Areas of mathematics that could be self-taught

[mewhoexactlywhat]

I'm currently taking Precalculus in school, and I've been trying to get ahead by teaching myself Calculus, however I would also be interested in learning about other areas of mathematics (especially those which also relate to physics). Does anyone know of a specific division of mathematics that would be useful to know, and could possibly be self-taught?
P.S. If the classes could not be self-taught I might be able to eventually take them at the local college next semester. Any textbook recommendations would also be helpful. Thank you.

 

[Learning Curve]

I'm in AP Statistics and it's a very simple subject IMO. There isn't anything in the field so far that couldn't have been picked up by reading out of a Princeton Review book.

 

[mewhoexactlywhat]

Thanks, I forgot to mention that I'm also currently taking Probability and Statistics. I was thinking about Taking AP Statistics next year, but depending on how I do I might just use a study guide and see how well I can do on the exam. Thank you.

 

[neurocomp2003]

mostly every area of mathematics can be self taught. Whether your looking to just comprehend or to apply is a idfferent story, because some profeesors can give you tips and tricks thorugh their experience.

and it also depends on the time and the amount of prereqs you'd need to learn before reaching your goal. And also on your motivation. and most importantly the book your learning from.

-Tensors (finally read a good chapter of opne of my physics books that explains tensors with clarity...though i can't remmeber which one...its either from my classical mehc or relativity book).
-senior university level analysis
-analysis in dynamical systems(bifurcation theory)
-some computational math.

my trouble isn't comprehending but remembering.

 

[mewhoexactlywhat]

mostly every area of mathematics can be self taught. Whether your looking to just comprehend or to apply is a idfferent story, because some profeesors can give you tips and tricks thorugh their experience.

and it also depends on the time and the amount of prereqs you'd need to learn before reaching your goal. And also on your motivation. and most importantly the book your learning from.
.

That's a good point, I've only taken Algebra 1 & 2, Geometry, and am currently in Precalculus and Probability and Statistics, and I've learned only some of the basic ideas of Calculus through both my Precalculus and Physics classes and some reading I've done. Does Calculus play an important role in most areas of math where it would be considered a prerequisite or is it separate? If it's very closely related to other areas I'll just concentrate on my current classes and self-studying Calculus first (I haven't received it yet but I order James Stewart's Calculus).

 

[Woozie]

If your looking for math that relates to physics then calculus is probably the most important type of math you will ever learn. Make sure you study calculus very hard because it is that basis of almost everything you will do in phyiscs and it is also important for many other types of math that you may get into. Stewart was the right book to choose. See my reveiw at
https://www.amazon.com/gp/product/A2UNMI6FGH/?tag=pfamazon01-20

I was in a similar position that you are in during my last two years of high school and I found that the best source of help was my high school teachers. When they found out I was teaching myself math they gave me some of their old textbooks. They also let me assist in teaching pre-calc and calculus and I tutored a lot of their students. My calculus teacher's husband was a professor at the local university and he started to come to my high school every week and he would give me textbooks, and after I would teach myself something he would help me if I needed it and he tested me on the subjects. The test he gave me counted as credit when I started college a few weeks ago so I didnt have to take classes I already knew. This same professor also found me a full scholarship (with money left over, so instead of paying for college I get paid to go to college) even though my grades in high school were horrible. He also got me into the honors program at my college even though I didnt meet the GPA and class rank requirements. My point is this: your teachers will be happy to help you. Go to them and ask the same questions you are asking us right now.

 

[neurocomp2003]

yes stewarts book is very useful for a person at your level. Its used in many cdn universiies. You might also want to pick up a good linear algebra book.
anton&rorres was the on i used before moving onto friedberg.

oh and if all else fails...mathworld.com is probably one of the best online sites.

 

[mewhoexactlywhat]

Thank you very much, you've been very helpful. Once I get the book if/when I have any problems I will ask my teachers, thanks for the advice.

 

[Learning Curve]

I'm also currently taking Probability and Statistics. I was thinking about Taking AP Statistics next year

weird, the first and only statistics class in my high school is AP stats. I had never heard of other schools having other stats classes before ap stats. Personally I don't think it's needed.

 

[neurocomp2003]

up in Canada we call it FINITE for some reason.

