First Discrete Math and now Linear Algebra… I hate this especially because I studied pretty hard (although in a somewhat disorganized way).
I can refuse to keep the grade and take these exams again in like three weeks, but seeing the kind of questions that were asked, I’m not sure I can master these topics in such little time. Also, in Februrary I have two other exams for which I didn’t even began to prepare for, so I would have to study a lot… And to throw more fuel, I want to graduate with honors… But something now tells me that it’s something that is very unlikely to happen.
I hate university, there is literally nothing I like about it.
Yo you need help? I’m doing my masters in discrete math, my lina is meh but maybe good enough for a first semester?
Also I’m doing math with add if you need studying tips for approaching dense topics plus the first sementer is the toughest, once you get a feel for how to think “mathematically” it becomes a lot easier.
Thank you very much, some help and tips would be super appreciated! What would you recommend doing?
These are the topics we did:
Discrete Math
Combinatorics, Group Theory (Cycles, cycle decomposition, parity, order, subgroups, cyclic groups, homomorphisms, Generators and relations, permutations of Sn, generators), Number Theory (Bezout’s Identity, Euclidean Algorithm, Euler’s Totien function ϕ, Euler–Fermat theorem, congruences etc.), Modular Inverses and Equations, and the ones that tricked me the most, Abstract Algebra. I think these should be all.
Linear Algebra
Complex Numbers (with Polar coordinates and roots), Matrices (Matrix operations, trace and determinant, inverse, special matrices, ranks), Vector Spaces (subspaces, linear independence, coordinate vectors and change of basis), Linear Transformations (Eigenvalues and eigenvectors, diagonalization, and some other stuff), Inner Product Spaces (I literally know almost nothing about this)
I’m sorry is that in one semester? That’s all over the place, who designed this curriculum? Thats a completely new topic every other week. Horrible pedagogy.
Anyway for exam prep what I do is I collect all the stuff there is to know, write down headings, theorems etc. Exactly like you did there. That’s the battle plan. I’m ticking of topics as I go through them and so I can see what still needs to be done in what time.
Then sort the wheat from the chaff.
- What are the basics. Basic definitions, like Whats a vector space, whats a linear function.
- What was the main theorem? Every topic is usually built up like definitions -> examples -> lemmata -> main theorem -> corollaries.
- What was the main example? Usually there is one function, or set or something that gets refined and used over and over to show the topic at hand.
Write it all out, then try to trim it down. Lots and lots of paper get written on but never read again, it’s the act of writing it, organizing it, rewriting it that helps me make connections. Try to get it all on an A4 page.
What you’re going for is the basics, skip what lemmata seem unimportant (you can always come back later) and go for the main topic whenever you understand the word that get used. Don’t get bogged down in an abstract representation, if you can reproduce the proof of the main theorem on the main example you’re done. That’s more than good enough. For example cyclical group = Z5 or Z6. You know what’s happening there, awesome golden. Yeah you have elements a_1,…,a_n but honestly who goes above n=6 ? Write whatever you got down and then move on. Cycle back on another day.
Fuck corollaries. No one ever asked me about the corollaries.
Also who gives a shit about inner product space, good lord no one ventures outside of euclidean anyway… Basically the inner product guarantees you can talk about angles. If you know what the inner product is on R^n (x_1y_1+x_2y_2+…+x_n*y_n) you can then test on that. Don’t actually learn proofs using positive-definiteness but look at how the proof works on the standard inner product. Once you got that the rest will come almost on its own. Same with abstract algebra really, but I wouldn’t worry about them too much. The basics are way more important, those things might be the difference between an A and a B+. Which kinda stings, but it’s a lot of effort for the last few percentage points, when the easier basic stuff has better pay-off.
Basically for learning there is the formally correct way and the actually usable way. An inner product space is when Rn with that multiplication, summation thingy. <x|x> is positive for all the x except for 0, thats why they call it positive definite (it’s all squares x_12+x_22+…) Only wrinkle for complex numbers is that you have that conjugate messing up symmetry. That’s really it tbh.
If you have more questions feel free to ask me. On matrix I’m @marxemathics:matrix.org Kinda hard to explain in a lemmy comment tbh and it’s a bit late.
In a somewhat disorganized way? Tackle that first. Analyze your own usage of time and plan appropriately for extra time to study your notes. Learn from your mistakes and none of them will be wasted effort. Look into assistive technology for note taking and organization.
Yessir
Next time it will be different.
sorry to hear that, comrade. failure and setbacks can definitely be discouraging sometimes, but there is no success without failure and vice versa. revolutionary optimism applies to the self, too.
in this case failure just seems to indicate a weakness in your strategy/tactics rather than a lack of effort. may i ask how you studied?
Thank you ❤︎ You are right, it is true that, as Mao said, failure is the mother of success. The best thing to do in the face of defeat is to learn from it.
