Don't know what to do in mathematics =/

[Nano-Passion]

I'm having trouble deciding what to do in mathematics. I was self-teaching myself calculus and vector spaces but at one point my mentality changed to -- what's the point if your going to learn it again in college and -- your going to make yourself really bored in the lectures if you self-teach yourself the material beforehand. <-- lectures at my community college are about 3.5 - 4 hours long for calculus.

That is besides burning myself out because I devoted all my time to study of calculus and physics for a period of time. But I've taken a break and I want to go back to mathematics. But what should I do?

 

[lase]

How did you go about learning calculus? Depending on your level, you may find it useful to go back through and work with a book such as Apostol volume 1 in order to see calculus in a more rigorous light. Have you done multivariable calculus yet? What about ordinary differential equations? Linear algebra? What are you interested in?

 

[battousai]

I study math because I find it interesting. I don't see it as a "race to the top" or a "race to finish as many books as possible". I study the topics that really fascinate me, in my own pace, so I can absorb it and appreciate it better.

 

[chiro]

I'm having trouble deciding what to do in mathematics. I was self-teaching myself calculus and vector spaces but at one point my mentality changed to -- what's the point if your going to learn it again in college and -- your going to make yourself really bored in the lectures if you self-teach yourself the material beforehand. <-- lectures at my community college are about 3.5 - 4 hours long for calculus.

That is besides burning myself out because I devoted all my time to study of calculus and physics for a period of time. But I've taken a break and I want to go back to mathematics. But what should I do?

When you get to higher level mathematics, in my experience you need to do a lot of self study to even follow or reinforce what is going on in the lectures.

I'm doing C* algebras right now and the amount of stuff that is taken for granted is very large. This kind of stuff has all this context that (at least for me) is hard to get after getting one perspective on the material. Granted I have had no formal coursework in topology, real or functional analysis, but even in saying that I find that I really have to re-read the material more than once and let it settle before I can even start connecting the dots in a large context (i.e. understand it enough to actually ask meaningful questions and clarify assumptions or connections between different parts of the material).

I can understand with the lower level courses, but as you go higher and higher I think you'll find that the pre-study you do is beneficial and you will be happier that you did it before formal classes start.

Just my 2c.

 

[DrummingAtom]

I study math because I find it interesting. I don't see it as a "race to the top" or a "race to finish as many books as possible". I study the topics that really fascinate me, in my own pace, so I can absorb it and appreciate it better.

I agree with this and also what chiro said about it will eventually pay off.

I do a lot of self studying and if something doesn't interest me I'll stop studying it. If I have to take a class in a subject that I don't like then I'll have school pressure me through it. If it's something I like then it doesn't even feel like work.

It sounds to me like you're trying to force yourself to like something you don't. Maybe down the road you might like math more who knows. So why not use your free time for something you enjoy?

 

[Fizex]

Once you reach a certain point you start branching out to other topics in math you don't have time to take classes for or are reserved for the math majors. Like topology for instance.

 

[Nano-Passion]

How did you go about learning calculus? Depending on your level, you may find it useful to go back through and work with a book such as Apostol volume 1 in order to see calculus in a more rigorous light. Have you done multivariable calculus yet? What about ordinary differential equations? Linear algebra? What are you interested in?

I haven't done any of these. I did some calculus I, a little bit of two, and looked over vector spaces a bit.

I'm not so sure what I am ultimately interested in because I don't have a wide experience over different subjects. But I've did calculus and know that I am interested in it.

I study math because I find it interesting. I don't see it as a "race to the top" or a "race to finish as many books as possible". I study the topics that really fascinate me, in my own pace, so I can absorb it and appreciate it better.

So true. :!)

When you get to higher level mathematics, in my experience you need to do a lot of self study to even follow or reinforce what is going on in the lectures.

