MTH2021: Linear Algebra and Applications

2 assignments worth 6% each
12 moodle quizzes worth 0.5% each
A midsemester test worth 16%
Applied class participation worth 3%
Lecture poll participation worth 3%
Exam worth 60%

I didn't really enjoy this subject. It is very much a pure subject, with some applications tied in. The basic structure of the course notes is to provide a definition and then provide theorems/lemmas/corollaries about the definition, with some examples tied in. Which would be fine, if the subject wasn't a key part of other areas of maths. I enjoyed the content any time proofs weren't involved, especially the applications.
Areas of study included:

• Linear systems and matrices(with applications in graph theory and economics)
• Determinants
• Euclidean spaces
• Vector spaces(with applications in coding theory)
• Linear transformations
• Eigenvalues and eigenvectors(with applications in Markov chains, search engines, and differential equations)
• Inner product spaces(with applications in data fitting and linear regression)
• Orthogonalization(with applications in data compression and principle component analysis)

Tim was a pretty good lecturer but the content was pretty dry and I often found myself lost in all the mathisms of the proofs and pretty confused.
The applied classes involved doing questions together in a group on a whiteboard. My tutor was pretty helpful in getting us to understand the proofs on the problem set.

The assignments were quite difficult but I did appreciate that there was only 2. Tim also gave a lot of hints for the more difficult questions, which definitely helped
The moodle quiz was a 5 question mostly multiple choice quiz at the end of each week, reviewing everything. It wasn't too difficult and forced you to stay up to date.
The midsemester test was a 16 question moodle quiz, similar in format to both the weekly quizzes and parts of the exam. It was pretty nice, all things considered
If you went to and participated in 8/11 of the applied classes, you go the applied class participation marks
To get the lecture poll participation marks, you had to correctly answer 75% of the lecture flux polls within 24 hours of each lecture. 24 hours was a bit rough and I often found myself flicking through the lecture to the flux quiz instead of watching it regularly.
The exam was online and invigilated. The sample exam was quite similar in format and content to it, which was helpful. There were a few 'rigourous proof' questions, which I found quite challenging.
All in all, there weren't many assessments, which made this subject a bit less stressful than some of my others

Don't do this subject as an elective(unless you are a fan of pure maths). Wherever your passions lie, this subject will help you improve your resilience and problem solving skills(if it doesn't break you first)

Tim Garoni

There was 1 sample exam with solutions

3 out of 5

Lectures were done over zoom, with their recording, including screen sharing, uploaded.

Course notes, which were provided online but also available at the bookstore for a small price if you prefer to handwrite notes
Elementary Linear Algebra with Applications 11ed was recommended but completely unnecessary. The course notes cover everything needed.

3 x 1 hour lecture
1 x 1.5 hour applied class

2021 Semester 1

96 HD

Three written assignments (6%, 7%, 7% respectively)
One midsemester test (10%)
Final exam (70%)

This unit basically extends upon the concepts covered in part of MTH1030 (the matrices, Gaussian elimination, eigenvalues/eigenvectors part), and also tries to generalise some of the concepts of vectors into a more abstract sense.

The ordering of topics here doesn't quite reflect the order in which they will be covered in semester, but rather, a grouping that reflects the links between the familiar and the more abstract.

Interpretation of linear systems, Gaussian/Gauss-Jordan elimination, elementary row operations, matrix operations, determinants and inverses (largely a revision of MTH1030 bringing everyone up to speed, this will be at the start of semester).

General vector spaces - introduces the idea that there are really a LOT of things that can be called 'vectors', goes through some of the properties of these, including span, linear independence, basis and change of basis, dimension, subspaces. Links back to matrices are found in row space, column space, rank, nullity. This is really the foundation of a lot of the unit, so it's good if you understand the concepts here.

Dot products, angles between vectors, scalar and vector projections, magnitude and distance between two vectors are then covered, which is also revision from Spesh/MTH1020/MTH1030. There are a couple of new things (like the matrix of orthogonal projection), but most of the stuff is revision. Later on in the semester, these concepts are learnt in a more abstract sense. Instead of dot products, you now have inner products and inner product spaces. Instead of perpendicular vectors, you now have orthogonal vectors. Instead of magnitude, you now have the norm of a vector.