Basically, once the lessons concluded and they gave us a month off, I started by going over the program from start to finish, by using the notes for each lesson; afterwards, I began doing exercises that our teachers gave us to prepare. I already understand a few mistakes I did, for example it would have been better to study theory and then do exercises about what I just studied. Furthermore, I also didn’t revise enough. Another error I did was relying exclusively on my university’s material, which wasn’t enough to give me full expertise (in my opinion).
sounds like you already have a lot of ideas on how to improve, and that’s great! seems like it was a fruitful experience after all. i’m no math whiz, but whenever practicing anything i always try to remember the adage “if you practice like you play, then you’ll play like you practice.” try to simulate the form, content and experience of the exam as much as possible when practicing, while also changing those variables up often enough to keep yourself on your toes. that way no matter what happens or how you feel, you’ll likely feel more prepared. hope that helps!
I’m sorry to hear you are having a hard time. It’s worth talking to your academic advisor to see if you can do an extended first term or something similar to get yourself more used to the way university is. I had several classmates do something similar and they got through the rest of university. I know it’s not offered everywhere, but it’s worth asking. That is, assuming you want to continue university and not take some time away from school, or maybe switch majors.
Thank you. ❤︎ I will check if an academic advisor is avaible at my faculty, and if I meet any more problems I’ll talk to them. These two were the first ones, so I think it’s way too soon to consider dropping our or switching majors. Besides, to switch major would mean losing a year, and I wouldn’t even know what to study for it to land me a job. Since my university major is just 3 years long, if I can manage, I’d rather to endure it. (With honors possibly… that dream is not yet dead!)
You may speak with an advisor about delaying the math classes until you take one that can bring you to the level of these classes?
I’m not sure of how it works abroad, but here in Italy every exam is done multiple times and you can join that as many times as you want, within some rules.
For example, some people will do the same exams that I have just done in February, and if I wanted to I could take it with them, exchanging my current grade with a new one. I’d rather pick a date that is the furthest away from now though, something like May or June instead of February, so I can focus on these two after I’ve dealt with all other classes. These two seem to be particularly tricky.
Now that a semester passed we will have new classes, so I won’t have these ones anymore (although I will have Analysis 1, which is still math, but Analysis 1 doesn’t require much from Linear Algebra or Discrete Math so it’s basically another section of math). Luckily because of this I don’t have to delay any class, and I don’t even know if it’s possible to do this in Italy, since they have a very ‘you-do-you’ approach.
I’m not sure of how it works abroad, but here in Italy every exam is done multiple times and you can join that as many times as you want, within some rules.
Ah, no, that wasn’t an option for me, I don’t know if anything has changed in another couple of decades. I’m very pleased you have that option and are able to utilize it optimally. Best of luck to you, although I doubt you will need it.
Thank you, you’re too kind 💖
Sorry you’re struggling. Maybe it’s the wrong subject for you?
Thank you! But… is math the right subject for anyone, really? /s
Jokes aside, I am studying computer science. I think I’m pretty good at it, it’s also what I studied in high school. It’s just these classes who are particularly hard (and stressing)
I did philosophy A-Level and loved it, then went on to start philosophy at university, and it was totally different and I hated it. In the end I had to drop out due to illness anyway, but yeah sometimes a subject is just different and much more difficult and less enjoyable at a higher level.
True. I think it also depends on the way it’s taught, some really good teachers can make you like a class you would normally dislike. It works vice versa too, haha.
I love philosophy. Although you dropped, do you still read anything about it? I know outright studying can be very difficult with chronic illnesses. Hell, I can barely study with a cold.
Tbh I hated it at uni level so much that I have a real aversion to philosophy now.
That’s true trauma!
Tbf it’s not always the work as much as a comprehension gap between the way an instructor teaches and a student learns. Maybe you need a remedial class. Maybe a tutor?
Mmh, I’m 99% positive that there are no remedial classes in here. As for the tutor, I don’t think I need one, since even the hard things I studied, with enough time I understood them. I was also a very good student in high school, so I don’t think I have any learning disability. The problem was mainly practice and what I didn’t study, as well as my disorganizaiton.
I wasn’t implying a disability, I’m saying teaching style sometimes clashes with learning style. I had an issue with geometry, but I had a break between that and another class. I was fortunate that a different professor for a different class shared the break room at the same time and took me under his wing and tutored me on the lesson just prior, so I was able to pull a great grade from the class (and introduced me to Camus)! A couple of decades later I had a teacher for geometry and no option for a remedial class or tutor, so I dropped the class and wasn’t able to complete the course of study.
Oh, I see! Having a teacher that makes things click for you is indeed great. It’s kinda weird though, my teachers explain certain things with a lot of clarity, yet make a lot of other things needlessly complicated from my point or view.
That seems pretty universal, even in conversations with close friends, in my experience. Maybe part of it is how we relate to how certain words are put together in certain ways because of different upbringings and real world personal experiences. Kind of like the small confusion just prior among you and I.
Anyway, apologies for the confusion, and thanks for affording me the benefit of receiving my explanation! Best to you. 🫡
Sorry to hear that comrade :( education sometimes feels like it’s designed to crush you. I have a medical licence exam in a month and I am freaking out too :/
Thank you ❤︎, I’m sorry to hear that you’re in the same boat. It’s true what you said about education, it really does feel like that. Solidarity and good luck with you medical licence exam!
Good luck! 🤞
