MAST10009: Accelerated Mathematics 2

2x Written Assignments (5% each), Mid-Semester Test (10%), Final Exam (80%)

This subject is part of the accelerated stream and covers the rest of Real Analysis and Calculus 2 (roughly 90% and 70%, respectively) that aren’t covered in its sem 1 counterpart, Accelerated Mathematics 1. Despite being a first-year subject, this subject puts a lot more emphasis on RA than Calc 2 so expect the difficulty to be of at least a second-year subject. Moreover, this subject covers the content of pretty much two subjects (although there are some overlaps) in the span of one semester so the pace will be very fast, in fact much faster than AM1.

If I were to describe this subject with one word, it would be rigour. Many computations we used to do straight away are not allowed in this subject. Nearly every step requires proper justification and any assumptions made must be stated clearly (even when doing a simple integration by substitution). Visual proofs are also pretty much worthless in this subject, so some theorems that are obvious will take about half a page to prove. One of my mates described this subject as a mathematical essay, which I think is why this subject is a hit or miss (albeit much more likely to be a miss).

I find one of Barry’s quotes to be fitting in describing this subject:
"A common emotional response to my treatment is: this stuff was so easy at school, why does Barry make it so hard? Well, the reason why I make it so hard, is either that your teachers lied, or probably more likely, they have carefully protected you from things that might be troubling. However, most of you are over 18 now, so you can deal with R-rated Mathematics"

Nonetheless, if you find the pace to be bearable and you’re willing to commit extra effort to appreciate the content, this can be a very eye-opening subject. You get to encounter numerous R-rated concepts that are crucial and interesting in mathematical analysis but are often neglected.

The topics covered in this subject are (in order):

Yes, with screen capture. However, Barry writes on the whiteboard which isn’t recorded, so lecture attendance is necessary (or alternatively you can borrow someone else’s notes).

Prof. Barry Hughes

Yes, Final Exam 2009-2018. No short answers/solutions given, but the 2017 and 2018 Final Exam were discussed on the last two lectures.

4.5 out of 5

Barry's Accelerated Mathematics 2 Printed Notes, which is available at UniMelb’s Co-op. The book contains all the lecture slides and exercises with short answers and is realistically necessary.

For each week: 4x 1-hour lecture, 1x 1-hour tutorial

2019 Sem 2

97

> 2 written assignments (10% total, equally weighted)
> Mid-semester Test (10%)
> Examination (80%)

Important Notes: MAST10008 Accelerated Mathematics 2 is the second of two subjects in the first year accelerated mathematics stream. Taking both MAST10008 Accelerated Mathematics 1 and MAST10009 Accelerated Mathematics 2 is equivalent to taking the three subjects MAST10006 Calculus 2, MAST10007 Linear Algebra and MAST20026 Real Analysis. MAST10008 Accelerated Mathematics 2 covers all of MAST20026 Real Analysis, and the remaining parts, (which is pretty much all of) MAST10006 Calculus 2 (where the rest would have been covered in MAST10008 Accelerated Mathematics 1). The accelerated mathematics stream requires a minimum raw score of 38 in VCE Specialist Mathematics, or equivalent (roughly, top 13%).

Just like MAST10008 Accelerated Mathematics 1, I thoroughly enjoyed this subject and was by far, my favourite subject of the semester. Students should be careful though. MAST10009 Accelerated Mathematics 2 is much more difficult in comparison to MAST10008 Accelerated Mathematics 1. This subject develops the theory behind many very important parts of mathematics in mostly chronological order. The content here is covered very quickly, and it is highly unlikely that at students will not digest everything upon first presentation. There are even comments about MAST10009 Accelerated Mathematics 2 being one of the hardest first year subjects due to its pace, and because it covers around 1.6 subjects worth of material. It will be very important that you stay on top of things and are studying regularly. This subject is very unforgiving if you fall behind even for strong mathematics students. That being said though, taking the subject is has been an amazing journey, and I strongly encourage students to take it if they are up for a rewarding challenge.

Lectures:
Barry is very interesting and delivers lectures very well. However, given the sheer amount of content that needs to be covered, sometimes, he necessarily needs to skip a few details, and so you have to teach yourself (as well as utilising consultation regularly). This is the only reason I didn't give this subject a 5 out of 5. Barry essentially uses lecture slides and walks you through the concepts. (All notes are in the text). He then does the examples on the whiteboards (which can sometimes be frustrating given the whiteboards are not recorded). You should take notes only on the examples. You can annotate your text if you like, but not much more is required. Your focus should be on listening and understanding what Barry is saying.

Practice Classes (Tutorials):
Tutorials were awesome, though since the questions are essentially from the text, if you are prepared, this class can be pointless. Nevertheless, it can be fruitful to answer questions again with a tutor watching your logic and reasoning so that they can make any necessary corrections. In this class, you complete a set list of questions in groups on the whiteboards. Selected hints / solutions are found at the back of the book, but you will find them useless if you don't understand the content in the first place. You should consult your tutor and/or utilise consultation hours should you need assistance.

Assignments:
All assignments are handwritten. The questions on the assignments are generally of high difficulty. Although it will seem like some are easy, do not be fooled. There are small nuances everywhere to catch those who are not focused. Like most mathematics at university level, assignment questions are not the same as exam questions, and so it's important that you do not start assignments the night before they are due. The questions are not necessarily straight forward and trust me, Barry will make sure you have thought about it for days before coming up with a solution.