I'm doing C* algebras right now and the amount of stuff that is taken for granted is very large. This kind of stuff has all this context that (at least for me) is hard to get after getting one perspective on the material. Granted I have had no formal coursework in topology, real or functional analysis, but even in saying that I find that I really have to re-read the material more than once and let it settle before I can even start connecting the dots in a large context (i.e. understand it enough to actually ask meaningful questions and clarify assumptions or connections between different parts of the material).

I can understand with the lower level courses, but as you go higher and higher I think you'll find that the pre-study you do is beneficial and you will be happier that you did it before formal classes start.

Just my 2c.

Up to what level of mathematics would you say pre-study helps in? I feel like me pre-studying calculus just makes me bored to death in lectures. It ends up all too easy.

I agree with this and also what chiro said about it will eventually pay off.

I do a lot of self studying and if something doesn't interest me I'll stop studying it. If I have to take a class in a subject that I don't like then I'll have school pressure me through it. If it's something I like then it doesn't even feel like work.

It sounds to me like you're trying to force yourself to like something you don't. Maybe down the road you might like math more who knows. So why not use your free time for something you enjoy?

I love calculus, but I found it a big waste of time to re-sit through the material again in the lecture. It all just ends up being soo boring if everything so easy. I like a challenge.

 

[ahsanxr]

Have you thought about taking advanced classes if these are too easy for you? Continue with these, they'll feel like a breeze since you know most of the material already while you work on harder classes which will provide the challenge you're looking for.

 

[chiro]

Up to what level of mathematics would you say pre-study helps in? I feel like me pre-studying calculus just makes me bored to death in lectures. It ends up all too easy.

There is no black or white answer to this question. Pre-study helps in every area of math but the amount that you need to do will go up as the scope of the content and level of intuitiveness goes up.

If or when you do something like analysis, or functional analysis, you'll find that it's not about using a particular formula, or doing algebraic transformations in the same way that you do to solve integrals, or differential equations. This level is more about proving things, and some of the proofs at the high level are just not really intuitive at all, and navigating a proof that takes all of these different ideas can be pretty tough.

As you go up the difficulty scale, you'll find that the background to proving results is very high in magnitude. To prove a main result you'll find you need weeks of background, and each week is cumulative in learning (that is, you need to get each weeks worth of material down solid to get to the next weeks material and so on). You probably found in the lower math classes that proofs could be done within the lecture and were for the most part easy to digest: this has the tendency to change in upper level classes.

 

[nonequilibrium]

To re-light your flame: let me tell you that I find Calculus the most boring part about math. The reason for this is because Calculus is actually not math, which you'll realize once you get to the "real math"; I'd call Calculus the way engineers look at Analysis (and Analysis is my favorite branch in math). Do you have access to a library where they would have an introductory book on Real Analysis? I'd suggest you take a look at that :)

That being said, I had never even done Calculus before starting university. Apparently it's not unthought of to have done it in English-speaking countries, but where I'm from (Belgium), people are not really suggested to do that. When I was in high school, I mainly read interpretative books (on my own initiative, reading university courses hadn't entered my mind), like on the meaning of certain theorems (Gödel's being an obvious one) or the history of math; or interpretative books about physics, like Penrose's. Not saying you have to read those books too, but just letting you know that not everybody interested in math and physics is expected to be cracking calculus in high school. As you said, I also never minded not having done it, as the lectures in university were self-evident and would otherwise have been boring (and they were still kind of boring, but I blame that on the fact of it not being "actual" math).

What wasn't boring at all, however, was that first class in proofs I had the first semester of my first year in university. That was magical. I couldn't believe I had been completely unaware of this kind of math my whole (short) life so far...

My point, I suppose, is that you shouldn't worry about it being boring, the actual math will never be :)

 

[bcbwilla]

I'm having trouble deciding what to do in mathematics. I was self-teaching myself calculus and vector spaces but at one point my mentality changed to -- what's the point if your going to learn it again in college and -- your going to make yourself really bored in the lectures if you self-teach yourself the material beforehand. <-- lectures at my community college are about 3.5 - 4 hours long for calculus.

