What's the difference between self-teaching and taking courses in college?

[Woozie]

I am a freshman in college with a double major. Most of what I know I am self taught in. I have talked to different professors about what courses I should take and some of them recommended taking courses that I already know. Some said to do this for an easy A and this does make sense. But others say I can't really learn things on my own. I tried proving them wrong. I did this by testing out of all of my required calculus classes, differential equations, and elementary classical physics I and II (which is the first level of calc based physics). Even after testing out of classes that people said I couldn't do on my own (many have told me that I couldn't learn calc II and III and differential equations on my own and my physics professor doesn't think I am ready for modern physics even though I already read the whole textbook and done almost every problem) I still have people tell me I should take the courses. I also had a professor tell me to take quantum mechanics I and II even though he knows that I know this already.

A question that has been bothering me for a long time is, what's the difference between self teaching and taking courses? Why should I take a course in classes that I already know instead of testing out of them?

 

[Pseudo Statistic]

I'm in a situation similar to yours, but in high school...
I think the answer to that is simple, or atleast this is how I see it; being in a classroom gives you a completely different experience from doing courses privately.
e.g. The teacher could bring up a discussion about, say, integrals and start sharing his theories and what he thinks are right and wrong, and the class can start a debate and... well, you get the point.
It's just experience I guess.
Think of it this way, if a man was left alone to learn EVERYTHING, he would probably not end up gaining as much knowledge as he were if he were to learn with others and hear other people's views on things.
That and you might meet the girl of your dreams in Calculus III. ;)

 

[Pengwuino]

That and you might meet the girl of your dreams in Calculus III. ;)

Thats funny... even though I did see a somewhat cute girl in Calculus 3... she was obviously an alien because cute girls don't know math.

 

[LeonhardEuler]

I am a freshman in college with a double major. Most of what I know I am self taught in. I have talked to different professors about what courses I should take and some of them recommended taking courses that I already know. Some said to do this for an easy A and this does make sense. But others say I can't really learn things on my own. I tried proving them wrong. I did this by testing out of all of my required calculus classes, differential equations, and elementary classical physics I and II (which is the first level of calc based physics). Even after testing out of classes that people said I couldn't do on my own (many have told me that I couldn't learn calc II and III and differential equations on my own and my physics professor doesn't think I am ready for modern physics even though I already read the whole textbook and done almost every problem) I still have people tell me I should take the courses. I also had a professor tell me to take quantum mechanics I and II even though he knows that I know this already.

A question that has been bothering me for a long time is, what's the difference between self teaching and taking courses? Why should I take a course in classes that I already know instead of testing out of them?

I think it would be good to take the classes for an easy A if you really know it will be easy because this way you can demonstrate to others, such as grad schools, that you really do know what you say you do.

 

[Woozie]

I'm in a situation similar to yours, but in high school...
I think the answer to that is simple, or atleast this is how I see it; being in a classroom gives you a completely different experience from doing courses privately.
e.g. The teacher could bring up a discussion about, say, integrals and start sharing his theories and what he thinks are right and wrong, and the class can start a debate and... well, you get the point.
It's just experience I guess.
Think of it this way, if a man was left alone to learn EVERYTHING, he would probably not end up gaining as much knowledge as he were if he were to learn with others and hear other people's views on things.
That and you might meet the girl of your dreams in Calculus III. ;)

Last year (my senior year in high school), when my calculus teacher found out that I already knew calculus, she made me an assistant teacher and in that course we never had any sort of discussions or debates and I didnt learn anything new. The only difference I seen between self teaching and taking courses is that about half of the people who took the course didnt learn proofs and didnt really understand concepts (when I was at a study group I was suprised to hear that half of the students didnt know that the derivative was the slope and we were already done with derivatives). I was also an assistant teacher in pre-calculus last year and had a similar experience. I don't know if this happens in all classes or if your teahcers were just better than mine.

By the way, where I am from the cute girls rarely ever take calculus (or anything else that requires thinking). Maybe I should enroll in Pengwuino's class.

 

[Math Is Hard]

By the way, where I am from the cute girls rarely ever take calculus (or anything else that requires thinking). Maybe I should enroll in Pengwuino's class.

For that matter, I haven't seen very many cute guys in calculus class either.

