Calculus concerns at dual-enrolled school

[dirty ethel rackham]

Ds17 (a rising senior) is scheduled to take calculus at the local liberal arts college next year through their Lederman Scholar program. He is excited to be taking math in a classroom rather than distance learning through Art of Problem Solving. After reading several posts here about the rigor or lack of rigor of certain textbooks, I have some concerns. They use the Stewart book. My older son used it and he did very well. But, he is a bio major and it was a "good enough" text for him. But ds17 plans to either major in physics or math, so I am concerned that this book will not be adequate preparation for him. Although I majored in Math many years ago, I don't remember squat (except a very vivid memory of my professor nearly dislocating his shoulder to explain something about cluster points.) I really don't think I can help him as he has far outpaced me in this department.

 

So, my question is ... how do I help him get a rigorous enough Calculus experience for what he wants to do? I don't want to do another distance learning class (nor does he.) I am tempted to email the head of the math department (as he is also in charge of the Lederman Scholars program) and ask him.

[Arcadia]

Mathwonk reply to me on this thread might help. I was asking about Stewart and Spivak Calculus for a refresher for myself.

http://forums.welltrainedmind.com/topic/478021-harold-jacobs-geometry-and-elementary-algebra-out-of-print/#entry5039489

[dirty ethel rackham]

Hmm ... so he should do the Stewart course at the school and then I should have him go through the Spivak book on his own later. That's an idea. I just have my doubts he will do that unless he has an outside structure.

[kiana]

Stewart is a fairly standard text and many universities use it for math majors. It depends on where he wants to go to college. If he goes to a non-flagship state school, or a smaller LAC, that will probably be what they used for math majors. If he goes to someplace really good, he should look at repeating their honors calc course. For example, MIT uses Apostol in their honors sequence. Other universities use Spivak. Many of the students at these universities have already had a course like the one your son will be taking.

[Arcadia]

If you want to refresh your memory of calculus, Spivak, Apostol and Courant have PDF copies floating around the Internet. I found Spivak and Courant at archive.org.

MIT Calculus with Theory OpenCourseWare is using the Apostol Calculus Volume 1.

http://ocw.mit.edu/courses/mathematics/18-014-calculus-with-theory-fall-2010/assignments/

 

I prefer using two textbooks concurrently. One for exam prep when I want a breather and another to make me think abit more.

 

Spivak

http://archive.org/details/Calculus_643

Courant Vol 1

http://archive.org/details/DifferentialIntegralCalculusVolI

Courant Vol 2

http://archive.org/details/DifferentialIntegralCalculusVol2

[dirty ethel rackham]

Stewart is a fairly standard text and many universities use it for math majors. It depends on where he wants to go to college. If he goes to a non-flagship state school, or a smaller LAC, that will probably be what they used for math majors. If he goes to someplace really good, he should look at repeating their honors calc course. For example, MIT uses Apostol in their honors sequence. Other universities use Spivak. Many of the students at these universities have already had a course like the one your son will be taking.

 

 

Well, he will probably end up at a smaller LAC, but we are looking for strong math/physics programs. The reality is that he will likely go on to grad school at a bigger university so I don't want him short-changed. My nephew just got his PhD in Applied Math from Northwestern U, but he felt that his preparation at a smaller LAC for undergrad was lacking despite its academic reputation. He joked about finally finishing the 27th grade! Maybe I should ask him what he thinks.

If you want to refresh your memory of calculus, Spivak, Apostol and Courant have PDF copies floating around the Internet. I found Spivak and Courant at archive.org.

MIT Calculus with Theory OpenCourseWare is using the Apostol Calculus Volume 1.

http://ocw.mit.edu/c...10/assignments/

 

I prefer using two textbooks concurrently. One for exam prep when I want a breather and another to make me think abit more.

 

Spivak

http://archive.org/d...ls/Calculus_643

Courant Vol 1

http://archive.org/d...ralCalculusVolI

Courant Vol 2

http://archive.org/d...ralCalculusVol2

 

 

Thanks for the info. I don't think I'll be ready to jump back into Calculus as I have other relearning to do in Math. I graduated college 27 years ago and Real Analysis was the last look I had at Calculus. I didn't really brush up on upper high school math (other than elementary algebra needed for everyday life) because my boys largely self-taught Math (it sort of happened when I was busy nursing or changing a diaper only to find that they had done their math lesson.) As they got older, I couldn't help them anymore when they were stuck because I was jumping in the middle after not keeping up. We got away with looking for other resources and asking them questions to help them come to their own responses and by taking AoPS classes. It will be different with dd as she needs more explicit instruction so I will be refreshing along with her.

[8filltheheart]

Is your ds open to working through the AoPS cal book on his own in addition to the cal class he is taking?

 

This is my perspective as someone who does not remember anything beyond alg 2 and has outsourced all math beyond alg 2 for 4 kids already and has zero intention of changing that path for the remaining 4. ;)

 

Our oldest used Stewart. It is what the universities used and provided him an excellent applied math approach for his engineering degree.

 

Our rising 12th grader used AoPS. The AoPS books (I don't think it was just the cal book. He mentioned different parts of alg 3, pre-cal, and cal) exposed him to proofs and understanding that has been pulled upon in the upper level math courses he has taken. The AoPS books provided a theoretical understanding far beyond what he is getting in the traditional classroom setting for the math courses he is now taking. He really misses that approach. His multivariable cal professor told him that in all of his yrs teaching that ds is the only one that has ever asked for more proofs. (I find it sort of sad that that is true at the university level.)

