Is it Possible to Teach Yourself Advanced Math Topics?

  • Thread starter Substance D
  • Start date
In summary: I was motivated and worked hard. If you are not motivated, it won't work.You are correct, self-taught skills usually only work well if the person is motivated. When I was at university I studied most of the courses on my own. I noticed that I did far better at exams in the subject I had studied... if I was motivated and worked hard. If you are not motivated, it won't work.
  • #1
Substance D
49
0
Hello,

Currently I am a 2nd year physics major, I'm an ok student, I could probably work harder for my marks. I was thinking about doing a major in Mathematical Physics because of the extra math classes it involves that sound interesting, but to do this, it would involve around 2 more years of just math classes basically. I was thinking about the extra time and $$$ involved in that and was wondering if I could just teach this stuff to myself, since I basically do that already with most of my math classes because I have a hard time following my prof. I'm basically interested in Number Theory, Differential Geometery, Topology, Non-Linear Dynamics/Chaos Math... I was wondering if anyone has taught any of these subjects to themselves just for the fun of it? Its obviously hardwork and I'm of average intelligence, just wondering if anyone else was in the same boat.

Thanks!
 
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  • #2
Yes, but it's going to take longer than it would with a professor, tutorials etc to help explain it to you.
 
  • #3
Yeah, that's for sure. I guess I've also being somewhat disapointed in my math profressors lately because I just end up teaching myself the entire course it seems, and making zero reference to any of their notes.
 
  • #4
Substance D said:
I was thinking about the extra time and $$$ involved in that and was wondering if I could just teach this stuff to myself

The whole point of being in school is to take advantage of the expertise of the faculty (and sometimes graduate students or even other undergrads if your school is very good) to learn the most in the least time, and to learn it as well as possible. So I'd urge you to either focus on improving your grades in the courses your already taking, or to decide to get serious about studying and increase your course load and redouble your effort.

Substance D said:
Yeah, that's for sure. I guess I've also being somewhat disapointed in my math profressors lately because I just end up teaching myself the entire course it seems, and making zero reference to any of their notes.

Sounds to me like you may not be taking advantage of office hours. If that is so, you should reform immediately! College is a once-in-a-century opportunity to really learn a lot and to make something of yourself intellectually; if you are not devoting your full attention to getting the most out of the experience you are cheating yourself.
 
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  • #5
Substance D said:
Yeah, that's for sure. I guess I've also being somewhat disapointed in my math profressors lately because I just end up teaching myself the entire course it seems, and making zero reference to any of their notes.

I'm in the same boat.

Chris does have a point too though.
 
  • #6
I would recommmend not teaching yourself everything, go take a proper course and teach yourself the holes from the course. Most of what I know is self taught, and I have tonnes of holes that wouldn't be there if I was allowed to enter higher level courses.
 
  • #7
Most of what I know is self-taught, so there really is nothing amazing about teaching youself. All you need is motivation.
 
  • #8
I agree of course that above a certain level, most of what we know is self-taught. That's just the natural consequence of achieving a certain level of expertise! But let's not lose sight of the point that the OP is not yet an expert but hopes to become one. I insist that he will maximize his chances by taking his formal coursework much more seriously and applying himself harder, taking advantage of office hours, the math and physics research libraries at his uni, inexpensive access to computer software like Mathematica, Maple, Matlab, and other resources offered at his university.
 
  • #9
Its kind of a class by class thing, I know with my physics profs, I've done great in the class and learned from their notes and have had conversations with them etc. I guess its just this one prof I have right now has been disheartening to me, I've talked to him and borrowed some of his textbooks, so I wouldn't say I am wasting my experience because I generally am trying, I guess what worries me is that in order to take some of these higher level math classes I would have to re-take some other math classes for no credit, so that's a lot of extra time and money, and yes I know school is a once in a lifetime chance etc, but those are real factors to include
 
  • #10
Teaching yourself should work ok. if you are disciplined enough. When I was at university I studied most of the courses on my own. I noticed that I did far better at exams in the subject I had studied myself. I did less well at the courses that I followed at university.

I don't know what the rules at your university are, but we were allowed to sit exams for any subject...
 
  • #11
Personally, when given the option, take the course, because during the course, nothing is stopping you from learning the content ahead and by yourself. The advantage of taking the course is the obvious teaching experience of the teacher, who most likely knows the content extremely well, and will be able to give better insights into the topic that he/she has acquired from teaching it for years and years, than you can from learning it for the first time for yourself.
 
  • #12
It really depends on the student what is better. In my case, I was used to studying myself. In high school I was far ahead and I studied math from university books. So, I guess that I'm not so good at sitting in a room and listening to a lecturer...
 
  • #13
I'm curious if anyone here knows anyone in the science field(physics is what I am interested in) who had to learn a branch of math or something on their own for work?
 
  • #14
Every researcher has to teach himself/herself/itself stuff all the time. But UG students should take advantage of the opportunity to learn how to do that efficiently from faculty who are well practiced in this art.