Now, our teacher for one of the classes was gorgeous - she looked like a Persian Marilyn Monroe. The gals did much better than the guys in that class - I think the males were a little distracted!

 

[mattmns]

There was a very cute girl who sat next to me when I took calc 3, I still managed to pass somehow

As for skipping classes that you already know the material for. If you passed the exams you are probably good to go. I doubt you could pass without having a good knowledge of the material. Still, though, it never hurts to go over the material again, and it will make your gpa look good for the first few semesters

 

[Dr Transport]

This is something you are going to have to take up with some of the faculty and ultimately the Registrar of the school. The Registrar in many cases has the ultimate authority to overrule the department on what courses the student uses towards a degree and whether or not they count. For example, if the university requires Physics I & II for an engineering degree, the only way you can test out is to pass the Advanced Placement tests.

Another case in point, I took a series of courses in graduate school getting my masters, when i went back for a PhD I tried to transfer thoses credits. The Registrar said that the level wasn't high enough, i.e. they were 500 level course numbers, not the 700 level course numbers that they assigned, so they couldn't be transferred and that I'd have to take them again. SInce teh university president was a faculty member in my department, I appealed to him and ultimately won my case and didn't repeat them.

The bottom line is to be careful, retake the courses if you are advised to and keep the Department in the loop at all times.

 

[Poop-Loops]

You did the labs on your own?

PL

 

[jtbell]

This is something you are going to have to take up with some of the faculty and ultimately the Registrar of the school. The Registrar in many cases has the ultimate authority to overrule the department on what courses the student uses towards a degree and whether or not they count. For example, if the university requires Physics I & II for an engineering degree, the only way you can test out is to pass the Advanced Placement tests.

Different colleges and universities surely have different policies and procedures on exempting students from required courses. Where I teach, the department can authorize waivers from specific requirements for specific students, subject to review by the Vice President for Academic Affairs (who many schools call the Dean or the Provost or the Chief Academic Officer). At my school, the Registrar doesn't set academic policy, but simply enforces policies set by the VPAA and the departments. In general, I would start with the department chairman, and find out what the policies and procedures are at your school. In extreme cases you might go directly to the VPAA/Dean/whoever.

 

[Woozie]

We don't really have any definite policy at my college. I was told that I would have to take placement exams or pass the A.P. test. I got a five on my electricity and magnetism physics c test which should have gotten me out of elementary classical physics II. But when the professors found out that I never really took the course, I only took the test for the course, they recommended that I take the course anyway, as if there is a real big difference between taking the course and teaching myself. Because of this, they wouldn't let me in modern physics at first, until I repeately insisted.

Also, in math I was supposed to have taken test in calc II, and III, and ordinary differential equations. They told me that the test that I had already taken didnt count. Then they went ahead and gave me credit for these classes based on the test that supposedly didnt count.

 

[sony]

Hmmm, there's quite a few cute girls in Calc.1 at the university I attend... :P

 

[mathwonk]

i seem to recall a novel by jean paul sartre "l' autodidacte" (the self educated man) in which the title character had learned only by reading. he was sort of a pitiful ignoramus in the opinion of the author it seems.

Of course you are not really self taught, you are a student of the author of your book.

Now sadly, it is normal practice in most universities to use books that are written by mathematicians or even physicists who are actually less well informed on many topics than are the professors teaching the class.

so to take as your teacher the book's author instead of the class lecturer may well mean you are choosing the poorer of two alternatives.

The other problem is that if not truly self taught, you are indeed truly self examined, and that is a major problem. I.e. you are the one deciding whether you know the material or not, or at best you are exposing yourself only to some possibly trivial problems in the book, and maybe to one attempt at a comprehensive exam, to exempt the course.

Now it is very very hard to design an exam whose successful passing truly guarantees that you know a subject.

Of course it is possible that you do really know this material well, but it is not usually the case for most students.

If you are at anything like a decent school, your professors are active researchers, whereas most textbook writers are not so current, but are writing things that they themselves learned long ago.

If you are at a school like Harvard your attitude is absurd, as the professors are far above the level of almost all textbook writers, and their lecture notes could be published as is, to form textbooks better than most existing ones.

Years ago George Mackey did essentially this and produced one of the best texts on complex analysis as a van nostrand paperback.

