What math course comes after Calc BC?

[Sharon77]

My son just finished Calc BC and found it easy. He is definitely math bent!

He wants to take the next math class.

What would that be? He's more business oriented, not science.

 

Any suggestions? I never went past Algebra so this all new to me!

[Kassia]

Multivariable Calculus (Calc 3) or Linear Algebra

 

He could also take AP Statistics

[JenneinCA]

Differential Equations was the class that happened for us after finishing the calculus sequence.

[Sharon77]

Multivariable Calculus (Calc 3) or Linear Algebra

 

He could also take AP Statistics

 

I looked at the Cal 3 class description and he said he already covered all of it.

He did say Linear Algebra would be interesting. Is this correct? What even is that?!

 

Is there nothing called Calc 4?

[vonfirmath]

I looked at the Cal 3 class description and he said he already covered all of it.

He did say Linear Algebra would be interesting. Is this correct? What even is that?!

 

Is there nothing called Calc 4?

 

No. Evidently Calculus 3 IS considered the next course some places. Maybe going more in depth on subjects that are addressed in BC?  I passed the Calculus BC exam in HS and went on to further math like Differential Equations and Discrete Mathematics in college. No more additional Calculus. 

Edited July 12, 2016 by vonfirmath

[Kassia]

I looked at the Cal 3 class description and he said he already covered all of it.

He did say Linear Algebra would be interesting. Is this correct? What even is that?!

 

Is there nothing called Calc 4?

 

 

Differential Equations can also be called Calc 4.  My son took it without taking Calc 3 first and did fine, but did say there was Calc 3 in the course.  I don't really know what Linear Algebra is, but two of my sons took it and my math-y son loved it.  I'm not a math person at all!

[Brad S]

If your DS hasn't taken AP statistics, I would strongly recommend that.  It's very practical and used in lots of areas.  Starnes, Yates, and Moore Practice of Statistics is an excellent text (next to last version is still good and cheaper), and he could probably learn it from the book.  Since it's somewhat separate, he could also take another math course at the same time.  There are a lot of options after AP Calculus BC:

1. Linear algebra. The Gilbert Strang text is excellent as well as practical and a corresponding MIT OCW class is available.  This could also be done on his own.
2. Discrete math could be covered.  I'm not sure what he's had in that area, if anything, so it's hard to say.
3. Calc 3 is more than what's covered in AP Calculus BC, so unless he's covered more than that, perhaps a different calc 3 course would be appropriate.  He may want to have a business-focused class if that's really his interest so he can see the applications at the same time.
4. A second statistics class if he's already had one.  He may want to take a business statistics class IF he's sure he's interested in business, but make sure it doesn't completely start from the beginning -- maybe something that says "a second course in statistics."  If not, he could get a book on "regression analysis"; the book by Neter and Wasserman, Applied Linear Statistical Models, has a lot of business problems but is relevant to any field and is very clear, solid, and practical.
5. Differential equations, but he may want to make sure it has a broad range of applications since those classes can sometimes be very focused for physical science and engineering.
6. If he's interested in theoretical math, classes with the title of "advanced calculus" or "mathematical analysis" would come after AP Calculus BC.  A very elegant book is by Spivak on calculus: it starts from the beginning and proves the results of calculus, which a minimal AP calc class does not do at all.

There are a whole host of other college math classes that could be taken after calculus, depending upon interest.  For example, if he already took AP statistics, though it is definitely not required for the course, he could take probability; a good text is Sheldon Ross's A First Course in Probability. 

Edited July 12, 2016 by Brad S

[chiguirre]

For business the most useful math classes past Calc 2 are statistics and linear algebra. Statistics will definitely be required for a BBA. Linear algebra is less common but some schools do teach it either as a stand alone or combined into the second semester of business calc even though it is a separate area of math.

[EKS]

At our CC Calculus 4 is multivariable calculus.