IMO, this thread is marching in circles. Does this discussion have a point and if so can someone tell me what they think it is?
 
  • #15
I'm not trying to disrespect the faculty or anything, I really wish someone would understand my situation of not wanting to spend the extra few years and thousands of dollars for classes that I may not be good at...but anyways. Thanks for all your replies, and sorry for wasting your time Hillman ;)
 
  • #16
I'm glad you've kept your sense of humor. Speaking for myself, I do sympathize, but it is especially when you are "not good at" T that you most need the help which faculty can provide! If I could offer a better solution than "soldier on", I would!

I am sorry that you are feeling frustrated with some of your math courses right now, but at some point, math courses have already been made as easy as we can make them, given limits on resources (especially faculty time) and given the relentless pressure (in part from students who wish to get out as quickly as possible!) to compress the curriculum to a far more compact form than is consistent with good pedagogy. I hope you have a good Thanksgiving (if you are in the U.S.) and feel better after the break.
 
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  • #17
Definitely teach it to yourself, the math department does not cater to physics majors, and so you would find the majority of those classes irrelevant for your future in mathematical physics. Instead you should teach it to yourself in your spare time, graduate quickly in whatever non-mathematical physics major you have already started. If you went to a average graduate school, you would never miss having taken official versions of those math classes.
 
  • #18
Crosson said:
Definitely teach it to yourself, the math department does not cater to physics majors, and so you would find the majority of those classes irrelevant for your future in mathematical physics.

I don't understand--- are you intimately familar wit the math and physics departments at the OP's university? Or are you making an unjustified and probably unjustifiable general statement about all math and physics departments?

Crosson said:
If you went to a average graduate school

Did the OP say what school he is enrolled in? I can't find that, although I agree that it seems one can infer from what he says about course offerings that he is enrolled at some university strong in math/physics.
 
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  • #19
"Don't let schooling interfere with your education." - Mark Twain

"Too many people are thinking of security instead of opportunity." - James F. Bymes

"Schooling is no longer about the opportunity to learn. It is about future job security."

I have lots of opinions (negative) of how academia works. It certainly isn't a constructive system we have. From elementary to university, we have lost the opportunity to learn.
 
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  • #20
Thanks everyone for your input, just another reason why I think these forums are by far the greatest on the internet. Since I am only 2nd year, I've got a long way to go. I think after my 3rd year (when I take my final math class - Complex Anaylsis) I should have a better idea of where I am at. I start the xmas holiday soon and a week after I come back (Jan 6th) I have a exam on Laplace transforms, so my plan is to get some extra textbooks on it (although my uni is on strike right now, so I may not be able to take them home) and really try my hardest to ace the test, see what I am capable of!

So seeing how my 3rd year goes, after my 4th, I may stay a few years and get my major in math, I think it will be worth, obviously for job reasons but also intellectual ones, not to mention I could probably start to contribute to these forums a lot better :)
 
  • #21
Since you're in the second year why not consider a theoretical physics option as opposed to a mathematical physics one? The math is there but more localised towards analysis and sometimes analytical number theory. The texts in this area are great, and the costs and burden should be somewhat less for the course.
 
  • #22
Of course you can! Many great minds in history were self-taught or were auto-didacts like : Issac Newton, Benjamin Franklin, Nietschze, Chris Laegan, and many others. I think in some cases , school can lower your self-estem because you might be labeled with a "learning disability" when in reality, the teacher isn't presenting the material clearly to you. The best option might be teach yourself.
 
  • #23
I teach myself all math the time. I don't really think I'm missing much, because math is all on paper anyway. In science courses you sort of need the diagrams and demonstrations. So far, I have been doing well - evident by taking midterm tests found on the web. The only disadvantages to this are that you sort of don't have guidance, or a prof who gives you intuition. You can compensate by waching online lectures and finding solutions on the web.
 

1. Is it possible to teach yourself a new skill or subject?

Yes, it is definitely possible to teach yourself a new skill or subject. With access to various resources such as books, online tutorials, and practice exercises, one can learn almost anything on their own.

2. What are the benefits of teaching yourself?

Teaching yourself a new skill or subject can have numerous benefits. It allows for self-paced learning, personalized study methods, and a sense of accomplishment. It also helps in building self-discipline and critical thinking skills.

3. How do I know if I am capable of teaching myself?

Anyone can teach themselves with dedication and determination. It is important to have a growth mindset and be willing to put in the time and effort to learn. With the right resources and mindset, anyone can successfully teach themselves a new skill or subject.

4. Are there any tips for effectively teaching oneself?

Some tips for effective self-teaching include setting specific goals, creating a study schedule, using a variety of resources, and seeking help from experts or mentors when needed. It is also important to stay motivated and take breaks to avoid burnout.

5. Can I teach myself a subject without any prior knowledge?

Yes, it is possible to teach yourself a subject without any prior knowledge. However, it may require more time and effort. It is recommended to start with the basics and gradually build upon your knowledge. Seeking guidance from experts or joining online communities can also be helpful in this case.

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