EPTIt's a lot of fun, and very hard. Hopefully I can succesfully finish my Bachelor and Master, because I don't know what else I would want to study
Anyone has study tips specifically for Math?
My first month in Math.
| Blogs > Recognizable |
|
Recognizable
Netherlands1552 Posts
It's a lot of fun, and very hard. Hopefully I can succesfully finish my Bachelor and Master, because I don't know what else I would want to study Anyone has study tips specifically for Math? | ||
|
calh
537 Posts
| ||
|
OOHCHILD
United States570 Posts
| ||
|
hns
Germany609 Posts
If there's a book/script for your lecture around, prepare the next lecture - just go through the next few pages and check out what will be done, it will help you understand/categorize what's happening in the actual lecture. This obviously includes attending the lecture. Go through the lecture again afterwards. Those are the basic tips I'd give everyone. As you proceed further and begin to think mathematically, go ahead and ask yourself further questions: What did we ACTUALLY do in the proof/exercise? What was the critical component? Did we do such a kind of proof/exercise again and what were the similarities? Why do we actually need such a result? Those are the more advanced questions, however, which need a certain experience, so don't try them right now  | ||
|
Recognizable
Netherlands1552 Posts
If you find the solutions PDF to your textbook, you don't have to do all the homework. ....? I'm trying to learn something here ^.^ Do the exercises. If allowed, discuss them with a few buddies, but make sure you write them down yourself and see to it that you understand every step for yourself. This is the most important part. Go to the office hours and ask questions. How to ask questions: Make sure to be specific and have tried at least something ("not knowing what to do in general" is not a serious question). Also, know your definitions or look them up. Most questions come from not knowing exactly what a certain object/thing is. If there's a book/script for your lecture around, prepare the next lecture - just go through the next few pages and check out what will be done, it will help you understand/categorize what's happening in the actual lecture. This obviously includes attending the lecture. Go through the lecture again afterwards. This is pretty much what I've been doing. There is no such thing as office hours here tho? But there are plenty of opportunities to ask questions, which I always take ofcourse. Yep, knowing definitions is very important. I screwed up an assignment for Analysis because I didn't fully understand the formal definition of limsup and only had an intuitive notion of what it was. And again, I screwed up an assignment for lineair algebra because I misread the definition of lineair independency. Right now for me lineair algebra is the hardest class. Many agree with me, combination of having a terrible book which assumes you know how to read Mathematics and a terrible lecturer. At this level it is best to learn through solving problems rather than reading first. Start with the simple ones and work your way up, it will make sure you understand your theory instead of just knowing it. Also set theory is a pretty good foundation for analysis (well for anything really), so make sure you got it down good. Other than that just ask away at your lecturer, I'm sure they're happy that someone is interested in their stuff (I assume you're starting university?) I've definitely priortized doing the exercises instead of reading the book. A selection of problems is assigned to us after every lecture and expected of us to make. Which I do, ofcourse. All the students are highly motivated and interested in my classes tho. I haven't met anyone who was slacking off. Everyone actually seems more brilliant and more motivated than me ^.^ I think having unmotivated students in your class is something which happens more often in colleges in the US? Because of how the first year is basically a random selection of classes and because of how pretty much everyone can go to college. | ||
|
corumjhaelen
France6884 Posts
| ||
|
Recognizable
Netherlands1552 Posts
On September 28 2013 18:15 corumjhaelen wrote: You should do the exact opposite. Solving excercises is a waste of time if you don't know everything in your lesson perfectly, including proofs, examples and so on. If you don't like your textbook, go find another one you like more. Alright, thanks. The problem is that there is a limited amount of time(available to me) and as such sometimes I don't have to the time to fully understand every different example/theorem in the books and I'd rather do the exercises and refer back to the book if necessary. The pace of all the classes is very high. Ofcourse I still try to read and understand everything first. What book would you recommend for a first class in lineair algebra? It should be aimed for a math class tho, and not for a physics class. My friend in physics his classes take a different approach to lineair algebra than mine. | ||
|
And G
Germany491 Posts
- You can play chess on grid paper and still look like you're doing math stuff to the casual observer. - You will eventually get to a point where you're constantly doing stuff that is repetitive and just doesn't interest you. The first (and only the first) time this happens, consider switching majors. Since you said you found the basic stuff hard, really consider switching. Once you're determined to continue, just think of the money you'll make. | ||