[wapiti]

I might have missed it but what grade is this student? If this is for 11th or earlier, I might look to take a really good discrete math course (something for talented students like him, perhaps something aops-ish) and then pick up the next calc course in 12th. If this is for 12th, I'd probably just go with the next calc course. Alternatively, if he is interested in stats, I'd see if he might be able to satisfy the prerequisites for a calc-based stats course rather than AP level.

[Mike in SA]

I looked at the Cal 3 class description and he said he already covered all of it.

He did say Linear Algebra would be interesting. Is this correct? What even is that?!

 

Is there nothing called Calc 4?

 

Ordinarily, calc 3 is multivariable.  BC definitely does NOT cover multivariable calculus, so it's worth a double-check.

 

For a business-oriented student, my vote would go for one of the following:

 

AP statistics (very basic, but enough for management or accounting)

Calculus-based probability and statistics (more solid, good for economics or analytics)

Discrete math (if interested in information technology, economics, or analytics)

Linear algebra (only if interested in information technology or analytics)

Game theory (if interested in economics or analytics)

 

If a second degree in mathematics is a possibility, then one of the following:

 

Multivariate calculus

Linear algebra

Differential equations

Calculus-based probability and statistics

Introductory analysis

[MarkT]

take AP statistics or Linear Algebra formally

self-study MIT OCW Calculus to keep fresh and see what you did not learn in the AP classes:

http://ocw.mit.edu/index.htm

 

Many folks consider AP BC not quite a full Calc 2 class.

Edited July 13, 2016 by MarkT

[kiana]

At public universities in some states, Calc BC is split into calc 1, 2, 3, and calc 4 is multivariable. Usually in these states calc 1-3 are 3 credits each. In other states, Calc BC is covered in calc 1 and 2, which are usually 4-5 credits, and calc 3 is multivariable. 

 

Other than this terminology issue which I think is worth clarifying (I was surprised the first time I encountered the calc 1-4 as well), Mike in SA has some great recommendations. 

 

BTW, for a business-oriented student who is very mathy, he might be interested in actuarial science when he gets to university. It requires a lot of math and so I think continuing with calculus would be an entirely reasonable decision. 

[MarkT]

At public universities in some states, Calc BC is split into calc 1, 2, 3, and calc 4 is multivariable. 

?  

Never heard of AP Calc BC going beyond Calc 2 content in a semester based school (maybe a quarter based school).

Many medium to higher rated colleges don't like to place out students from Calc 2 unless they received a 5 on the BC exam.

Edited July 13, 2016 by MarkT

[kiana]

?  

Never heard of AP Calc BC going beyond Calc 2 content in a semester based school (maybe a quarter based school).

Many medium to higher rated colleges don't like to place out students from Calc 2 unless they received a 5 on the BC exam.

 

Because you are thinking of Calc 3 as multivariable. But in these states calc 3 covers the end of what you are probably thinking of as calc 2, that is, sequences and series. Calc 4 is multivariable. 

 

3 credits each in calc 1, 2, 3 covers the same as 4-5 credits in calc 1, 2 at other schools. It is semester based.

[vonfirmath]

Many folks consider AP BC not quite a full Calc 2 class.

 

That would explain why I struggled after getting a 5 on the AP BC test and then moving on in math. I attributed it to taking a year off from math (I got that 5 in 11th grade, and my HS didn't offer any higher math classes, plus my parents could not afford for me to take a class at Blinn or Texas A&M (the choices).  But I ended up wishing I had gone back and taken at least the Calculus 2 again at the college level before moving forward into new math.

[Mike in SA]

Many folks consider AP BC not quite a full Calc 2 class.

Myself being one of those folks :)

 

Actually, I find that both calculus 1 and 2 get short changed on depth. Focusing on calculator use over theory is really just fine for applied purposes, but not enough prep for advanced math.

 

Lots of unis are starting to offer introduction to analysis for precisely this reason.

[cjzimmer1]

My DS took Calc BC his freshman year, and AP stats his sophomore year.  Then junior year he took Mutivariable calc and differential equations with John Rosasco and then Complex Analysis with John senior year. 

 

Not sure if that is a normal progression but it worked well for my DS.

