/graph theory) but Ive actually done quite a lot of that before... sorta keen to try random stuff, some friends also recommended 3961 and 3962 (metric spaces, rings/fields/galoistheory) but would they be too hard

 

[study-freak]

Also dunno if anyone this applies to will see this by tomorrow, but USYD enrolment day is tomorrow and me and a few other friends I know are using TSP to overload and take 2nd/3rd year maths units - definitely 2962 (real/complex analysis) and probably 2961 (vector calc), but what others are really worthwhile? I was looking at 2967 (discrete maths/graph theory) but Ive actually done quite a lot of that before... sorta keen to try random stuff, some friends also recommended 3961 and 3962 (metric spaces, rings/fields/galoistheory) but would they be too hard

Idk anything about 3rd year maths, but hmm MATH2961 without having done 1901? Wouldn't it be a little hard?
but 2962 should definitely be doable and interesting.

Some people I know also took logic and foundations (3rd yr unit) in their first year.

 

[Carrotsticks]

Also dunno if anyone this applies to will see this by tomorrow, but USYD enrolment day is tomorrow and me and a few other friends I know are using TSP to overload and take 2nd/3rd year maths units - definitely 2962 (real/complex analysis) and probably 2961 (vector calc), but what others are really worthwhile? I was looking at 2967 (discrete maths/graph theory) but Ive actually done quite a lot of that before... sorta keen to try random stuff, some friends also recommended 3961 and 3962 (metric spaces, rings/fields/galoistheory) but would they be too hard

I did not know you could do that, otherwise I most surely would have!

I was stuck in Semester 1 doing only 2 subjects because I didn't know you could take Maths subjects from other years. Likewise for Semester 2, but for 3 subjects.

Perhaps you can also try MATH2963, Mathematical Computing and Non-Linear Systems?

 

[Carrotsticks]

Idk anything about 3rd year maths, but hmm MATH2961 without having done 1901? Wouldn't it be a little hard?
but 2962 should definitely be doable and interesting.

Some people I know also took logic and foundations (3rd yr unit) in their first year.

I was thinking that too.

Vector Calculus with no Linear Algebra or Differential Calculus.

However, the Diff Calc in Sem 1 was quite simple. Very few formulas (compared to 1905 lol), and most things were relatively intuitive. All you really need (so far by reading the textbook) are directional derivatives etc and gradients along surface planes.

Linear Algebra... you would need knowledge of determinants, eigenvalues/vectors etc but that can be quickly learnt from a textbook within the span of a week or two of study (assuming no prior knowledge of matrices etc).

 

[largarithmic]

Idk anything about 3rd year maths, but hmm MATH2961 without having done 1901? Wouldn't it be a little hard?
but 2962 should definitely be doable and interesting.

Some people I know also took logic and foundations (3rd yr unit) in their first year.

I was told that 2961 isnt that bad if you teach yourself some of the 1901 stuff before the start of the course, which Id plan to do anyway so I can get away with skipping some of the lectures

And some close friends of mine who did logic and foundations say it became really boring after a while - the first half of the course was pretty interesting and good (a lot of stuff along the lines of what I posted earlier with countability etc) but then it becomes really tedious. But iunno never done it of course.

I did not know you could do that, otherwise I most surely would have!

I was stuck in Semester 1 doing only 2 subjects because I didn't know you could take Maths subjects from other years. Likewise for Semester 2, but for 3 subjects.

Perhaps you can also try MATH2963, Mathematical Computing and Non-Linear Systems?

Im pretty sure you can do it if you go talk to the right people - the SSP and TSP coordinators told me I could do stuff like that, as long as I told them about it beforehand. A few of my friends in USYD maths are doing that right now.

Not sure how interesting mathematical computing would be (Ive done quite a bit of it before, would rather do random stuff Ive never tried before) - and Im also doing INFO1903. Dunno what the crossover would be though, probably not thaat much...

 

[Carrotsticks]

Im pretty sure you can do it if you go talk to the right people - the SSP and TSP coordinators told me I could do stuff like that, as long as I told them about it beforehand. A few of my friends in USYD maths are doing that right now.

Not sure how interesting mathematical computing would be (Ive done quite a bit of it before, would rather do random stuff Ive never tried before) - and Im also doing INFO1903. Dunno what the crossover would be though, probably not thaat much...

I'm doing MATH2963, but I'm more interested in the Non-Linear systems, versus the Mathematical computing itself.

Too late for me to try to accelerate =(

Oh and one of my subjects for 2nd Year is Fundamentals of Physics. I chose that to replace Discrete + Graph Theory, because I never really enjoyed Discrete Maths.

 

[seanieg89]

You can do it by just counting it.

So if you think about it, the nPk = n(n-1)(n-2)...(n-k+1) right? Thats pretty easy to justify; n possibilities for the first, n-1 for the second, ... n-k+1 for the kth. So thats nPk. Now the question is, whats the relationship between nPk and nCk?

Now if you have some combination of k elements from the original set of n, how many permutations of it are there? Well there are k! right? So each combination corresponds to exactly k! permutations, while each permutation corresponds to only one combination. It follows from this there are k! as many permutations as combinations, right? Because for each combination, there are exactly k! permutations "corresponding" to it.

