How Are College Calculus Courses Structured?

[Robokapp]

Okay. I'm a senior high school and I'm taking Calculus AB. There is an option for Calculus BC which I'm not taking. I was informed that for my major I need 5 calculus classes. Does that mean calculus ABC and Calculus 2-5 or Calculus A-E or...how does it work?

I mean how are the classes named and how are they placed in time? How long are they?

 

[amcavoy]

Okay. I'm a senior high school and I'm taking Calculus AB. There is an option for Calculus BC which I'm not taking. I was informed that for my major I need 5 calculus classes. Does that mean calculus ABC and Calculus 2-5 or Calculus A-E or...how does it work?
I mean how are the classes named and how are they placed in time? How long are they?

I am a senior in high school as well. As far as calculus goes, I took a single-variable calculus course in one semester, then multivariable in another. After that I took linear algebra and am currently taking differential equations. As far as I'm concerned, I only took calculus I and II. However, I believe some places split calculus up into 2 single-variable courses (presumably AB and BC), and one multivariable course. There is also one further most colleges offer called Advanced Calculus. I can't really help you on that though, as I don't know which 5 specifically your major requires.

 

[gravenewworld]

It all depends on what schools you go to. Usually you have
Calc I (differentiation/limits)
Calc II (integration)
Calc III (multivariable calc)
Calc IV (differential eq)
Calc V (I am guessing is real analysis aka advanced calc. Analysis is just the million dollar word for calculus. This is the course undergraduates hate the most and have the hardest time with)

If you took AB calc then you can skip Calc I and II. It will be rehash. The only topics you will miss will be sequences and series, so talk to your advisor about it. I never studied series cause I took the AB credit as well, I just taught it to myself. Usually series are only about 1 extra chapter in a intro calc book.

 

[matt grime]

Okay. I'm a senior high school and I'm taking Calculus AB. There is an option for Calculus BC which I'm not taking. I was informed that for my major I need 5 calculus classes. Does that mean calculus ABC and Calculus 2-5 or Calculus A-E or...how does it work?
I mean how are the classes named and how are they placed in time? How long are they?

this information (for the major) is likely unique to the institution involved; they employ people to answer questions exactly like this. ASK THEM, or any of the people employed at your high school and responsible for this information. Do not ask anyone over the internet, they do not know you, your school, or your intended major. Any information you receive may be wrong.

 

[Robokapp]

My calculus book contains the follwoing chapters:

Recap from precalc
Limits
applications of limits
Derivatives
Applications of derviatives
Integrals
Sequences
Applications of integrals
SOmething about differenciation
SOmething about ploar vectors or something like that.

......

So...that falls under AB

 

[JasonRox]

this information (for the major) is likely unique to the institution involved; they employ people to answer questions exactly like this. ASK THEM, or any of the people employed at your high school and responsible for this information. Do not ask anyone over the internet, they do not know you, your school, or your intended major. Any information you receive may be wrong.

Very true.

You can end up taking 3 courses in Calculus then later find out none of them will transfer. That's a waste of time, money, and effort when careful planning would have avoided this.

 

[gravenewworld]

My calculus book contains the follwoing chapters:

Recap from precalc
Limits
applications of limits
Derivatives
Applications of derviatives
Integrals
Sequences
Applications of integrals
SOmething about differenciation
SOmething about ploar vectors or something like that.

......

So...that falls under AB

Trust me when I say this- you still have no idea what a limit is (not until you take advanced calc at least). You will be seeing some of these same topics again later on.

 

[shmoe]

For the handful of math major programs I'm familiar with, there will be a "complex variables" course as well. Usually courses called "analysis" (and taught at the depth this title conveys) are reserved for honours programs.

As already stated this can vary greatly from institution to insititution so check out your intended universities website, calendar, counsellors, etc for info that's definitely applicable to you. It can't be stressed enough that the only way for you to get accurate information is from your university.

