Level-2 maths subjects

[Pappa-Bohr]

hi guys my name is Justin, I dont make many posts on this website but i read it every now and then..
so I have to pick my UoM subjects for next semester (Im doing new gen Bachelor of Science) and I was wondering if anyone has done 'Vector Calculus' or 'Real analysis with applications'
1. how hard are they compared to first year subjects (calc/lin alg)
2. Does it help to take them together (i.e do they compliment each other)

also if you've done any other upper level maths courses could you tell me a bit about them
thanks!

[Neobeo]

Hey there. I'm a second year student at UoM majoring in pure maths.

"Vector Calculus" ought to be pretty straightforward if you found Calculus 2 straightforward (or at least understand the concepts properly). You can think of it as just an extended version of calculus.

I didn't specifically do the subject "Real analysis with applications" but I've been told it can require a bit more imagination. It's not a "difficult" subject, but probably a bit more abstract than linear algebra or calculus.

What are you majoring in? If you're majoring in any maths or physics then you'd probably need to do both subjects anyway.

[midas_touch]

I'm currently on the verge of completing an applied maths major, however im a pre melbourne model student so a number of the subjects ive done have been, or will be replaced by different ones. However in saying that I've done Vector Calculus along with a number of people on these forums. It basically looks into the calculus of functions with two or more variables, which you would have been exposed to briefly in Calculus 2. Its quite an interesting subject which isnt too overly difficult. Now in later years, maths subjects are quite distinct from each other and can be put into one of a number of categories (with some overlap):

- Pure maths
- Applied maths
- Discrete maths
- Statistics/ Probability
- Operations Research

I suggest consulting http://www.undergraduates.ms.unimelb.edu.au/ and the subject handbook to get more information

[mark_alec]

I did vector calculus and found it rather non-challenging. If you are comfortable with multivariable calculus, then there isn't much that should be confusing. The exams have also been the same format for yonks, so studying for them is straightforward.

[Pappa-Bohr]

thanks for that.
so has anyone else done the real analysis subject (and give me an idea of it's rigor)?

Also by the way what is discrete maths/operations research? (and is it easy/hard?)

note: my major is probably physics or something but I havent decided

[Ahmad]

If you haven't already you can get an idea of what the subject offers here: https://app.portal.unimelb.edu.au/CSCApplication/view/2010/620-295

It's an analysis subject (not calculus) so you'd expect it to be rather rigorous, i.e. you'll be expected to become friends with the epsilon-delta brothers and even (god forbid!) perform simple proofs

[darlok]

Hey, I'm currently doing both vector calculus and real analysis. I decided to do them both in my first year and I found real analysis much harder than vector calculus. Vector calculus is pretty much dealing with integrals in ~15 different ways. You really won't learn anything new, just new ways to apply what you already know. Real analysis is pretty much learning maths from scratch, properly. You will learn the definitions of things you never thought even needed to be defined, you will learn to do proofs for major concepts that in the past you have just took the lecturers word for being correct. It's not an insanely difficult subject, but I did fairly well in calcII and linear (93,82) and managed to fail an assignment(luckily only worth 3%). And I have also acknowledged that I will not be shooting for a H1 in this subject. I don't think that doing one before the other is really better, maybe doing one per semester would be a good idea though as they don't compliment each other and take quite a bit of study.

[QuantumJG]

hi guys my name is Justin, I dont make many posts on this website but i read it every now and then..
so I have to pick my UoM subjects for next semester (Im doing new gen Bachelor of Science) and I was wondering if anyone has done 'Vector Calculus' or 'Real analysis with applications'
1. how hard are they compared to first year subjects (calc/lin alg)
2. Does it help to take them together (i.e do they compliment each other)

also if you've done any other upper level maths courses could you tell me a bit about them
thanks!

I'm doing a mathematical physics major so I am going to be doing both real analysis and vector calculus next year. These are required for the major. My biggest decision was
picking either dynamic systems and chaos or group theory and linear algebra. Both are very useful to the major and group theory and linear algebra opens the doors to more third year subjects.

If you are wanting to do any form of maths or physics as your major you will need to do those two subjects.

The reason why I picked mathematical physics is I enjoy my physics and maths. At uni the difficulty of physics has jumped right up, whilst maths has been easy. But for me studying maths has NEVER been a chore though, so for me the more maths the better. Physics has conceptually really tested me, whilst maths hasn't reached that yet.

[Pappa-Bohr]

thanks for the info guys.
what about Probability, and like 'Statistics' subjects? what are they like? easy/hard?
and btw if you major in mathematics, how many level 3 subjects do you need? do you have to follow the plan on the MS website or can you do like some statistics and some pure maths at level 3?

cheer, Justin.

[QuantumJG]

thanks for the info guys.
what about Probability, and like 'Statistics' subjects? what are they like? easy/hard?
and btw if you major in mathematics, how many level 3 subjects do you need? do you have to follow the plan on the MS website or can you do like some statistics and some pure maths at level 3?

cheer, Justin.

You need to do the 4 that are allocated with majoring in that area.

e.g. Pure maths:

You need Complex Analysis, Algebra, Metric and Hilbert Spaces plus one of Graph Theory, Geometry or Discrete Maths.

One question to people are further down the track with maths than me, should I try and include a probability subject or is that only required for people wanting to do Discrete Maths and Operations Research or Statistics and Stochastic Processes? I definately don't want to do either of these!

[humph]

I haven't done any probability since yr11

[Ahmad]

what about Probability, and like 'Statistics' subjects? what are they like? easy/hard?
and btw if you major in mathematics, how many level 3 subjects do you need? do you have to follow the plan on the MS website or can you do like some statistics and some pure maths at level 3?

You need 4 level 3 subjects for a major. You're allowed to mix maths subjects, so long as by the end of the year you've done 4 subjects from at least one area required for a specialisation e.g. pure maths. For example I plan to do probability and PDEs in third year, both of which aren't part of the pure maths specialisation.

QuantumJG, probability is recommended for both applied maths and pure maths majors, regardless of whether you wish to do subjects which require it in the future. I'm a pure maths major and did probability, statistics and plan to do a rigorous probability subject in 3rd year (link in previous paragraph).

[Gloamglozer]

Ahmad, is the probability you do at uni a lot different from the probability you do in Methods?  Or is is just an extension?

[Ahmad]

For one thing it's more rigorous and is developed from the probability axioms, which I felt made things a lot clearer (although it could be more rigorous still, which would be my preference). I thought that that made the subject "feel" different to how I remembered it in methods, in a positive way. That said it does cover everything you learn in methods, but it also covers a lot lot more. If you want I can email you the lecture notes.

[Gloamglozer]

For one thing it's more rigorous and is developed from the probability axioms, which I felt made things a lot clearer (although it could be more rigorous still, which would be my preference). I thought that that made the subject "feel" different to how I remembered it in methods, in a positive way. That said it does cover everything you learn in methods, but it also covers a lot lot more. If you want I can email you the lecture notes.

Thank you for the explanation.  I've always wondered but didn't know who to ask.

Also, can you please upload the lecture notes into your next post so other people can have a look at it as well?

To do this, click "Additional Options" when you are writing your post.