Matrix transformations/linear transformations - using matrices to transform vectors into other vectors (think rotations, reflections, stretches and skews, as well as just turning vectors into other vectors). Later on in the semester, we get the more abstract 'general linear transformations'. Now, we're no longer just mapping vectors from R^m to R^n, but from any vector space to any other vector space. Isomorphism, onto and one-to-one transformations, linearity of transformations and change of basis are covered here.

Eigenvalues and eigenvectors, eigenspaces, similarity and diagonalisation, as well as applications to quadratic forms, internet search engines, multivariable calculus, solving systems of differential equations. Later on, this gets combined with inner products/orthogonality to form 'orthogonal diagonalisation' (one of the best things Jerome will ever say with his French accent).

Finally, the last chapter is about some other applications in probability (if you remember Markov chains from Year 12 Methods probability, and how we used matrices there, it's a bit like that), and a bit about coding, and a bit about fields and modular arithmetic.
On the whole, this was also a pretty good unit for me (compared to MTH2010, for example). Both Tim and Jerome put in a decent effort to explain things, as opposed to just filling in the lecture notes booklet. On that note,

Weeks 1-6: Tim Garoni
Weeks 7-12: Jerome Droniou

Yes, two available. One has answers.

4.5/5

Yes, with screen capture.

H. Anton, C. Rorres, Elementary linear algebra (applications version) (10th ed. in Sem 1 2013). Not a compulsory buy. Did not consult much throughout semester.

3 x 1 hour lectures per week1 x 2 hour tutorial per week (

Semester 1, 2013

Unknown at this point.

3 Assignments - 6% & 7% & 7%, Midsem test - 10%, Exam - 70%

To be honest, I absolutely hated this unit throughout the semester, but over the day or two of cramming right before the exam, I've warmed to it a little bit more. I should note that this has nothing to do with the lecturers, who were fine, it has more to do with me not enjoying the course content, pure maths just isn't my thing. The first four weeks are not too hard, you start off with basis concepts dealing with matricies, determinates and such. After about 4 weeks you start on vector spaces, which is where everything seems to go downhill. A lot of the cohort struggled with this (me included), and once you down understand the first parts to it, you get lost and have no clue with the next couple of weeks of the course. We were told that the median mark for the semester was below 50%. After a bad midsemester result I may have started not attending lecturers as much. In short, I was still learning content the day before the exam. The main annoyance with this unit is that you have to remember a lot of material, it's not hard once you get it, it's just a lot.

Although, after I actually sat down and went through the course properly, and after it clicked, it isn't actually that hard, you've just got to remember how to do everything (a lot of things), and small, small notes here and there. There are proofs (it may be labelled an applied unit but it's basically an intro to pure maths with a few applications thrown in). About 12% of the exam was proofs with another 10% or so of 'show that' which required you to have the knowledge to do a proof of similar nature.

When I approached cramming for this (I did it in 1 day.. one long day...), I knew that I wasn't going to be able to get proofs down in time, and focused on learning how to do things from past exams, not exactly why.. (this is a very bad way of learning, if you can call it learning at all, don't do this unless you run out of time in the end). This required a fair bit of memorization, although I started to enjoy the unit a little bit, when I could actually do questions. There are some applications that can make a few things a lot easier, and so simple compared to other methods we would have used. (Think about cutting down 2 pages of working into a few lines using another method, this was actually quite cool).

For those who want to go ahead, the following are the topics covered:
- Gaussian Elimination
- Elementary matrices, LU decomposition
- Determinants, Cramer's Rule, Constructing curves and surfaces
- Euclidean Vector Spaces, Orthogonality, Real Vector Spaces and Subspaces
- Spanning sets, linear independence, Bases and Dimension
- Coordinates, change of basis, Fundamental matrix spaces
- Matrix Transformations, transformations of the plane
- Eigenvalues and eigenvectors, diagonalization
- The power Method, differential equations
- Inner Product Spaces, Gram-Schmidt Algorithm
- Least Squares solution, fitting data
- Orthogonal matrices and diagonalization
- Quadratic Forms, Optimization
- General Linear Transformations
- Applications: Markov Chains, Discrete Dynamical Systems, Error Correcting Codes

Week 1-6: Dr Tim Garoni, Week 7-12: Dr Jerome Droniou

Yes 2, 1 with solutions. (there are more out there though)

