Should I Take Calculus 2 and 3 in High School?

[yyttr2]

I am about to be a senior in high school and I have the opportunity to take distance calculus two and three ( I passed Ap calculus AB with a 5 and my school does not offer BC). The classes I am already taking for high school are:
1. A.P. English lit.
2. Oral com/art
3. A.P. Chemistry
4. A.P. World history.
5. Anatomy and physiology
6. Botany and zoology
7. Study hall.As a math major would it be beneficial to do this? To take calculus two, then calculus three during my senior year. Is there some reason why I should wait for college? Should I only take calculus two? If you have any advice or reasons to do or not to do various things please post! I have the correct things to apply to these classes ready to be sent off. I am just unsure about whether or not I should.

 

[kamikaze1]

If u truly want to become a mathematician and learn math in depth and want a good foundation, I suggest you look back at calc I and learn the theory behind it using a textbook different from the one ur high school used. here is a helpful link https://www.physicsforums.com/showthread.php?t=122924

At the same time, u can take calc 2 at college, the quality of teaching should be better since the prof/instructor should be more knowledgeable than ur hs teacher.

 

[TylerH]

I suggest you look back at calc I and learn the theory behind it using a textbook different from the one ur high school used.

IMHO, that would be suicide without a proof class or, at least, a gentle intro to proofs by reading a the first few chapters of a proof book.


It would be hard to take a math with your schedule. I wouldn't want to, but if you think you can handle it, then there's no reason not to. Does your state pay for dual enrollment? That's one reason why it would be REALLY beneficial. Obviously, the more college classes you can take that are payed for by the state, the less you have to pay for yourself when you're in college.

 

[yyttr2]

I obtained some updates on this. Each calculus class last one semester and high-school has told me that I can obtain half a credit in high school for each college semester I take. If then I take both calculus two and three the Mathematics chair at my school said I can have sort of an 'independent study' class in high school. So my courses now look like:

1. A.P. English lit.
2. Oral com/art
3. A.P. Chemistry
4. Calculus2/Calculus3 (i'm not sure how this would work exactly.)
6. Botany and zoology
7. Study hall.
(I need English to Graduate, and I wish to take all the other science courses so world hist is the best option to get rid of.)
As for what kamikaze1 said, I try to study a lot independently and I would hope that, along with what I know now, I could have independently gained the mathematical maturity needed to handle something such as linear algebra or Differential equations before my freshman year. I own a lot of calculus books, including Walter Rudins "principles of mathematical analysis" (My calculus teacher let me have all her old books). (I have yet to get through the first chapter of Rudins book, I suspect it is impossible haha)
I do have to pay for both the courses, there is no getting around that. I am obtaining money from my school for other reasons that would cover the cost however.

 

[TylerH]

You could self-study the linear algebra before you're done with the cal sequence. AFAIK, cal and LA are independent.

 

[WannabeNewton]

Just a quick question: is your calculus 3 course the same thing as a multivariable calculus course? I ask because my high school offers multivariable calculus but it isn't under the name Calculus 3 and I would like to inquire with them as to why they do not offer it if calculus 3 does indeed have a different course description from multivariable. Thanks.

 

[TylerH]

Calc III is multivariable calc.

 

[eumyang]

Calc III is multivariable calc.

That presumes a three-semester sequence in the US. (Probably obvious, but I figure I'd mention it.) Some colleges in the US offer Calculus as a 4-quarter sequence, with multivariable calc. in Calc. IV. And some offer Calculus in only 2-semesters (either in an accelerated form, with knowledge of basic calculus in high school assumed), with multivariable calc. in Calc. II.

 

[yyttr2]

I will just post the topics covered in each course.
Ap calculus AB (Highschool):
1. Limits
2.Differentiation
3.Applications of differentiation
4.Integration
5. Logarithmic, exponential and other transcendental functions
6. Applications of integration

Calculus II (colllege):
1.Applications of integration
2.Integration techniques, L'hopitals', improper integrals
3.Infinite series
4. Conics, parametric equations and polar coordinates
5. Vectors and the geometry of space


Calculus III (college):

1. Vectors and the geometry of spcae
2.Vector-valued functions
3.Functions of several Variables
4.Multiple integration
5.Vector analysis
6. Differential equations