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Gil

Advanced Calculus Texts -- Opinions? Experiences? Feedback?

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I'm on the lookout for the most readable text for calculus that might interest a pure-math enthusiast. The theoretical underpinnings that gets glossed over or raced through in applied calculus texts is what I'm after for our next pass.

Courant  - vol 1 and vol 2
Apostol - vol 1 and vol 2
There was a 3rd name, but I forgot it.

I'm looking for a book/series to give a complete coverage of single and multivariable, which is why I didn't include Spivak.

If you know of anyone else who wrote a calculus book on the same wavelength/level as the 2/3 above, please mention it.
 

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Gil, I would suggest you try the high school board as there are some mathy people over there.  Also, PM Kathy in Richmond because she helped me with this exact topic.  In the end, my ds decided to study Baby Rudin on Analysis, rather than any of the texts you have mentioned. Apparently, Rudin is like what you are talking about but even more theoretical. 

Ruth in NZ

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On 9/27/2019 at 3:27 AM, lewelma said:

Gil, I would suggest you try the high school board as there are some mathy people over there.  Also, PM Kathy in Richmond because she helped me with this exact topic.  In the end, my ds decided to study Baby Rudin on Analysis, rather than any of the texts you have mentioned. Apparently, Rudin is like what you are talking about but even more theoretical. 

Ruth in NZ

I don't think that I want something even more theoretical. I'd like something that he can begin work on sooner, rather than later, but that'll offer value on repeated readings, exploration etc.

It'll be a self-study/independent text, so I don't want something that's too big of a stretch for him. I'm hunting for a text that'll stoke, not extinguish his interest.

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15 hours ago, Gil said:

I don't think that I want something even more theoretical. I'd like something that he can begin work on sooner, rather than later, but that'll offer value on repeated readings, exploration etc.

It'll be a self-study/independent text, so I don't want something that's too big of a stretch for him. I'm hunting for a text that'll stoke, not extinguish his interest.

I totally get it. My son did AoPS Calculus for the theoretical side and Anton for the engineering side. When picking his next text, I think he felt that he had done enough calculus having gone through 2 books.  Have you looked at AoPS Calc?  My ds liked it.  It is written to the student. 

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On 10/1/2019 at 3:22 PM, lewelma said:

I totally get it. My son did AoPS Calculus for the theoretical side and Anton for the engineering side. When picking his next text, I think he felt that he had done enough calculus having gone through 2 books.  Have you looked at AoPS Calc?  My ds liked it.  It is written to the student. 

I've almost maxed out the math that I am willing to co-learn so whatever I get, he's on his own with it for the most part. It needs to be a text that's not too scary format wise and he can at least make some progress in most chapters of.

I'm an applied-math-guy at heart, I find the heavy-theoretical stuff boring and difficult to get through. So naturally I have a kid who is interested by the heavily-theoretical stuff so I have to try and find the perfect book that's going to be friendly enough for him to work on on is own, and engage him.

AoPS only covers single-variable calculus. We found some of AoPS Intro books incredibly boring and slowopaced so he has a low opinion of the AoPS math books from that experience. He thinks that he might be ready to go give AoPS another try in 8th grade since it's "practically the standard" but I'd like something to gift him for his impending 7th grade year.

 

 

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On 10/7/2019 at 3:57 AM, Gil said:

 

I've almost maxed out the math that I am willing to co-learn so whatever I get, he's on his own with it for the most part. It needs to be a text that's not too scary format wise and he can at least make some progress in most chapters of.

I'm an applied-math-guy at heart, I find the heavy-theoretical stuff boring and difficult to get through. So naturally I have a kid who is interested by the heavily-theoretical stuff so I have to try and find the perfect book that's going to be friendly enough for him to work on on is own, and engage him.

AoPS only covers single-variable calculus. We found some of AoPS Intro books incredibly boring and slowopaced so he has a low opinion of the AoPS math books from that experience. He thinks that he might be ready to go give AoPS another try in 8th grade since it's "practically the standard" but I'd like something to gift him for his impending 7th grade year.

Gil, we sound similar. I maxed out with maths with my 7th grader when we worked together to get him into the IMO camp at the end of that year. It was horrible work for me, as I too am an applied-maths-gal at heart. I have a degree in mathematical biology. It is not that I am afraid of math or something. But *theoretical* maths is just something I really don't care for, and the year that I pounded it with my son left me incredibly burned out and it took me over a year to recover. I never helped him with maths again. But here is the thing, he could do it on his own by that time, so it was ok that he studied for 5 years on his own. He took one foray into the world of the local university, and those two maths classes left him convinced that he would go it alone. The classes were just too easy and slow paced and dull. 

What I did was give him a selection of books to read. For calc, I gave him AoPS calc, Anton (which I had), and Apostol. I also gave him Algebra by Artin and Analysis by Rudin. I figured that would keep him going. He also self studied combinatorics with random resources he found on the internet to a level that he has walked into graduate level courses in Combinatorics last year, and that was without a textbook at all in high school. 

So I guess it depends on how good your ds is at self-learning. You have always been so involved in their maths, and been such a good teacher for them, it might be hard for both you and him to make a change. But if a kid is keen, they can make it work even without academic support. I did a lot of listening for 5 years about all this exciting maths he was so keen on.  I really didn't know what he was talking about at that point, but my role was to be cheerleader. So that is how I supported his efforts. And interesting, one of his essays for university applications was about having to go it alone in maths, and that because he could not find a local community in maths, that he built his community in music.

Good luck with finding a path.

 

Edited by lewelma
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My child is taking AP Calc BC using Calculus by Varberg, Purcell, Rigdon (9th edition). She doesn't care for her teacher's explanations so she is essentially teaching herself. The school doesn't provide the student workbook so I need to get it to see if that will help.

Other child took it last year and made As with the same teacher. First child is more theoretical, second very applied; maybe that's the difference. The teacher does have health issues currently so that could also enter into it.

Second child has tried to self-tutor using various online resources. I am familiar with Larson, which is much simpler stuff than her textbook. 

Searching today, I found recommendations for Leithold's Calculus, as well as this rec from a physics forum: "Ralph Palmer Agnew's 1962 book Calculus. Analytic Geometry and Calculus, with Vectors is freely available on the internet and a joy to read."

So maybe one or more of the three.

Question hijack: any suggestions for dealing with Varberg's Calculus, or tips on hiring a calc tutor with experience with Varberg?

Thanks.

Edited by LeeK

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