 

BUt, it has also translated across into his physics classes. He understands the theory of the math behind what he is doing. (at least that is **my** understanding of what ds tells me. I only understand about 1% of what he actually says, but I think that is the gist of his sentiment. He isn't here for me to confirm. ;) )

 

Anyway, that is a long way of saying that I wish our ds had the opportunity to continue learning math in the AoPS manner. But, it wasn't an option for him b/c he finished AoPS's courses and the local universities are the only realistic resource. You are correct, though, it isn't the same. We know it isn't the same. Ds laments that it isn't the same. So.....if your ds is willing to work through the AoPS book, at least it is accessible with a complete solutions manual and could supplement what he doing at the college.

[AdventureMoms]

I used the Stewart text for Calc 1&2 in my Engineering college. I got a math minor too. The math majors used the same text. It's a very standard text and I don't think it would be a problem. The instructor's skill is more important, IMO.

[jhschool]

May I ask why AoPS online Calculus will not work for you?

 

I ask because we are planning on AoPS online Calculus, and would

love to know more about your decision--in case there is something we

haven't thought of.

 

Sorry to hijack. I can PM if you wish.

[Candid]

Well, he will probably end up at a smaller LAC, but we are looking for strong math/physics programs. The reality is that he will likely go on to grad school at a bigger university so I don't want him short-changed. My nephew just got his PhD in Applied Math from Northwestern U, but he felt that his preparation at a smaller LAC for undergrad was lacking despite its academic reputation. He joked about finally finishing the 27th grade! Maybe I should ask him what he thinks.

 

I'd talk with the nephew. It couldn't have been that lacking if he ended up with a PhD from Northwestern, but if it was then it was probably not so much the use of one specific text but an overall department wide problem. One thing I found interesting in 8 First Choice is the suggestion to use the college catalog to map out how many courses and professors a department you are interested in has at each college. Also look at add ons like concentrations, research options, etc. But even top ranked schools may have smaller departments in some areas.

 

I think in reading through this thread that the part I bolded is unlikely in the senario you are painting. The local LAC is using a fairly standard text. All texts (yes even AoPS) have "holes" in them. Obviously some have bigger and more frequent holes but all have them having lacking areas. There is a level where it may not matter and I think you might be there. The one factor that I would look at more carefully at this point is the actual instructor at the local school. Since your ds wants to take a live and in person class, it would be nice to assure that whoever teaches it is both competent and charming.

[Arcadia]

The one factor that I would look at more carefully at this point is the actual instructor at the local school. Since your ds wants to take a live and in person class, it would be nice to assure that whoever teaches it is both competent and charming.

 

 

:iagree:

Hubby and I both had a terribly incompetent math lecturer in university first year who stared at his OHP (overhead projector) slides all the time and never looked up the entire lecture. Second year onwards we had competent and helpful math lecturers. None of our lecturers were charming LOL

[dirty ethel rackham]

I'd talk with the nephew. It couldn't have been that lacking if he ended up with a PhD from Northwestern, but if it was then it was probably not so much the use of one specific text but an overall department wide problem.

Nephew took a few tries to pass his boards to get his masters degree from UCLA after a BS from a smaller LAC (that has fairly high admissions standards.) He also took a year longer to get his PhD - he was no longer subsidized and had to take on some outside work to pay bills. But, he did finish - defended his dissertation last month and graduated a week ago and has a postdoc in the fall at University of Washington with a professor he has been wanting to work with. He did say that his undergrad program did not prepare him well. I guess I am looking at getting ds off to a good start so he doesn't end up behind the 8-ball from the get-go.

One thing I found interesting in 8 First Choice is the suggestion to use the college catalog to map out how many courses and professors a department you are interested in has at each college. Also look at add ons like concentrations, research options, etc. But even top ranked schools may have smaller departments in some areas.

 

Thanks for the suggestions. We are doing some of this, but we probably need to focus on this a little bit more. The Physics department chair at Hope College (where my oldest goes and one on this ds' list) has encouraged ds to apply to do research at Hope before his freshman year if he goes there as this prof feels ds is a strong candidate. Research is definitely on ds' agenda. There are so many factors to look at when choosing a school. He definitely wants a smaller school for undergrad. We also have to consider finances - lots of merit money or he will have to go to the local college and distance as we can't afford to add travel expenses on to an already expensive college situation.

 

 

I think in reading through this thread that the part I bolded is unlikely in the senario you are painting. The local LAC is using a fairly standard text. All texts (yes even AoPS) have "holes" in them. Obviously some have bigger and more frequent holes but all have them having lacking areas. There is a level where it may not matter and I think you might be there. The one factor that I would look at more carefully at this point is the actual instructor at the local school. Since your ds wants to take a live and in person class, it would be nice to assure that whoever teaches it is both competent and charming.

 

Thanks for the reassurances. I know that the instructors at the LAC where he will be taking calculus are good. My older son (who is not as strong in Math as ds) breezed through calculus at this school and had many of the same professors. He raved about them. But older ds is a bio major and doesn't need as rigorous a math background - at least not in calculus.

[Candid]

None of our lecturers were charming LOL

 

I couldn't quite come up with the right word. I was privileged to have a couple of professors who had won my large university's teaching award and the difference is amazing. One guy was in statistics and his class was mostly graduate students from a variety of departments. The following semester I had a horrible guest lecturer. The difference is huge!