|
Recognizable
Netherlands1552 Posts
| ||
|
corumjhaelen
France6884 Posts
I'm going to repeat myself. You're doing it wrong. It's no use doing any exercise in linear algebra if you don't know exactly what linear independance is. The best application of the concept is understanding what finite dimension is. It is (or will be soon) in your lessons. Basic examples help to, but basic is the important word here. You have to learn perfectly what's in your lessons. Or it's like you're trying to build the roof before the foundations of your house. If you do that well, in a few months, you'll get used to the pace, you'll be able to learn the curriculum faster, and then you'll find time for more exercises. Anyway most ideas you need to solve exercises are... in your lessons. | ||
|
Recognizable
Netherlands1552 Posts
On September 28 2013 18:41 corumjhaelen wrote: Can't help you for the textbook, because I had very competent teacher in undergraduate (classes prépa), and most of those I use today are in French... Just go to your unis library, look at a few of them, and choose one you like, we all have different taste anyway. I'm going to repeat myself. You're doing it wrong. It's no use doing any exercise in linear algebra if you don't know exactly what linear independance is. The best application of the concept is understanding what finite dimension is. It is (or will be soon) in your lessons. Basic examples help to, but basic is the important word here. You have to learn perfectly what's in your lessons. Or it's like you're trying to build the roof before the foundations of your house. If you do that well, in a few months, you'll get used to the pace, you'll be able to learn the curriculum faster, and then you'll find time for more exercises. Anyway most ideas you need to solve exercises are... in your lessons. Thanks for the advice. I will try harder to take your approach. I just looked it up on wikipedia: A geographic example may help to clarify the concept of linear independence. A person describing the location of a certain place might say, "It is 5 miles north and 6 miles east of here." This is sufficient information to describe the location, because the geographic coordinate system may be considered as a 2-dimensional vector space (ignoring altitude and the curvature of the Earth's surface). The person might add, "The place is 7.81 miles northeast of here." Although this last statement is (approximately) true, it is not necessary. In this example the "5 miles north" vector and the "6 miles east" vector are linearly independent. That is to say, the north vector cannot be described in terms of the east vector, and vice versa. The third "7.81 miles northeast" vector is a linear combination of the other two vectors, and it makes the set of vectors linearly dependent, that is, one of the three vectors is unnecessary. Also note that if altitude is not ignored, it becomes necessary to add a third vector to the linearly independent set. In general, n linearly independent vectors are required to describe any location in n-dimensional space And this makes the relationship between lineair independence, basis and dimensions all clear. Well. I spent at least an hour trying to understand this from reading the book/lecture notes, and all that was needed was some trivial example. | ||
|
And G
Germany491 Posts
| ||
|
corumjhaelen
France6884 Posts
This is the approach I was told to follow in my first year of prépa, and I think it's simply excellent. Btw one of the rare stuff our education system is really good at is training mathematicians | ||
|
Toadesstern
Germany16350 Posts
Tip 2) Start doing your homework early on and don't do it the last day before you have to hand it in. You'll have situation where you just won't get anywhere and need a day or maybe two off due to some kind of brainblockage. You need some kind of buffer for that reason Tip 3) Learn to live with frustration. It will happen to you that you're sitting on something for weeks, you suddenly realize you can prove everything to be wrong with a simple example and you have to start from scratch. The hardest part about math isn't math, but being okay with those things imo. Tip 4) Make sure to get your Ana 1 done properly. That's what people have problems with. LA 1 and set theory is super easy. LA and set theory is easily doable on your own. Ana 1 will probably cause you troubles if you don't have some discussions with other people because you're doing everything on your own. That's all I can think of right now //Edit// Oh yeah just read what other people said. You really should check out scripts before and after lectures. Usually you won't have all that much time you have to spend at university itself. That however means that you're expected to put more time into it at home, so do that. | ||
Plexa
Aotearoa39261 Posts
