**Subject Code/Name:** MAST10013 UMEP Mathematics for High Achieving Students**Workload:** 1x2-hour class at a school centre per week

**Assessment:** 10 (?) assignments throughout the year, and 2 exams at the end of the year (usually late (20ish) November, after VCE exams are over). Exam 1 is usually on a Friday (3 hours) and exam 2 is the following Monday (2 hours).

**Recorded Lectures:** N/A

**Past exams available:** Yes, dating back to 2009 (not all relevant), all available in one of the required UMEP booklets. In addition, miscellaneous 'exam style questions' are also included in the booklet, but no answers (these questions are taken from numerous other university assignments/exams such as Calculus 1, Calculus 2, Linear Algebra, Accelerated Maths 1, etc.)

**Textbook Recommendation:** No prescribed textbook, instructor provides materials/prescribed UMEP materials. This really depends on the instructor. I did UMEP at Melbourne Grammar, the instructor Ms. Goureeve (<- awesome) provided very comprehensive printouts for each class. If you're more adventurous, Paul's Math Notes for Linear Algebra provide very detailed coverage of topics (Ms. G's printouts were often from Paul's Maths Notes anyway). Other classes I've heard that they just go through the UMEP booklet summaries (which imo are quite dry and condensed), but I'm not certain.

**Year & Semester of completion:** 2015, Year long

**Rating:** 5 out of 5

**Comments:** This subject was absolutely great imo. It has a distinctively different feel from VCE Methods and Specialist, both because it's mostly concerned with pure mathematics (rather than the general application and problem-solving emphasis of VCE maths), but also due to the overall different feel of maths at uni. Whilst there is a reasonable overlap between UMEP maths and VCE maths, it's not extensive, because UMEP maths is mainly concerned with things above and beyond VCE level (which is why people do uni maths, right?)

** What was it like?**UMEP Maths covers a wide range of topics, kind of picking up where Specialist leaves off. A major portion of the course is concerned with

**linear algebra** which is a distinct field of mathematics (i.e. as opposed to calculus/analysis), not really touched upon in high-school or VCE level maths (apart from a little bit of vectors in year 12!)

In terms of difficulty, the content was a lot more conceptual and abstract than VCE maths, and is quite a step-up from VCE level maths... just think - four dimensional planes, systems of equations in five unknowns, and stuff like that

. This, however, is compensated for in that the questions asked on assignments and exams were very straightforward - they'd simply ask you to perform an operation, solve an equation, or something like that which requires zero interpretation (unlike VCE exams, where figuring out

**how** to approach a question is half the battle).

Overall, then, I'd say UMEP Maths is a lot more advanced conceptually, but practically simpler.

* Note - I'm aware that the UMEP maths course is changing in 2016 to cover both Calculus 2 and Linear Algebra (previously it covered only Accelerated Maths 1). This means it now covers more content, but the final outcome (i.e. how much of a headstart you get on maths subjects in uni) turns out to be the same for certain reasons*The specific topics covered by UMEP mathematics are:

- Techniques of proof, number systems

- Complex numbers (in particular, the complex exponential and applications to integration/differentiation)

- Solid geometry (basically vector algebra involving cross-product, lines and planes)

- Matrices and linear systems (solving linear systems of arbitrary dimension using row reduction, determinants, inverses)

- Multivariable calculus (one of my favourite parts of the subject, partial derivatives, gradient, double and triple integrals, tangent planes)

- Vector spaces (vector spaces, subspaces, basis, span and dimension, coordinate vectors, polynomial and function vector spaces)

- Inner products (basically a generalised form of the dot product)

- Linear transformations (extends from the baby steps introduced in Methods, transformation matrices, kernel, Rank-Nullity theorem, etc.)

- Eigenvectors and eigenvalues (used for finding arbitrary powers of matrices, diagonalisation)

**Overall workload...**The actual classes were run once a week (every week of term for 3+1/2 terms). Each weekly class was 2 hours long, in which the instructor walked us through new topics, did examples on the board, and so on, just like in a VCE maths class except with more advanced material. So no, there weren't any 'lectures' per se for UMEP maths.

With my instructor, the pace of classes was moderate. Ms. G. was very relaxed, fine with doing an extra class here and there if people were particularly struggling with a specific topic, were super busy, or just too tired to pay attention.

In our class, at least, falling behind here and there was basically a given - it happened to all of us. Personally I don't feel that it impacted me, because the resources our instructor provided were super-comprehensive. Along with the prescribed UMEP resources (which are summary notes and practice questions), it's easy enough to catch up several weeks (the mild pace was also a plus here!).