Textbook writing is normally an activity people take up after retiring from research although not always.

Unless you are a very unusually gifted student, it is also likely that your professors really do know a lot more than you do, as most of them are functioning at a level far above the level of the courses they are teaching, and the best ones incorporate this knowledge into the classroom.

Remember, even if your physics class uses the lectures of the great Feynman, he has been dead for some time after all, and thus is hardly current, e.g. on string theory, or quantum cohomology.

Of course your professors may be poor ones, and your class time may be wasted, but then you would be better off getting into a better school perhaps.

There are many people fom whom you can learn profitably, and much faster than by reading. I would say it should take most students several hours to read and absorb what I can tell them in 50 minutes in class. Even longer perhaps to decide which is the most valuable thing to read.

I teach at a traditional state school, but every year that I teach my class, I introduce something that I have not done before, and which is not in our book, although indeed if you read only the best books, such as Courant, you will find almost everything I have ever thought of.

You might try having a conversation with some of your professors. If they impress and interest you, try their classes; if not, try finding some who do.

you are very fotunate to be able to elarn so easily by reading but the best mathematicians learn from other ones mostly, except perhaps Ramanujam. If you are like him, I have nothing to tell you, but then you would probably not be asking either.

 

[Dr Transport]

Different colleges and universities surely have different policies and procedures on exempting students from required courses. Where I teach, the department can authorize waivers from specific requirements for specific students, subject to review by the Vice President for Academic Affairs (who many schools call the Dean or the Provost or the Chief Academic Officer). At my school, the Registrar doesn't set academic policy, but simply enforces policies set by the VPAA and the departments. In general, I would start with the department chairman, and find out what the policies and procedures are at your school. In extreme cases you might go directly to the VPAA/Dean/whoever.

I mentioned the Registrar because in many cases they are the first in a long line to the VP of Academic Affairs...

 

[rocketboy]

For that matter, I haven't seen very many cute guys in calculus class either.

That's because you weren't in my class.

In reply to #1, I think it's true that the experience (as another poster stated - sorry I forget your name) is definitely worth taking again. You may see something from a different view, or perhaps realize something you didn't see previously. Not to mention the easy A+'s that you'll get.

 

[Woozie]

i seem to recall a novel by jean paul sartre "l' autodidacte" (the self educated man) in which the title character had learned only by reading. he was sort of a pitiful ignoramus in the opinion of the author it seems.

Of course you are not really self taught, you are a student of the author of your book.

Now sadly, it is normal practice in most universities to use books that are written by mathematicians or even physicists who are actually less well informed on many topics than are the professors teaching the class.

so to take as your teacher the book's author instead of the class lecturer may well mean you are choosing the poorer of two alternatives.

The other problem is that if not truly self taught, you are indeed truly self examined, and that is a major problem. I.e. you are the one deciding whether you know the material or not, or at best you are exposing yourself only to some possibly trivial problems in the book, and maybe to one attempt at a comprehensive exam, to exempt the course.

Now it is very very hard to design an exam whose successful passing truly guarantees that you know a subject.

Of course it is possible that you do really know this material well, but it is not usually the case for most students.

If you are at anything like a decent school, your professors are active researchers, whereas most textbook writers are not so current, but are writing things that they themselves learned long ago.

If you are at a school like Harvard your attitude is absurd, as the professors are far above the level of almost all textbook writers, and their lecture notes could be published as is, to form textbooks better than most existing ones.

Years ago George Mackey did essentially this and produced one of the best texts on complex analysis as a van nostrand paperback.

Textbook writing is normally an activity people take up after retiring from research although not always.

Unless you are a very unusually gifted student, it is also likely that your professors really do know a lot more than you do, as most of them are functioning at a level far above the level of the courses they are teaching, and the best ones incorporate this knowledge into the classroom.

Remember, even if your physics class uses the lectures of the great Feynman, he has been dead for some time after all, and thus is hardly current, e.g. on string theory, or quantum cohomology.

Of course your professors may be poor ones, and your class time may be wasted, but then you would be better off getting into a better school perhaps.

There are many people fom whom you can learn profitably, and much faster than by reading. I would say it should take most students several hours to read and absorb what I can tell them in 50 minutes in class. Even longer perhaps to decide which is the most valuable thing to read.

