Maths is a wonderful thing (2 Viewers)

[Obvious]

Over the past few weeks I've been contemplating taking some more math (Real/Complex analysis + Linear Algebra & VC) next year. However, seeing as I've only done the normal units/MX1 I have some doubts about my ability to cope with the harder material whilst studying for several other demanding subjects.

In anticipation of this, I'm planning on doing some serious preparation over the summer break, hopefully making up for time lost by not applying myself more over the previous years. Firstly, are there any areas exclusive to MX2/MATH19** that will be assumed knowledge? Does the difficulty of the content increase noticeably past first year?

I'm stuck trying to think of some more direct questions, but I'd truly appreciate any guidance on how I should approach this.

 

[Carrotsticks]

Real and Complex Analysis might be difficult if your prior knowledge is mostly MX1 and Normal units.

It is a very big jump from 1st to 2nd year, especially with Analysis where rigour is introduced.

The jump is bigger and bigger each year.

 

[Obvious]

Real and Complex Analysis might be difficult if your prior knowledge is mostly MX1 and Normal units.

It is a very big jump from 1st to 2nd year, especially with Analysis where rigour is introduced.

The jump is bigger and bigger each year.

I didn't pick up MX2 for the same reason, and it's something that I regret immensely. I plan on studying over the entire summer, which I hope will give me sufficient background to tackle the harder material while still keeping me in the rhythm of uni work.

Would you consider this achievable? I'd appreciate your honesty, but in the end I think I'm going to go through with it.

 

[seanieg89]

If you truly find it interesting than you will find it much MUCH easier than most to make progress. Getting to the level of being able to take second year courses is certainly doable if you as driven as you sound.

 

[Carrotsticks]

Actually, a month of solid work would suffice for it IMO. Your dedication is respectable. Not much assumed knowledge per se from the advanced units. Just the level of understanding.

It's not so much the actual content, but the amount of detail that it goes into, and moreso the fact that rote learning is much more difficult than for normal units.

I would suggest heavily revising:

1. Ratio Test, Comparison Test etc etc and all of those 'Series/convergence-type' things from 1003.

2. Definitely get your LA up to scratch. 2nd Year LA is a lot more intensive than 1st year.

3. Get your partial derivatives and tangent planes etc etc stuff up to scratch.

In terms of learning the actual content ahead of time, buy one of those big FAT calculus textbooks from coop. The James Stewart ones.

It will cover 100% of the Vector Calculus content (and more!), 40% of your Real Analysis content and maybe 5% of your linear algebra content.

However, there is a very nice LA textbook, written by Howard Anton, in the coop bookshop that covers 100% of your LA course with MUCH detail. It also has plenty of exercises to work on.

 

[Trebla]

Are you going to be taking MATH2061 or MATH2961?

 

[Obvious]

If you truly find it interesting than you will find it much MUCH easier than most to make progress. Getting to the level of being able to take second year courses is certainly doable if you as driven as you sound.

Excellent, your assurance is appreciated.

This is the last time I'll have an opportunity to catch up without putting the rest of my education on hold. It's a scary thought, and (more so for several other reasons) I'm convinced that the results will be worth every effort.

Actually, a month of solid work would suffice for it IMO. Your dedication is respectable. Not much assumed knowledge per se from the advanced units. Just the level of understanding.

It's not so much the actual content, but the amount of detail that it goes into, and moreso the fact that rote learning is much more difficult than for normal units.

I would suggest heavily revising:

1. Ratio Test, Comparison Test etc etc and all of those 'Series/convergence-type' things from 1003.

2. Definitely get your LA up to scratch. 2nd Year LA is a lot more intensive than 1st year.

3. Get your partial derivatives and tangent planes etc etc stuff up to scratch.

In terms of learning the actual content ahead of time, buy one of those big FAT calculus textbooks from coop. The James Stewart ones.

It will cover 100% of the Vector Calculus content (and more!), 40% of your Real Analysis content and maybe 5% of your linear algebra content.

However, there is a very nice LA textbook, written by Howard Anton, in the coop bookshop that covers 100% of your LA course with MUCH detail. It also has plenty of exercises to work on.

Thank you! This is exactly what I was looking for. I downloaded all the relevant information from both of the unit websites last semester, and I'll also be borrowing the course notes from a friend.