If you already know calculus going into college you can skip some of the introductory classes which leaves time to take more advanced and interesting courses that others won't get the chance to.

 

[verty]

I would focus on the interesting parts. For me, related rates type problems, inversion of matrices and solving systems of linear equations are the interesting parts, and there are very boring parts like eigenvalues or (most of) integration which are rather dry and best left till last or till you are interested in them.

 

[Nano-Passion]

Have you thought about taking advanced classes if these are too easy for you? Continue with these, they'll feel like a breeze since you know most of the material already while you work on harder classes which will provide the challenge you're looking for.

Well there isn't really much in my hands that I can do. I have to finish calculus I for me to take calculus II, then I have to take calculus II for Calculus III and Differential equations. I think I can take Linear Algebra with Calc II, but other than that, there is nothing I can do.

There is no black or white answer to this question. Pre-study helps in every area of math but the amount that you need to do will go up as the scope of the content and level of intuitiveness goes up.

If or when you do something like analysis, or functional analysis, you'll find that it's not about using a particular formula, or doing algebraic transformations in the same way that you do to solve integrals, or differential equations. This level is more about proving things, and some of the proofs at the high level are just not really intuitive at all, and navigating a proof that takes all of these different ideas can be pretty tough.

As you go up the difficulty scale, you'll find that the background to proving results is very high in magnitude. To prove a main result you'll find you need weeks of background, and each week is cumulative in learning (that is, you need to get each weeks worth of material down solid to get to the next weeks material and so on). You probably found in the lower math classes that proofs could be done within the lecture and were for the most part easy to digest: this has the tendency to change in upper level classes.

Well yes, I agree. I did a couple proofs outside the textbook and they are much more technical.

And I agree there isn't a black and white answer, though for calculus it seemed that I didn't gain much of per-studying the material. Easy is boring to me. I would love to start studying for differential equations and quantum mechanics but then that would mean I would need an in-depth study of calculus I, II, and III. Which brings me back to the point of being very bored at lectures.

 

[bcbwilla]

Well there isn't really much in my hands that I can do. I have to finish calculus I for me to take calculus II, then I have to take calculus II for Calculus III and Differential equations. I think I can take Linear Algebra with Calc II, but other than that, there is nothing I can do.

If you already know them, you can test out of those courses when you enter college.

 

[Nano-Passion]

To re-light your flame: let me tell you that I find Calculus the most boring part about math. The reason for this is because Calculus is actually not math, which you'll realize once you get to the "real math"; I'd call Calculus the way engineers look at Analysis (and Analysis is my favorite branch in math). Do you have access to a library where they would have an introductory book on Real Analysis? I'd suggest you take a look at that :)

That being said, I had never even done Calculus before starting university. Apparently it's not unthought of to have done it in English-speaking countries, but where I'm from (Belgium), people are not really suggested to do that. When I was in high school, I mainly read interpretative books (on my own initiative, reading university courses hadn't entered my mind), like on the meaning of certain theorems (Gödel's being an obvious one) or the history of math; or interpretative books about physics, like Penrose's. Not saying you have to read those books too, but just letting you know that not everybody interested in math and physics is expected to be cracking calculus in high school. As you said, I also never minded not having done it, as the lectures in university were self-evident and would otherwise have been boring (and they were still kind of boring, but I blame that on the fact of it not being "actual" math).

What wasn't boring at all, however, was that first class in proofs I had the first semester of my first year in university. That was magical. I couldn't believe I had been completely unaware of this kind of math my whole (short) life so far...

My point, I suppose, is that you shouldn't worry about it being boring, the actual math will never be :)

I'm surprised haha, I find the theorems in calculus to be surprisingly beautiful and elegant, not to mention brilliant. If Calculus is very boring in comparison to higher maths as you say then I'm very intrigued. I'll definitely look into some introduction to real analysis. What math knowledge is a requirement to such a book?

And I would read non-university texts on the side but frankly I have no idea where to start.