I teach at a traditional state school, but every year that I teach my class, I introduce something that I have not done before, and which is not in our book, although indeed if you read only the best books, such as Courant, you will find almost everything I have ever thought of.

You might try having a conversation with some of your professors. If they impress and interest you, try their classes; if not, try finding some who do.

you are very fotunate to be able to elarn so easily by reading but the best mathematicians learn from other ones mostly, except perhaps Ramanujam. If you are like him, I have nothing to tell you, but then you would probably not be asking either.

Thank you for this info. This is the best argument I have seen yet for taking the courses. Now I won't feel like I am wasting time or anything. This question of taking courses that I already studied has been bothering me for some time and I am glad I got a really good answer. From now on I will probably take the courses that I already know if the professors suggest it. I will definitely take quantum mechanics now instead of testing out of it as I had intended to do. I wish I had heard this argument earlier; it may have affected what courses I enrolled in.

But I am still wondering why I didnt see any big difference between what I taught myself pre-calc and calc and when I was in the classroom. My only experience with pre-calc is as an assistant teacher (I never took the class as a student) but I still did all the homeworks and tests and, if I wasnt the one teaching, I participated in class almost as a student. I was technically enrolled as a student in calculus even though I didnt really function as one. I didnt really see any difference between self teaching and course work. But then again, these where high school courses and maybe college will be different.

 

[Poop-Loops]

Let me try this again: Did you do the LABS on your own? Labs are a part of physics, like it or not. It's more than just the math. It's a science, therefore it needs experiments.

PL

 

[Woozie]

No I didnt do any labs yet. I am currently enrolled in intermediate lab II (which, at my school, comes before lab I). Our school only requires 2 semesters of labs but I am going to try to get into some research so that I can get more lab experience.

 

[neurocomp2003]

certtain classes are by the book because of the teacher...and the books if good are sufficient them selves...heh i should know i skpped like 60% of my classes(though i probably shouldn't have skipped QM and neuropsych 2-3...
Some easy courses that come to mind when i was learning are analytical mech/combinators/graph/relativity/dynamical systems...self learning is a good thing...but can you apply it.
Some things to note.
[]The universities want is the money...see if you can just sit the class(usually 1/2 the price).
[]Another thing is to associate your workhabits with other students in the program
[]profs like to get ot know people
[] see if you can get TA jobs.

LASTLY
If you have project courses...not labs...i suggets you ask to enroll in it to test out your knowledge. Or do an individual side project with a professor...if not i suggets talking to the professors and seeing if you can do a side project that's worth the full of the grade of the course you have to take...some teachers are lenient because they enjoy testing the students skill i found but others don't want hte hassle.

Oh and haveyou a firm grasp on pertubation theory applied to QM? or on QFT and algebra and clifford algebras and field theory and dynamical systems and i guess stat mech.

 

[Woozie]

I don't know how firm my grasp on quantum mechanics is but I think it is good. I have worked with a professor a little on it and he thinks I am good. So far I have only read one textbook on the subject (which is usually enough). In this case though I plan on reading a few more textbooks that are at the same level to be sure I know it well. The reason for reading multiple texts is that I plan to go into particle physics and everyone keeps telling me that quantum mechanics is very important. And I need more work on pertubation theory so I will continue to study it. I want to study QFT but I am not sure if I have the math yet (I haven't finished abstract algebra or group theory yet). And barely even studied stat mech but I do plan on taking the course.

 

[mathwonk]

In high school. most calc teachers are people who at most have taken calc in college, and that's it. In college there is a great diversity of instructors. the least qualified are graduate stuidents who are working on graduare degrees, usually PhD's, and some of them are excellent teachers. They are also working toward higher degrees than most high school teachers have.

the most qualified mathematically, are full professors who have done years of research in mathematics and have taught the course for decades. Of course the older they are, sometimes the less energetic they are.

the best are usually the younger full or associate professors who are also considered excellent teachers, and not of them all are excellent.

so scout around, ask other students, and read teaching reviews, and look at the rank of the teachers and talk to the teachers.

It is certainly possible to get a bad teacher in college, but it is also possible to get someone who reaslly knows a lot and can also teach.

at least in college there are people who are active researchers in the subject sometimes at a world class level, and this almost never happens in high school.

Hint: The best professors are often found teaching honors classes.