Do you have any recommendations/comments for MATH2965/2968/2969/2988? From what I've heard the second can be particularly challenging.

Are you going to be taking MATH2061 or MATH2961?

MATH2961

 

[Carrotsticks]

2965 (PDE's): Fairly straightforward. Quite rote-learnish though and a bit bland. Dem transforms.

2968 (Algebra): Very challenging. The hardest subject I have taken so far IMO. Heavy on the Pure side of Mathematics and I wouldn't suggest doing it if you're more of a 'I need to see it to get it' kind of person.

2969 (Graph Theory): Wouldn't know, never did it, but looks cool.

2988 (Number Theory): Not very difficult, but the coding gets quite tedious sometimes.

Before I make any recommendations, perhaps you could tell me which units from 1st year you enjoyed? What part of Maths you like?

 

[Obvious]

2965 (PDE's): Fairly straightforward. Quite rote-learnish though and a bit bland. Dem transforms.

2968 (Algebra): Very challenging. The hardest subject I have taken so far IMO. Heavy on the Pure side of Mathematics and I wouldn't suggest doing it if you're more of a 'I need to see it to get it' kind of person.

2969 (Graph Theory): Wouldn't know, never did it, but looks cool.

2988 (Number Theory): Not very difficult, but the coding gets quite tedious sometimes.

Before I make any recommendations, perhaps you could tell me which units from 1st year you enjoyed? What part of Maths you like?

MATH1001/1003 - These weren't that exciting. We didn't quite move into any of the theory/proofs, and the work was almost entirely mechanical integration/differentiation with few variations from MX1. Pretty bland. The latter parts of both were slightly more interesting (Taylor series, some vector stuff, and groups of differential equations) but this was probably because the work was a bit more involved.

MATH1002 - I liked it, it was refreshing to do something completely new. Vectors are great. Andrew Crisp was great.

MATH1004 - The best. The material related to counting/combinatorics was my favorite. The greater reliance on logic for breaking down and solving these problems was a highlight.

 

[Carrotsticks]

MATH1001/1003 - These weren't that exciting. We didn't quite move into any of the theory/proofs, and the work was almost entirely mechanical integration/differentiation with few variations from MX1. Pretty bland. The latter parts of both were slightly more interesting (Taylor series, some vector stuff, and groups of differential equations) but this was probably because the work was a bit more involved.

MATH1002 - I liked it, it was refreshing to do something completely new. Vectors are great. Andrew Crisp was great.

MATH1004 - The best. The material related to counting/combinatorics was my favorite. The greater reliance on logic for breaking down and solving these problems was a highlight.

Real pity that 1003 wasn't exciting. MATH1001 I can understand but 1003 (1903 in my case) was so good. Take a look at this, for example:







Do you look at these and think 'ermagerd cool'? If you do, then I suggest taking MATH2962.

You said you didn't like 1001 that much, so you most likely won't like 2961 that much. However, the second component LA is REALLY pretty. Personally, I didn't like Vector Calculus that much, but that's just me.

You enjoyed Discrete, so I strongly suggest taking 2969.

So overall, my suggestions are:

1st Semester: MATH2961, MATH2962, MATH2969. If you can only pick two, then ditch 2962.

2nd Semester: MATH2965, MATH3061 (Geometry and Toplogy was heaps cool and I think you'll like it. However may be difficult without 2962 and 2968).

 

[Obvious]

Real pity that 1003 wasn't exciting. MATH1001 I can understand but 1003 (1903 in my case) was so good. Take a look at this, for example:

Do you look at these and think 'ermagerd cool'? If you do, then I suggest taking MATH2962.

Yes, even though I'm sure I'm not fully appreciating their significance, they do look fascinating.

You said you didn't like 1001 that much, so you most likely won't like 2961 that much. However, the second component LA is REALLY pretty. Personally, I didn't like Vector Calculus that much, but that's just me.

You enjoyed Discrete, so I strongly suggest taking 2969.

Don't get me wrong, it wasn't that bad. More so the level at which the content was taught didn't inspire a lot of interest. From what I can tell, the streams themselves are more oriented towards engineers and applied disciplines, and as a result a lot of the intricacy of the deeper theory is omitted.

In the end, all we did was just routine max/min, tangent-planes and directional vectors. Bleh. I'm guessing this probably isn't going to be a good representation of what I'll encounter in second year.

