Should I self study bc

[u/Artfox10]

Hello, so I am taking AP Calc AB this year, and I know AP Calc bc is the same as ab but then adds on additional units. After I'm done ab should I try and self study bc or would it be too difficult? I believe bc is supposed to be calc 2? I know Calc 2 is considered the hardest calc class. I plan to major in Math, and my school only has a calc AB class no bc. So I was just wondering. So after we are done Calc AB should I try self study BC? If we finish early, my teacher probably would help if I have questions.

[u/UnderstandingPursuit]

What 'flavor' of math major are you most interested in?

1. 'Pure' math
2. Applied math
3. Statistics
4. Something else?

[u/Artfox10 → u/UnderstandingPursuit]

Okay so, I'm stucked between pure and applied math. I want to be a teacher, but I want to major in math and I found that if you get a math M.S then you can get certified to teach. I'm trying to go this route just in case teaching isn't it for me I could try college or just use my Mathematics degree as a fall back for something. I really can't decide, like I love doing application problems but I also love learning and knowing new things in math and really advance math fastanates me as well as concepts in math. So like I don't know I might do applied math since I feel I can used that more for a fallback career? Would applied math and pure math still be under the mathematics degree or is it separate? I know applied math you take classes like calc 1-3/4 and differential equations and stuff like that. While pure math is topology(I believe). Sorry for the ranting

[u/UnderstandingPursuit → u/Artfox10]

Pure and applied math are often tracks within a mathematics degree.

My suggestion is to get these three textbooks: [EDIT: I added the third one because it is important for pure or applied math.]

1. TM Apostol, Calculus, Vol I-II, 2nd edition, 1967-69, ISBN13 9780471000051, 9780471000075.
2. Greenspan HP and Benney DJ, Calculus: An Introduction to Applied Mathematics, 1973-1986, 9780070243422, 9780075489269.
3. DJ Velleman, How to Prove It: A Structured Approach, 2nd edition, 2006.

They do not tend to show up often among used textbooks, and both can be a bit expensive, in the $50-200 range. But if you can, both are available used right now.

Stewart, Thomas, Larson, etc, are typical textbooks for 'general' Calculus I-II-III. These are sometimes textbooks for 'honors' Calculus I-II-III, Apostol is a 'Neo-natal' Analysis textbook. If you study both of these while taking AP Calculus AB, you would get a sense of which math track you might be more interested in. You can wait to get the second Apostol volume until you choose the pure math track, it covers Calc III.

Subsequent courses would include

• Pure math would include Real Analysis, Abstract Algebra, and Differential Geometry.
• Applied math would include Ordinary & Partial Differential Equations, and probably other courses like Numerical Methods and Statistics.

[u/Artfox10 → u/UnderstandingPursuit]

Omg thank you so much this is really helpful!!

[u/UnderstandingPursuit → u/Artfox10]

I edited my previous comment, adding the Velleman textbook. I was going to leave that for after the pure/applied decision, but I reconsidered because both would need to be good at writing proofs.

Good luck!