 

[mewhoexactlywhat]

I was considering taking AP Statistics, but eventually decided not to because supposedly a majority of the people that do well have taken regular Statistics first. It's really easy though so far, and my teacher, who also teaches AP, said that the only difference was the pacing of the class. I didn't switch though because I'd already moved my schedule around too much and it was around two weeks into the year already.

 

[Manchot]

I'd like to add one more thing. If you are studying from a textbook, make sure that you do the problems in each section before moving onto the next one. Obviously you don't have to do all of them, but if you do none, you'll fall into the I-think-I-understand-this-but-I-really-don't-now-that-I've-read-the-next-section trap.

 

[mewhoexactlywhat]

Thank you, I'll make sure I answer at least some of the questions.

 

[ludi_srbin]

I agree that problem when teaching yourself is not comprehending but remembering and especially applying. My current teacher doesn't teach us anything. The less I listen to her the more I understand. It is possible to do it by yourself but it takes more time. I had good luck that my Pre. Calc. teacher was great and she taught us a lot about derivatives so now I can pretty much chill for the whole semester. When you take Calculus take BC.

 

[mewhoexactlywhat]

I was intending to take BC but I'm confused now because the teacher said something about AB material on the exam and that you would need to take AB first, and AB is paired with Math Analysis (which I've heard is pretty much just an extension to make the class two hours long) and I don't understand why a more difficult class would be one hour whereas the easier one would be two hours. Does any of this make any sense?

 

[leon1127]

I'm in AP Statistics and it's a very simple subject IMO. There isn't anything in the field so far that couldn't have been picked up by reading out of a Princeton Review book.

The pain of AP stat will come after the chrismax. Though, it is true that no AP can't be picked up from Princeton Review Book.

 

[G01]

The calculus courses at my university use Stewart's book. It's one of the best math books I ever used IMO.

 

[neurocomp2003]

heh stewart earned an honourary degree at my graduation in mcmaster. Don't remmeber if he did his Phd, OR taught there. but he never taught me he moved onto another university whe i got their i think...

but i remember his speech...the mainly point was that if you cna't or don't want to be a science researcher bnut want to remain in the realm of science you can always fall back to science writing for the public...which is a respectable job in itself.

 

[notmuch]

Calculus is a very good self-study topic to learn for a high schooler. If you are able, then do it.

Because of some schedule problems, I could only take up to pre-calculus in high school. I talked to the AP calculus teacher, said that I would want to study for the test and take it... he laughed and said "good luck." Really, it's not that hard. I took his statement as a challenge and learned the topic in exactly half of a semester (1.5 months), took the test, and scored better than most of his class (I started studying calculus with no prior knowledge other than pre-calc).

In other words, if you feel intimidated by it, don't.

 

[mewhoexactlywhat]

Wow, that's great. Thank you. I've actually received the book and it's similar to the precalculus book that we use and so far it's been a really great book (clear, understandable,etc.).

 

[Learning Curve]

The pain of AP stat will come after the chrismax.

huh? what is chrismax?

 

[FluxCapacitator]

I taught myself basic Calculus between 10th and 11th grades, and I found it invaluable. The only real problem I found was that I didn't learn the chain rule properly the first time around, and for some reason integrating by parts just stumped me for a week, but other than that, it's definitely possible.

However, I've been teaching myself math for quite a while, since my Algebra II teacher was horrible, and my precalculus teacher went really fast. In my experience, just teaching yourself basic concepts before a teacher goes over it can help loads, and when you get more horrible teachers in the future, (like my multivariable calculus one), you can just teach it to yourself and end up doing well in the class.

However, I'm not sure what to learn now. I'm currently a high school senior taking Multivariable Calculus this semester and differential equations next semester, but I still want to learn more. I was considering learning linear algebra, but someone told me that it was really hard to learn by yourself.

Any recommendations? Suggestions?

PS- My ultimate goal is to know the math necessary for understanding General Relativity. I know it's difficult, and will take serious time and effort, but I want to start now.

 

[amcavoy]

Calculus is pretty easy to self-study (especially with the help of forums like these). Like someone said above, Calculus by James Stewart is an excellent book. It covers single and multivariable.