So overall, my suggestions are:

1st Semester: MATH2961, MATH2962, MATH2969. If you can only pick two, then ditch 2962.

2nd Semester: MATH2965, MATH3061 (Geometry and Toplogy was heaps cool and I think you'll like it. However may be difficult without 2962 and 2968).

Well, I am now officially enrolled in all three first semester units! I only need twelve credit points of chemistry to continue through third year, so everything else is being taken purely out of interest.

Leading on from that, MATH2965 and 2968 would be the logical choices and they're there too. Third year math seems a bit hard core for now, lol.

Lastly, would you recommend any textbooks for ^?

 

[Carrotsticks]

Then it it settled =)

As for textbooks...

James Stewart Calculus (Coop): MATH2961

Howard Anton Linear Algebra (Coop): MATH2961

Discrete: Not sure of any good ones.

Analysis: I know a couple good complex analysis ones, but none specifically for real analysis (the 2962 course is 90% real analysis).

These will help for Vector Calculus + Real Analysis

View attachment Analysis.pdf

View attachment Vector.pdf

I would have recommended 2988 Number Theory over 2968 Algebra because you will most likely find it to be a LOT more interesting. Some of the stuff there is really cool. An excellent book for it is Intro to Number Theory by Hardy.

And for 2965... I don't know of any specifically good books because so much of it is just formula-based and just calculations etc.

 

[seanieg89]

Then it it settled =)

As for textbooks...

James Stewart Calculus (Coop): MATH2961

Howard Anton Linear Algebra (Coop): MATH2961

Discrete: Not sure of any good ones.

Analysis: I know a couple good complex analysis ones, but none specifically for real analysis (the 2962 course is 90% real analysis).

These will help for Vector Calculus + Real Analysis

View attachment 26863

View attachment 26864

I would have recommended 2988 Number Theory over 2968 Algebra because you will most likely find it to be a LOT more interesting. Some of the stuff there is really cool. An excellent book for it is Intro to Number Theory by Hardy.

And for 2965... I don't know of any specifically good books because so much of it is just formula-based and just calculations etc.

Rudin- Principles of mathematical analysis is an amazing book to accompany R&C analysis.

 

[iSplicer]

Hey Carrot, does MATH29XX scale as insanely well as first year advanced did? I remember I absolutely loved the math but didn't have much time to study it - barely attempted half the MATH1902 paper and still got a near HD haha. I imagine you got mid-high 90s for both?

 

[Obvious]

Rudin- Principles of mathematical analysis is an amazing book to accompany R&C analysis.

Downloaded. I'm a bit apprehensive of these 4 x 8 AM R&C lectures...

 

[jet]

MATH2961 was at 8 am when I took it. MATH2962 was at 9 am.

 

[Obvious]

MATH2961 was at 8 am when I took it. MATH2962 was at 9 am.

Oh yeah, you're right. I put the lectures down in the wrong row on my spreadsheet.

 

[CookBookStew]

It does but it is also much more difficult. The jump between first and second year math courses is quite large. I would say it scales less because less "not advanced" students take the second year advanced units. The jump from second to third year is less though.

 

[600monkeys]

I did some second year math this year. Unfortunately I had a pretty terrible year for personal reasons and registered a couple of fails, largely because other things that were going on caused me to miss a lot of class time. I will be redoing MATH2069 in 2013 for this reason, so you might see me there. Other second year subs I did were 2061,2065 and 2068. Looking forward to 3rd year math in '13!

But to the OP, if you find math interesting, you'll enjoy second and (I presume) 3rd year. Math is awesome, and some of the instructors (Alex Molev for example) are just great.

 

[Obvious]

I did some second year math this year. Unfortunately I had a pretty terrible year for personal reasons and registered a couple of fails, largely because other things that were going on caused me to miss a lot of class time. I will be redoing MATH2069 in 2013 for this reason, so you might see me there. Other second year subs I did were 2061,2065 and 2068. Looking forward to 3rd year math in '13!

But to the OP, if you find math interesting, you'll enjoy second and (I presume) 3rd year. Math is awesome, and some of the instructors (Alex Molev for example) are just great.

Haha, maybe. Discrete math was one of my favorite subjects last semester, although I didn't attend most of the lectures/tutorials (bad timetable, would have had several 2-3 hour breaks).

The class was pretty good when I was there, and Molev was definitely more engaging than most of the lecturers I've had.