On September 28 2013 18:41 corumjhaelen wrote: Can't help you for the textbook, because I had very competent teachers in undergraduate (classes prépa), and most of those I use today are in French... Just go to your unis library, look at a few of them, and choose one you like, we all have different taste anyway. I'm going to repeat myself. You're doing it wrong. It's no use doing any exercise in linear algebra if you don't know exactly what linear independance is. The best application of the concept is understanding what finite dimension is. It is (or will be soon) in your lessons. Basic examples help to, but basic is the important word here. You have to learn perfectly what's in your lessons. Or it's like you're trying to build the roof before the foundations of your house. If you do that well, in a few months, you'll get used to the pace, you'll be able to learn the curriculum faster, and then you'll find time for more exercises. Anyway most ideas you need to solve exercises are... in your lessons. As a PhD student in math and having been a TA for many years, this, this, a thousand times this. The #1 reason why people get stuck in math is because they don't know their definitions. (The #1 error, however, is basic arithmetic! haha). Whenever you're posed an exercise or problem, you need to be thinking about what the assumptions are that are given in the problem. What do those assumptions mean? i.e. what is the definition of those assumptions. For instance, you could be given a question like suppose that U and V are subspace are R^3, show that the sum of U and V is a subspace. To show this obviously you need to us the fact that U and V are subspaces, and to do that you need to know what a subspace is! While this was a (trivial) abstract problem, even something like show that the sum of U=span{(1,0,3)} and V=span{(3,4,5)} is a subspace requires the definition to solve! In time, you'll build up from definition > application to definition > theorems > application! | ||
|
Catch]22
Sweden2683 Posts
| ||
|
bluQ
Germany1724 Posts
On September 28 2013 19:45 Toadesstern wrote: Tip 1) Get a study group. Especially in maths that's really helpful imo. There's just situation where you have to discuss and work on things in a group. Make sure you're all on the same level. Doesn't help anyone if one of them explains EVERYTHING to the other guys all the time. 3 to 4 people and you're good. Tip 2) Start doing your homework early on and don't do it the last day before you have to hand it in. You'll have situation where you just won't get anywhere and need a day or maybe two off due to some kind of brainblockage. You need some kind of buffer for that reason Tip 3) Learn to live with frustration. It will happen to you that you're sitting on something for weeks, you suddenly realize you can prove everything to be wrong with a simple example and you have to start from scratch. The hardest part about math isn't math, but being okay with those things imo. ^This. Study groups are one of the most important things imo. You will either have someone who can explain stuff you don't quite grasp or you will be the one explaining. Both benefit greatly from that, explaining stuff to my mates was one of the best things to succesfully memorizes learned things and be able to present them in different ways. Frustration is another big thing. You will hit walls constantly, try to take breaks (Tip2!!). You will need maybe a good cup of sleep and on the next day you can crack the nut! GL&HF | ||
|
CoughingHydra
177 Posts
On September 28 2013 19:45 Toadesstern wrote: Tip 4) Make sure to get your Ana 1 done properly. That's what people have problems with. LA 1 and set theory is super easy. LA and set theory is easily doable on your own. Ana 1 will probably cause you troubles if you don't have some discussions with other people because you're doing everything on your own. and these links are extremely helpful: career advice for mathematicians math stackexchange | ||
|
Toadesstern
Germany16350 Posts
Just like with us men, the percentage of chicks looking decent and being normal is a lot better if you're looking at those who're doing maths to become a teacher. At least here in Germany they have to do the same Ana 1-3 and LA 1-3 and not some kind of "math for biologists" (or whatever it'd be for teachers) so you'll be sitting in the same lectures. The ones doing math to get a bachelor and plan on making a masters afterwards are a lot more nerdy, which I probably don't have to explain to anyone here. So if you're looking for people who are a bit more down to earth you should be looking over there. People starting out in maths, when comming from highschool tend to be huge dicks the first 1 or 2 semesters until they realize they aren't geniuses. | ||
|
corumjhaelen
France6884 Posts
On September 28 2013 20:06 Plexa wrote: As a PhD student in math and having been a TA for many years, this, this, a thousand times this. The #1 reason why people get stuck in math is because they don't know their definitions. (The #1 error, however, is basic arithmetic! haha). Whenever you're posed an exercise or problem, you need to be thinking about what the assumptions are that are given in the problem. What do those assumptions mean? i.e. what is the definition of those assumptions. For instance, you could be given a question like suppose that U and V are subspace are R^3, show that the union of U and V is a subspace. To show this obviously you need to us the fact that U and V are subspaces, and to do that you need to know what a subspace is! While this was a (trivial) abstract problem, even something like show that the union of U=span{(1,0,3)} and V=span{(3,4,5)} is a subspace requires the definition to solve! In time, you'll build up from definition > application to definition > theorems > application! Lol at basic arithmetic, that and failing to copy constants from one line to the following But yeah even "good pupils" often fail on basic stuff, like saying E=F+G, x not in F so x in G... (who has never been tempted by that sort of stuff in a complicated setting throw them the first stone) Edit : and linear algebra has applications everywhere. Learn it well, it will be "useful". | ||
| ||