Mid-semester Test: The mid-semester test might just be the worst score you will ever get on a mathematics test. If you are not prepared, you will not score well at all. The test contains content from the first 20 lectures (or first 5 weeks) of the semester. It's 45 minutes long, and is generally around 40 marks. (40 marks in 45 minutes as opposed to 40 marks in 60 minutes in VCE).

Examination:
Worth 80%, this is a massive assessment. You have no calculator and no notes. Only a pen is required. The exam, unlike the mid-semester test, is much more straight forward if you have done the work prior to it. The exam is always designed so that it is relatively easy to pass, but hard to score well in (just like MAST10008 Accelerated Mathematics 1).
Overall, I think MAST10009 Accelerated Mathematics 2 is a very rewarding subject if you put in the effort. It's also a subject that is really the turning point in most students' mathematics education. After completing the first year accelerated stream, students generally come out with a deeper appreciation for higher mathematics.

Yes, but only the lecture slides. The lecturer uses the whiteboard so it's best to attend.

Prof. Barry Hughes

Yes, 10 available (2009 to 2018) plus many MAST10006 Calculus 2 and MAST20026 exams (see comments for explanation).

4.5 out of 5

None. The lecturer provides his own text guide, which is essential. It's available at the university Co-op Book Shop.

Every week:
> 4 hours of lectures (1 hour each)
> 1 hour practice class

2018 Semester 2

First Class Honours (H1)

Written assignments 2 × 5%
Mid Semester Test 10% (45 minutes)
End of semester exam 80% (3 hours)

I had a love-hate relationship with this subject, or more accurately hate that turned into love. Initially, I struggled with this subject more than I have ever struggled with anything academic before, but with a lot of effort and persistence, this subject has taken me from someone who hated anything to do with mathematical proofs to applying to do the concurrent maths diploma with complex analysis in my plan (although finding out about HECS exemptions may have helped that too ). If you immerse yourself, you’ll see how truly fascinating and beautiful maths is.
It seemed harder than AM1 for most of the semester, but I ended up with a higher grade than I got in AM1, so good grades in this subject are definitely possible with a lot of hard work and understanding.
Content is essentially most of real analysis (a second year subject) and calculus 2 (minus some stuff done in AM1), meaning it's meant to be hard for first year students, but that taking it will give you more options for the rest of your degree. You cover sequences, functions, many theorems and definitions associated with these, Riemann integrals, integration, differential equations and infinite series. You’re expected to be able to remember and reproduce any formula or definition in lecture slides/notes, so aim to understand as much as possible to achieve this.
I think Barry was the primary coordinator who ran this subject, and he did a fantastic job at it. It was pretty clear he truly cared about what people got out of his subject, rather than just seeing it as a box people have to tick.

Lectures:
Involved Barry talking through slides and writing examples on the blackboard, meaning you pretty much had to be there to copy them. While this was quite a pain, the purpose was so that students could absorb as much as possible. I personally only missed a few towards the end of semester and don’t think that really impacted my score, but if I didn’t attend most I think I would have scored much lower. In all honesty, most of the written examples are much harder than the standard expected, but the more you understand, the better position you’ll be in to do as well as possible. Lectures seemed intimidatingly difficult at the start (you’d notice the number of empty seats increasing), but looking back it really just takes a while to get your head around, so don’t give up if you’re feeling this way at the start of semester

Practicals:
Involved working with groups of usually 3-4 on lecture note questions on whiteboards (unfortunately unlike AM1, no extra questions or worked solutions). However, attendance was still very important, as tutors provide what will be for most, much needed assistance. Most people including myself had pretty much no idea in the first couple of weeks, so again, don’t be too discouraged if you’re initially feeling this way. I had mixed feeling about different tutorials based on how much I felt I learnt, so I’d recommend making sure you’re with people who want to discuss and work through questions, otherwise it can feel like a waste of time.

Assignments:
The first is on sequences, and will most likely feel much more difficult than second on calculus 2. But both will probably require a substantial amount of effort (recommendation is 8 hrs each). For the first, you must really read over and understand the definitions and proofs. The second will mainly focus on mechanical calculations.

Mid Semester Test:
For most including myself, this was the lowest mark received in the subject, but looking back wasn’t insanely difficult or unreasonable. Requires a thorough understanding of all theorems/definitions covers so far, and the ability to apply them to simple proofs as well as application type questions (ect. Find limit). Many marks in this one for being able to correctly state definitions and theorems.

Final Exam:
Required what was mentioned for test, as well as knowledge of all the calculus techniques/applications (you’re also not supplied a formula sheet, in a sense making this section harder than it would be through doing calc2) and series. I found it to be a pretty fair and reasonable exam – nothing overly difficult or tricky, meaning through working hard to get the basics of what has been taught, good(or better) grades are more than possible.

Yes, with screen capture of slides, but without screen capture of blackboard where examples were written

Barry Hughes

10, without solutions (2 were discussed in last lectures)

5 Out of 5

MAST10009 Lecture notes from Coop, written by the lecturer - a must, contains notes of all theorems, definitions, explanations, background and some examples

4 × 1hr lectures per week
1 × 1hr practical per week

2017, Semester 2

H2A (79)