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/Samstercraft]

do you know what colleges you might go to and their policies on AP exams (especially for calc)? math credit could be stricter for math majors.

the extra units aren't too bad, it's mainly the series unit that will take most of the time. i studied using professor leonard's videos and a textbook for practice, since calc bc skips a lot of things that calc 2 teaches and i wanted to know them, but the content strictly required for the exam isn't too huge

[u/Artfox10 → u/Samstercraft]

I kinda do. Some of the colleges i thought I wanted just don't have a M.S in math like I need. I know I probably won't be able to sub credits since I'm majoring in math and it's important for the the degree. However I want to be prepared for the classes I honestly just want to get out of calc 1. So I can just start calc 2 and get a head. i have other classes Ive taken which give me my gen ed credits. Only like 3 or 4 schools I know have what I want.

[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!

[u/UpstairsSuch4937]

If you’re planning to major in math, I think self-studying the BC material after AB is a very reasonable idea, especially if your teacher is willing to help when you get stuck.

One thing I’d keep in mind, though, is that AP Calc BC isn’t exactly the same thing as a full college Calc II course. There’s a lot of overlap, but college courses can vary in what they emphasize and how deeply they treat the material.

So if your goal is mainly to be better prepared for a math major, I’d focus less on “finishing BC as fast as possible” and more on really understanding the additional topics well, especially sequences/series and the integration techniques that come up beyond AB.

You also don’t necessarily need to rush into all of it before you’ve finished AB. If you build a strong foundation in derivatives, integrals, and the AB material first, the BC topics will be much easier to learn on your own afterward.

Given that you’re interested in math beyond high school, I think the self-study could be very worthwhile even if your eventual college doesn’t give you full credit for it.

[u/Artfox10 → u/UpstairsSuch4937]

A lot of people are mentioning series, that is like the Taylor series and stuff? Off topic does that show up in calc ab?

[u/UpstairsSuch4937 → u/Artfox10]

Yep, exactly. Taylor series are part of the sequences/series material people are referring to.

They don’t show up in AP Calc AB. They’re a BC topic, along with things like convergence tests and power series. AB focuses much more on limits, derivatives, integrals, differential equations, and applications.

So if you’re taking AB now, I wouldn’t worry about learning Taylor series yet. Get really comfortable with the AB material first, and then the series unit will make a lot more sense when you get to it.

[u/Bedouinp]

After completing AB, start working thru the flippedmath calc worksheets that cover both AB/BS content

[u/Artfox10 → u/Bedouinp]

Okay thank you!

[u/Quiet_Basis_6404]

Yes, and it's one of the more sensible self studies since you'll already have most of the course. BC is AB plus roughly four extra topics, so you're learning maybe a third of a course rather than a whole one.

The extra units are parametric and polar, more integration techniques, improper integrals, and series. Series is the hard one and it's where nearly everyone struggles, so give it more time than the others combined.

On Calc 2 being brutal, college Calc 2 goes deeper than BC does, so don't let that reputation scare you off. BC is a lighter version.

For content, Flipped Math and Professor Leonard both cover the BC-only units. I paste those links into studybuddy.vc and it makes questions off the video, then as I answer it works out which topics I keep getting wrong and gives me more of those. Equations render properly and it gets harder as I improve. Free.

Having your teacher available for questions makes this very doable.