[kiana]

My DS took Calc BC his freshman year, and AP stats his sophomore year.  Then junior year he took Mutivariable calc and differential equations with John Rosasco and then Complex Analysis with John senior year. 

 

Not sure if that is a normal progression but it worked well for my DS.

 

How were those classes? His website has always intrigued me as he's one of the people I see offering online beyond-the-basics classes aimed at academically talented students. 

[Mike in SA]

My DS took Calc BC his freshman year, and AP stats his sophomore year. Then junior year he took Mutivariable calc and differential equations with John Rosasco and then Complex Analysis with John senior year.

 

Not sure if that is a normal progression but it worked well for my DS.

At that point normal is relative.

 

The sequence above is almost universally required of math majors, with one substitution: linear algebra instead of complex analysis. That said, many schools eventually require complex analysis, and it is a fun class with lots of relevance to physics and engineering applications.

[cjzimmer1]

How were those classes? His website has always intrigued me as he's one of the people I see offering online beyond-the-basics classes aimed at academically talented students. 

 

They were very very good.  Taught by someone who loves math for the beauty of math to students who love math for the same reason.  There wasn't much in the way of assigned homework and no tests but pure study of the subject just for enjoyment of it.  The second year we thought there'd be a schedule conflict with John's class and DS said he'd drop any other class to stick with John.  Thankfully we were able to make the schedule work but it said a lot to me because those other classes were also ones that DS was really looking forward to.

 

Before we ever started, John spent an hour with my son for a free assessment to make sure he was up to speed to join the calc class. If anyone has an advanced student at any age, I higher recommend talking to John as he offers classes for a lot of different maths.

 

Edited July 13, 2016 by cjzimmer1

[cjzimmer1]

At that point normal is relative.

 

The sequence above is almost universally required of math majors, with one substitution: linear algebra instead of complex analysis. That said, many schools eventually require complex analysis, and it is a fun class with lots of relevance to physics and engineering applications.

 

I know DS isn't exactly normal but wanted to give some idea of a possible sequence.  It was a long struggle for us to figure out what to do with DS because frankly there wasn't a lot of people for me to ask for BTDT experience so I like to share what we did in case it's helpful for someone else.

 

John taught Linear Algebra  somewhere before the mutlivariable class and so DS missed out on it.  John brought aspects of it to the other classes and offered some catch up classes if DS needed them but DS was able to keep up just fine.  DS isn't planning on majoring in Math so he actually has more math than he needs but I felt like I needed to have 4 years on his high school transcript and this was what I was able to find for him. He is planning an engineering major and I've been told complex analysis will be a benefit there but since the majority of what he has taken is over my head (I barely made it through Calc 2 and have forgotten nearly all of it over the years), I have no idea how to assess if that's true or not.

[AEC]

Differential Equations was the class that happened for us after finishing the calculus sequence.

 

me too, though CalcBC isn't the end of the calc sequence, generally (it's still fairly single variable IIRC)

[AEC]

if he's business focused you might look at the kinds of math normally used in ops-research.  Topics include:

 

-stats, as previously mentioned

-queuing theory/markov chains (how big a supply of toothbrushes do I need in my warehouse if I want to always have one when a customer orders it but don't want to store any extras)

-graph theory (multi-commodity flow is everywhere)

-numerical minimization/lin-alg.  As a bonus, this is sufficient to understand basic ML which is everywhere in business these days...churn models, AB testing, etc

 

all the above show up all the time in making informed business decisions.

[Sharon77]

I appreciate the responses, thank you!

 

Although I am still so confused! It's all a foreign language to me!

 

I think I need to talk to an advisor at the college!

[daijobu]

I agree with the PP's suggestions, but will also add for your consideration Data Science with R.  This coursera course looks interesting, though I don't have personal experience with this one.  

 

In addition to consulting a college advisor, I would just direct your ds to different textbooks or course descriptions and see what he wants to study.  Most students don't get past calculus in high school, so I would advise he should pursue his interest.  

[Julie of KY]

If you want to self-study, the MIT open courseware Multivariable calculus and Linear Algebra classes look really good.