Let me start off by saying that I am no Mathspert. In fact, after this maths subject, I wish to never add two numbers together again and marry my calculator.
Moving on
Linear Algebra! Most likely you are coming into this subject with fresh wounds from Calculus 2. The things taught in this subject are quite different from Calculus, introducing new concepts for you to wrap your head around. I have heard the term abstract being thrown around a lot. Linear Algebra requires you at times to visualise things in 3 dimenstions. It will take time to get your head around these ideas. From my own experience, trying to understand these ideas at first may be frustrating, but once it clicks, everything should seem pretty straight forward. But the one thing that never clicked for me were proofs (luckily they weren't prominent in the weekly assessments). I found it funny that at the back of the work book, the only solution to these questions was a short sentence saying proof required. Not shit! JUST TELL ME THE ANSWER!!! Do try to attempt them as best you can and go over them with the tutors. Some of these questions were work examples in the text book. Does this mean you have to buy it? No. Just borrow it and look at the relevant section. Proofs will be on the exam.
It will take work to keep up to date, and without constant work your next lecture or tutorial session may sound like complete gibberish (just a word of warning, the lectures can be pretty dull). I encourage that anyone who plans to take this subject to do all the questions set by the lecturer as soon as possible (typically around 6-10 questions are given each lecture). Preferably finish them on the same day they are given. You dont want to be that student who is on question 10, 6 weeks into semester. I'm not going to lie, for me, some of these were tough. It took quite some time for me to "get" what to do therefore consultation hours will be a valuable resource when you find yourself dwelling on something too long. Be smart, unlike myself, and save time by going to them (make sure you show them what you have done so far to make the most of those times, dont just go in and say, Im stuck). There were hours throughout the week, and for my semester there were 3 different tutors who were be happy to guide me through my work. Just make sure you plan out what you will ask.
The weekly tutorial is just like that in Calculus. You are given a question sheet and work in a group of 2-3 to solve problems on a white board while the tutor goes around checking if you did it right. By now, you should know that tutorials are important and helpful, so go to them! You are also handed worked solution for the questions, and these can be used as an indicator to show if you are doing your questions in the right way. This is also your chance to make friends and a study groups.
Each week you will have an assignment of around 3 questions testing you on what you have learnt the week before. If you have done the work book questions, these assignment questions shouldnt be harder than those. Unlike Calculus, only one out of the three questions is marked to encourage you to check your own work. They do post up a set of worked solutions, so look at them. I guess I was overconfident and believed that everything I did was right. Little did I know, 1 day before the exam, all my answers to linear transformations were wrong! Check them, reflect on them and ask your tutor if you need further clarification. Redoing them is also good practise I believe they are a good reflection of the level of difficulty you will be faced with in the exam. Also, it should be obvious, but you can check your answers with a calculator for certain questions
Following tutorials is a 1 hour computer lab. I didnt particularly enjoy these, but I do see how they can be beneficial. They are there to help you visualise and understand the concepts. For those who are more visually inclined, it can indeed be a very useful. Essentially in each session you go through questions from the lab book which can include things like matrix manipulation in the computer, forming 3-D graphs, etc. The instructions a pretty straight forward and they shouldnt be all too difficult. Dont panic if you dont get through all of them, the most important thing is going through your tutorial and workbook questions.
The end of semester test in week 12! This I found was well placed since by studying for this you are also prepping for the exam. Except! It requires the use of MATLAB; a computer program that is basically a beefed up graphics calculator. But don't let that deter you. The programming component is not all too complicated for a new user, and should be a refresher for you ESD2 survivors (if you remembered anything from that messily taught module). I believe that the extent of the programming you needed were in the first 2-3 weeks of the computer labs, involving the making of matrices, adding, multiplying, reducing, graphing etc. I was given a sample test (with no solutions) which gives you a pretty clear idea of their expectations in terms of programming. They will list the topics that may be on the test which you can study for by doing your workbook and tutorial questions.
Finally the exam. Since you have been diligently blazing through the workbook question each week and managed to finish all 200 something questions, the exam shouldnt be all too terrible. It seems as though they forced you to carry a 100 kilo rock throughout semester and for the exam they reduce it to 70. I was surprised at how simple some of the questions were. I was given answers to 3 past exams, but if you ask any of the guys who did Linear Algebra in the summer you can get a few more. I think I had 5 in total which is a good amount. Along with your assignments, tutorial sheets, and work book, you have plenty to get ready.
One important piece of advice. I will put this in caps so you can remember better. POLISH YOUR ROW REDUCTION SKILLS AND MAKE SURE YOU CAN DO IT QUICKLY AND ACCURATELY IN TIMED CONDITIONS. I found that I was constantly making mistakes with my row reductions as simple as it was, and this was probably due to the fact that I was relying too much on my graphics calculator throughout semester. Approach them in a systematic and organised way. Keep track of all those negative signs, and make sure every calculation is correct before moving onto the next otherwise it is a snow ball effect of mistakes. And I wished someone told me this early on, but you should avoid fractions if possible by multiplying rows to get the same whole numbers as the leading entries. It might not make sense now, but hopefully it will later and will save you time.
There are some very useful resources online that can help you to understand the concepts of Linear Algerba. Youtube has quite a few, including:
. Khan Academy
. PatrickJMT
. MathDoctorBob
Not to mention, a lecturer for Linear Algebra put up videos on how to solve certain problems in the exercise book based on what was requested on the discussion board.
So did I enjoy this subject? Eh, not so much. I was required to do it, so I had to push through. But if you are taking this subject, just know that there are numerous resources out there that can help you with your study, and you can do well if you put an effort into understanding the concepts.