 

[mathwonk]

as matt said, it is very hard to give relevant advice to someone we do not know about a school we do not know the name of.

and posters here tend to be smarter and better prepared and more serious than many of my own students.

nonetheless, on the off chance some of my experiemce transfers to your school or situation, i would like to remark that i give different advice from what some have done.

i never advise high school students to skip any calculus courses in a good college math dept based on AP courses taken in high school.

why?

several reasons:

1) college professors know a lot more than high school teachers and if you are lucky they will include what they know in the course, so the college course is not really comparable to the high school course.

caveat: many college teachers have become so used to weak high schoolers taking their classes that they do not teach more high powered courses having learned to water them down for the AP crowd, so you have to find out what your teacher will do.

2) high school AP students tend to be honors students, better than average students, so it makes no sense for them to use their AP experience to skip non honors beginning courses and only register in non honors intermediate courses. the point is to take honors courses, not advanced non honors courses.

e.g. i would take a course in arithmetic if it were taught by serre.

so the thing for a good student with AP credit to do, is find a good honors level, but beginning course in college from a good instructor, and take the material over again, at a greater depth than high school, in the company of other bright honors level students.

3) not people here presumably, but most of my AP grads in even my beginning calculus courses have learned essentially nothing in their AP courses, which tend to be trivial computation al courses with no theory or proof in them. so basically i can not tell the AP students from the others.

worse their schools have often minimized or omitted basic courses in algebra or geometry or trig, to teach the sexier calculus course and hence their grads cannot even simplify a fraction or visualize similar triangles, even if they have memorized a few integrals.

I.e. to me AP, especially AB level, generally means nothing, but I have met other professors who teach such mickey mouse courses that the AP students are indeed advised to skip them.

however the only real challenging AP courses is the BC, the AB is very low level and I cannot imagine a college course worth its salt that it would substitute for.and another thing, yattatta yattata,..

best wishes,

grumpy old poop.

 

[Robokapp]

Well, this is for mathwonk especially: So you're saying that taking the AP test is a waste of time? Because I am in a very good math class, and I have a good teacher who is hoping to get every student in Calc AB to get +3 on AP. However, AP is not mandatory and it's also pretty expensive. Further more, by that time Colleges have closed their application receiving. So would it be unwise to spend the 90$ on the AP?

What my teacher told me (he might be wrong...i don't know) is that AP is best for those who go into majors that require little math. Using the AP credits they will not have to take college math and get 1-2 credits without paying for the classes which is in their financiar advantage.

He also said that those who want to go into highly mathematiced majors (myself included) will have to take math classes anyway and the AP has a little inflence on them. So...I'm interested in Computer Engineering. Ohio State university claims I need 5 calc classes. I wonder...if I have the AP with a good result...and I'm pretty sure i'll get a 4...can i use that to get the credit for THE LAST calculus class rather than the first after AB?

Becasue I agree with you, I don't want to skip any steps. After Precalculus I was invited to join the BC class, that being college-level. I said no because I wanted the AB. Right now I'm enjoying it and not having many problems scoring the A's but that doesn't mean much for college classes as far as I know.

SO how does the AP work in report to the classes that I need credits for in clooege?

Trust me when I say this- you still have no idea what a limit is (not until you take advanced calc at least). You will be seeing some of these same topics again later on.

Very true...I was only stating the title of the chapters. The full titile is actually
"introduction to limits".

 

[dicerandom]

Okay. I'm a senior high school and I'm taking Calculus AB. There is an option for Calculus BC which I'm not taking. I was informed that for my major I need 5 calculus classes. Does that mean calculus ABC and Calculus 2-5 or Calculus A-E or...how does it work?
I mean how are the classes named and how are they placed in time? How long are they?

I'll tell you how my calculus/math courses went, although I'm a Physics major and not a math major. For the first two years there isn't much difference between the two though.

Calc I: Differentiation, limits. Ended with the Fundamental Theorem of Calculus.
Calc II: Integration, infinite series.
Calc III: Multivariable calculus. Functions of multiple variables, line, volume, area integrals, cartesian, polar, and spherical coordinate systems.
Calc IV: Vector calculus. Div, Grad, Curl, properties of vector spaces and vector valued functions.
Linear Algebra: Systems of equations, transformations between spaces, properties of vector spaces, a bunch of other stuff I've forgotten.
Differential Equations: Methods of finding solutions to DEs, uniqueness of solutions, numerical approximation techniques.