So that means that (nCk) times k! = nPk = n(n-1)...(n-k+1) = n!/(n-k)!. Then divide both sides by k! to obtain nCk = n!/(n-k)!k!.

Also dunno if anyone this applies to will see this by tomorrow, but USYD enrolment day is tomorrow and me and a few other friends I know are using TSP to overload and take 2nd/3rd year maths units - definitely 2962 (real/complex analysis) and probably 2961 (vector calc), but what others are really worthwhile? I was looking at 2967 (discrete maths/graph theory) but Ive actually done quite a lot of that before... sorta keen to try random stuff, some friends also recommended 3961 and 3962 (metric spaces, rings/fields/galoistheory) but would they be too hard

For Galois theory it is probably best to first take the 2nd year algebra course, but Metric Spaces is quite manageable without prereqs I think...

 

[largarithmic]

I'm doing MATH2963, but I'm more interested in the Non-Linear systems, versus the Mathematical computing itself.

Too late for me to try to accelerate =(

Oh and one of my subjects for 2nd Year is Fundamentals of Physics. I chose that to replace Discrete + Graph Theory, because I never really enjoyed Discrete Maths.

Oh I really like discrete maths, but thats sorta why Im not going to take it straight away And Im doing physics anyway as one of the compulsory non-maths science subjects.

For Galois theory it is probably best to first take the 2nd year algebra course, but Metric Spaces is quite manageable without prereqs I think...

Yeah looking at my level of overload doing both is probably too much... so Ill probably do metric spaces and not galois theory.

 

[Trebla]

Not sure how interesting mathematical computing would be (Ive done quite a bit of it before, would rather do random stuff Ive never tried before) - and Im also doing INFO1903. Dunno what the crossover would be though, probably not thaat much...

Seeing how you're such a pure maths person, I think mathematical computing (which is from the applied side) would be extremely tedious for you.

 

[cutemouse]

Complex analysis and vector calculus (several variables calculus) is pretty good I think. Although, most of my friends absolutely hated it for some reason (probably because there is no "formula" for each question and you need quite a bit before proceeding)...

I think I liked complex analysis because the end part of it (residues) heavily involves first year Taylor series and the alike, and I quite liked that stuff in first year...

I guess then I'm more of a pure person than applied...

 

[Carrotsticks]

I guess then I'm more of a pure person than applied...

Sounds like a Pure vs Applied thread is needed.

 

[math man]

IMO order of difficulty MATH1903 --> MATH1901 --> MATH1905 --> MATH1004 --> MATH1902, where Linear Algebra was the hardest.

I thought linear algebra adv 1902 was fairly easy last yr cause dave was such a good lecturer compared to santa in 1901...the only reason 1902 was hard was cause of the sem test...that was fairly hard...IMO order from easy to hard is :

Math1905>Math 1903>Math1902>Math1901

but they were all still easy and hard isnt a word i should use, merely not as easy is better...but i cant wait for this yr..this should be more challenging

 

[math man]

Sounds like a Pure vs Applied thread is needed.

vs Stats?? dont leave poor stats by itself

 

[Carrotsticks]

vs Stats?? dont leave poor stats by itself

Math Man! You disappeared for a good week or two.

Poor statistics! But I would have thought it would sort of be under Applied.

 

[largarithmic]

Anyway so results of enrolment day: MATH1901, MATH1902, MATH2961, MATH2962.

And wrarrr Im going to through my hands into the pure camp. But as much as I understand it, some aspects of cosmology/theoretical physics are actually much closer to pure maths (topology etc) than they are to anything typically considered "applied".

 

[Trebla]

For me, the first year units from easiest to hardest:
MATH1903
MATH1901
MATH1905
MATH1902
Linear algebra was a huge shock to the system in first year because it was mostly stuff I had never seen before in high school, but yeh now I'm more comfortable with it now. Integral calculus was by far the easiest especially for people who enjoyed integration and volumes in Maths Extension 2.

Oh and for the record, I'm an applied/stats person...

 

[cutemouse]

I'm an applied/stats person...

You must be a very boring person then... (joke) ... You honestly found stuff like the hypothesis test, anova and regression analysis interesting? I didn't. I could do it, but I found it hell boring. The stats department was too lazy to change the exams from last semester too. Of course they didn't give them out, but I knew someone who did the course in the previous semester and so yeah...

 

[study-freak]

You must be a very boring person then... (joke) ... You honestly found stuff like the hypothesis test, anova and regression analysis interesting? I didn't. I could do it, but I found it hell boring. The stats department was too lazy to change the exams from last semester too. Of course they didn't give them out, but I knew someone who did the course in the previous semester and so yeah...

Stats is awesome! Testing procedures are often tedious, but the theories behind them are interesting.

 

[math man]

Math Man! You disappeared for a good week or two.

Poor statistics! But I would have thought it would sort of be under Applied.

nah stats is the third maths field which i will be majoring in with financial maths...and yeh i was gone for like a week or so but i was checking the forums from every so often, however nothing really exciting to do till this thread.