Usually a good deadline to get up-to-date with course content is just before the assignment (one assignment per topic, given at the final class for that topic). Even if you don't fully catch up in time for the assignment, it's not the end of the world - the assignment is, of course, open-book and you can basically use whatever resources you need. Including your CAS calculator. But, as you'll see, the CAS becomes increasingly useless as you progress into higher level maths haha

As I was juggling 5 VCE subjects on top of UMEP maths, I naturally didn't have a lot of time to spare to study for it. I basically relegated all my study for the week for UMEP to three or four hours on Saturday mornings or afternoons. During those few hours, I'd go through the printouts, my own notes (if any) and online resources to get up to date with topics, compiling notes, and doing questions.

At this rate, I didn't find keeping up too difficult (although I'm not one to speak, I fell behind multiple times lol).

Overall, there is

**plenty** of time throughout the year, so minor trip-ups for a few weeks don't mean much at all. Missing up to one or two weeks of class also isn't a massive deal, but more than that might cause major problems. Our instructor always provided last week's notes to students who missed the last week.

The exams were held on Nov 20 and Nov 23, but it was well after all my exams had finished (my last exam was English Language, and I had a week to prepare for UMEP), so there is ample time for exam preparation as long as you have actually tried for most of the year. The exception is people who do languages (e.g. CSL) which from what I hear has exams in late November. However, imo that's not a major issue as all mainstream subjects (e.g. maths, science, humanities) finish up around Nov 15ish from what I know, and then people only have to study for like 2 subjects.

**How it affected me after VCE...**Doing UMEP maths was really cool in that students who get normal marks (iirc 70+) are given credit for MAST10008 Accel Maths 1 and then are given the option of doing MAST20009 Vector Calculus (a second year subject on multivariable calculus, a prerequisite for applied and pure maths as well as physics majors), before doing AM2 in second semester.

I was also to credit MAST10013 to a concurrent maths diploma, which means I have the option of (a) doing an extra subject in my degree or (b) not overloading for semester... somewhere

**Advantages of UMEP Maths...**- You get to pursue more advanced maths in Year 12. If you're wanting to do more maths in uni (like me), this will give you a headstart in your mathematical career at uni. On the other hand, if you love maths but are preparing to kiss maths goodbye after VCE (like some of my friends), take advantage of this opportunity to get as much maths as you can before you need to leave. Go on

- Counts as an extra 5th or 6th subject for VCE, in which it's definitely

**statistically** easier to get a 5.0 (equivalent 50) than it is in a VCE subject

. UMEP served as my 6th subject (and... contributed 0.5 aggregate points lol). You get a 5.0 increment if your score is 90+, 4.5 if it's 80+, and so on. I got a mark of 94 for UMEP maths despite doing badly on the exam (compared to my practice), so that was 5.0. If I had done another subject instead (say Bio), I would definitely not have gotten anywhere near 50 with that type of underperformance

.

- You get to be in a

**very, very** high-performing environment. The UMEP

**maths** cohort in particular is very high-achieving, and chances are you'll get to meet, make friends with, and get inspired by kids who are at the very top of their game.

- Special treatment by UniMelb (haha!), such as an invitation to VCE revision lectures hosted by UoM (for KLD and UMEP VCE students), pizza, a UMEP graduation ceremony (after VCE results come out).

- If you go to Melbourne Grammar, you'll get Ms. G as your instructor. She is SERIOUSLY AWESOME. You'll basically be able to chill through the year

- You get to fall in love with UoM (I did!)

**Disadvantages of UMEP Maths...**- Unless you're one of those fortunate kids who go to a school that offers UMEP, you'll have to travel to the nearest or most convenient school centre. In my case, I lived in an out-of-the-way place and had to travel for 1.5 hours each way to Melbourne Grammar in South Yarra. BUT DUDE WAS IT WORTH IT xD

- Be prepared to battle UoM admin before your first semester if you want to do any tricky things with the credit from UMEP (like doing MAST20009 or putting it in a diploma). This is fairly obscure for most uni staff and it won't be easy

But again, it's worth it!

- Again, you'll get to know UoM (via various opportunities) in more detail than other universities (Monash remains highly mysterious to me!), thus making it a lot more likely that you'll end up preferring UoM above other universities. Depending on what you want to do, this may be a good or bad thing :3

I think I've written enough

. Hopefully this will give future students good insight into what UMEP maths is really like. If I could encapsulate this post in two short points:

- It's not that hard.

- You should do it!