2.5 Out of 5

Yes, with screen capture

You don't really need it but - Elementary Linear Algebra - Howard Anton

3x1 hr lectures, 2 hr tute

Semester 1 2013

85 - HD

5 Assignments: 4% each, 5 Laboratory work (quiz): 2% each, 3 hours Exam: 70%

If you did CAS methods, it's probably a bludge unit. Sadly, I didn't. If you did MTH2010 it is probably again also a bludge unit. Sadly, I haven't yet, I'm doing it this semester instead. So, to me, most of the content was quite new, except the stuff covered in MTH1030. Tim is an awesome lecturer and really knows his stuff, the tutes were quite standard but I'd recommend trying to get Marsha Minchenko because I found she was really good and helpful and willing to go the extra mile. The content itself was mostly easy, and the exam was very doable but unfortunately for me I stuffed it up so got a D instead of an HD but oh well. Halfway through the semester they switched lecturers to a french guy called Jerome and he was okay but he had a really thick accent and so if you're not good with french accents it's a bit of an issue.

I really liked this unit, I would recommend it. If you've done methods and etc it is also a bludge unit, so added bonus there. for me it wasnt a bludge though because I've never seen most of the content before but it's easy enough to pick up.

Dr Tim Garoni and Jerome (cant remember his last name but it was long and started with D)

yes two, one with solutions.

4

Voice recorded lectures only

Printed lecture notes but also have a copy on moodle. also Elementary Linear Algebra, which is a pretty good book but you dont neeeed it unless you don't intend on turning up to class at all.

3 1-hour lectures and 1 2-hour support class per week

Sem 1 2012

D

5 Assignments: 4% each, 5 Laboratory work (quiz): 2% each, 3 hours Exam: 70%

This subject's name should be changed to MTH2021 - Maths Method (with a bit of matrices) with applications. The first couple of lectures were essentially revision for VCE materials and everything else after that is very simple, to the point whereI felt like I was doing level 1 maths but easier. Except for some matrices operation (tr(A), row(A), col(A) etc.), all other materials are taught in previous maths unit (MTH1030, and MTH2010 if you done it) so I didn't learn much from this unit. Though the lectures had general proves, we are not required to 'understand' it thus making this subject quite easy (of course its the best if you understand the proves, but its not necessary to achieve a HD). If you're looking for a bludge unit I'd say this is the one. The lecturer is apparently quite humorous and knows his stuff but I can't really comment on it too much since I haven't been to more than a lecture (I fell asleep on the time I went). Tutorial class is the same as every other maths unit, if you're up to date and feeling comfortable then its not going to be helpful.

TL;DR It's a bludge unit, if you're looking for an relatively easy HD then take this unit

Dr Tim Garoni

2 past exams are available but only 1 came with solution

3 out of 5

Voice recorded lectures only

Printed lecture notes if you attend lectures, its also available on moodle if you want to print it yourself or read it on a laptop/tablet etc.

3 1-hour lectures and 1 2-hour support class per week

Sem 1 2012

(Pending)

3 assignments, each worth 6%, each online quiz is worth 1.2%, tutorial participation is worth 6% and exam is worth 70%

Didn't go to any lectures, however I heard lectures were actually alright, not the best but nothing special and not much use for those mathematically talented. I actually found this applied maths unit alright, it focuses quite a bit on the application sides of things however there are proofs which are gone through which i thought was really quite neat. However the downside to this unit was that the online quizzes were quite useless and 2 of them weren't even up on time, they came on a whole week late and everyone panicked. Tutes were also pretty useless, as you just did the set questions from the tutorial booklet, so having tutes as compulsory to get the attendance marks were annoying as hell, almost each week i did work for another subject during tutes or just browsed maths wikis on the computers.

apparently it's Alan Pryde and Chris Hough (not too sure on this as i didn't attend any lectures)

Yes, there are around 3 exams, only 1 had solutions.

2 of 5

Yes, check MULO.

H. Anton and C. Rorres, Elementary Linear Algebra (Applications version) 9th ed - pretty good book.

3 Lectures per week (1 hr), 1 tute per week (2 hr), 3 assignments in total, 5 online quizzes and 1 exam

2011, sem 1

98 HD