I took Linear in conjunction with Calc II and DE in conjunction with Calc III. I highly recommend a good linear algebra class to anyone who's planning on going on in physics, the basics behind the properties of vector spaces, transformations between them, and sets of orthogonal bases are essential if you want to obtain a good understanding of quantum mechanics and many of the more difficult solutions to PDEs and boundary value problems (i.e. Laplace & Poisson equations in E&M and gravitation).

 

[shmoe]

I wonder...if I have the AP with a good result...and I'm pretty sure i'll get a 4...can i use that to get the credit for THE LAST calculus class rather than the first after AB?

Do you mean you would want to try to get credit for whatever the most advanced course in their calculus sequence is? That's certainly a resounding no. The AB will let you skip at most the first course in the calculus stream (check your school to be sure) and not a more advanced class. I hope I misunderstood you here, this sounds like trying to "skip steps" in a most obscene manner.

Based on my own experiences, I also suggest taking the university equivalent of your AP class even if you have the option to skip it, though of course this is entirely up to you. Worst case is you find it too easy at university having seen it before, but that will just ease your transition from high school to university. The added cost isn't going to amount to much if you consider the full 4+ years of your education.

 

[gravenewworld]

It all depends on what experience you have had in high school so far. My calc teacher in high school was absolutely BRUTAL. I have never taken a harder math class than my high school calc class. Not even the graduate math classes I have taken were harder. I guess I was lucky though, my high school calc teacher did get awards from the White House for excellence in mathematics education. Anyway, if YOU feel like you are well prepared after taking AP calc, then I would say move on. Retaking Calc I and II would not only be boring, but unecessary. Getting Calc I and II out of the way frees you up later on to take courses that may interest you, may allow you to get done other requirements faster, or simply take a less of a load later on in your junior and senior year.

 

[FredGarvin]

My calc teacher in high school was absolutely BRUTAL. I have never taken a harder math class than my high school calc class. Not even the graduate math classes I have taken were harder.

What grad program were yo in? Culinary arts? How could a HS calc class be anywhere near a graduate level calc class?

 

[gravenewworld]

LOL no. I took grad level number theory and linear algebra classes. THey weren't that hard at all. Damn I wish I had my old high school calc tests and could post some questions from them. The exams were REDICULOUS. Some of the averages on the exams, I remember, were in the 20's. Needless to say, for 10 straight years, everyone in my teacher's class got 5's on the AP calc exam.

 

[Chrono]

As far as calculus goes, I took a single-variable calculus course in one semester, then multivariable in another. After that I took linear algebra and am currently taking differential equations

Dang, all that in high school?

 

[amcavoy]

Dang, all that in high school?

They were taken at a local university. It's a sort of joint-admissions program until I graduate. I wish they were actually offered at my high school though.

 

[Robokapp]

LOL no. I took grad level number theory and linear algebra classes. THey weren't that hard at all. Damn I wish I had my old high school calc tests and could post some questions from them. The exams were REDICULOUS. Some of the averages on the exams, I remember, were in the 20's. Needless to say, for 10 straight years, everyone in my teacher's class got 5's on the AP calc exam.

That still can't come even close to a college advanced math calculus course. Coming from precalc where you whine that you don't get why cos of 180 degrees is -1 and not 1 and it screws up your whole thing (been there, done that 1000000 times until I finally remembered that "in between" quadrants still counts as quadrants :D) it's just no way you can swallow anything like Calc 2 or above. Even an advanced course of Calculus BC is something rough for your brain. I mean, too little time for too many concepts. When you come out of precalc you lack the mathematical language...the concepts of rounding up, estimating, not perfect answers...the dy/dx kind of thing. you don't understand limits, rectangle rule, integrals, derivatives...even if you aced all pre-calc you can't take anything past BC. you just can't unless you spent your summer doing extra studying...and even then, studying calculus AB by yourself is not something many can do!