If you already know calculus going into college you can skip some of the introductory classes which leaves time to take more advanced and interesting courses that others won't get the chance to.

I can take this test to see if I can skip a class, but they are relatively easy compared to what it should be and I would feel that I am cheating myself in the heart and breadth of the material. I aim to have a relatively high-level mastery of the material.

I would focus on the interesting parts. For me, related rates type problems, inversion of matrices and solving systems of linear equations are the interesting parts, and there are very boring parts like eigenvalues or (most of) integration which are rather dry and best left till last or till you are interested in them.

After pre-studying calculus, I don't really see the big point of skipping around if I'm going to come back to it later. I'm surprised though, I saw integration as being beautiful. =D

 

[QuarkCharmer]

I always study the lecture material before the lecture. In some cases I have worked through the whole course before taking it. Does that make the lectures boring? Not really. I always find things that I simply missed during self study. I also can spend less time on figuring out how to do homework problems and thus have more time to spend figuring out the proofs for theorems and such that some professors do not cover. It's also nice to be able to help out classmates, and sometimes they pose interesting questions during study sessions that really get you thinking. Sometimes it's boring in a course if I have previously worked too far ahead though. I usually stay about 3 weeks ahead of the class and if I reach that threshold I will simply look up other similar subjects or search the internet for good problems.

 

[Cruikshank]

Study for fun, whenever possible. If you are sick of Calculus and are curious about group theory, read that. If you like infinite series, or prime numbers, or geometry...do it for fun. There will always be something out there new and different and interesting. If you don't want to stray from Calculus too far for some reason, look up "Calculus of X", where "X" can be multiple variables, complex variables, variations, vectors, and more. Just nibble at the beginning. Learn some vocabulary. Explore.

I had the fun ground out of me for far, far too long. I had to tell myself that it was okay never to study math or physics again, in my whole life...only then, was I able to learn that some part of me still *wanted* to learn, for fun. Follow the fun, is my advice. If you need a practical reason, then reflect that anything you find fun you will learn 10 times faster than something you find boring. Math is rich and diverse. It's okay to wander off the central path. Good luck.

 

[Nano-Passion]

Study for fun, whenever possible. If you are sick of Calculus and are curious about group theory, read that. If you like infinite series, or prime numbers, or geometry...do it for fun. There will always be something out there new and different and interesting. If you don't want to stray from Calculus too far for some reason, look up "Calculus of X", where "X" can be multiple variables, complex variables, variations, vectors, and more. Just nibble at the beginning. Learn some vocabulary. Explore.

I had the fun ground out of me for far, far too long. I had to tell myself that it was okay never to study math or physics again, in my whole life...only then, was I able to learn that some part of me still *wanted* to learn, for fun. Follow the fun, is my advice. If you need a practical reason, then reflect that anything you find fun you will learn 10 times faster than something you find boring. Math is rich and diverse. It's okay to wander off the central path. Good luck.

Thank you. ^.^ My problem is probably not knowing where to go. My knowledge of mathematics is limited, I haven't explored other avenues. I want to study differential equations because I know you need it for quantum mechanics but I don't know what to do exactly. My plan is to not rush things: go through calculus and calculus II then I can look through differential equations.

I always study the lecture material before the lecture. In some cases I have worked through the whole course before taking it. Does that make the lectures boring? Not really. I always find things that I simply missed during self study. I also can spend less time on figuring out how to do homework problems and thus have more time to spend figuring out the proofs for theorems and such that some professors do not cover. It's also nice to be able to help out classmates, and sometimes they pose interesting questions during study sessions that really get you thinking. Sometimes it's boring in a course if I have previously worked too far ahead though. I usually stay about 3 weeks ahead of the class and if I reach that threshold I will simply look up other similar subjects or search the internet for good problems.

Thanks for your input. I'm only up to calculus and I study it relatively thoroughly so I don't see anything I missed during the lecture. However, I do agree of having more time for proofs and things like that.