**Subject Code/Name:** MTH2021 - Linear Algebra with Applications**Workload:** 3x1 hr lectures, 2 hr tute

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

**Recorded Lectures:** Yes, with screen capture

**Past exams available:** Yes 2, 1 with solutions. (there are more out there though)

**Textbook Recommendation:** You don't really need it but - Elementary Linear Algebra - Howard Anton

**Lecturer(s):** Week 1-6: Dr Tim Garoni, Week 7-12: Dr Jerome Droniou

**Year & Semester of completion:** Semester 1 2013

**Rating:** 2.5 Out of 5

**Your Mark/Grade:** 85 - HD

**Comments: ** 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

**EDIT: 100**^{th} review in this thread! \o/