What people don't tell you . . It really matters where you want to end up:
Engineer lite / non-STEM
Abstract mathematics
Heavy-duty STEM
Want the option of a solid graduate program, for example.
And how you want to get there for 2/3. Pain now, easier later? Easier now, cliff later? Or...
I think this is the best forum.
Since no one has answered and these are probably useful for someone:
Brent Nelson at Berkeley used Pugh for 105: syllabus, and notes, assignments and midterms for chapters 5 and 6 (with solutions). Notes are at the right, by section and are handwritten.
Here...
I think these (below) problems are somewhat illustrative of their respective texts. Feel free to present your own experiences. I feel this comparison adds light to the discussion.
Esty holds your hand in looking at this interesting artifact of sound waves, letting you work the calculations into...
Moving this addendum to a separate post for clarity:
I think one contributing factor to this is that Geometry was taught at university for hundreds of years. It wasn't untll 1726 that Harvard required arithmetic for entrance after aquiring a mathematics professor. I believe it...
Sorry guys, I think I mixed up student's reception to Euler's "Introduction to Analysis of the Infinite" with Cauchy's student's reception to Cauchy's "Cours d'Analyse." I don't recall the book I read it in (maybe Stillwell?) so can't immediately confirm which. I am updating that point...
Everyone here loves math. It makes me warm and fuzzy. :-)
I am currently a student, not a mathematics PhD, so please forgive any important point I accidentally omit, here. I am not arguing against any alternative approaches suggested here (all of which appear useful), just trying to fit AoPS...
Hi Chandller,
Thanks, I appreciate that. Nice to see your enthusiasm and the Collingwood mention. I saw those too. There are many ways to approach mathematics. What is important is finding an approach that inspires you to further study and allows you to find success in progression.
Given this...
Hi Chandller,
It looked interesting so I just ordered a copy.
PF is an incredible resource for textbook recommendations (see the search box). One free pdf book recommended by some here sounds like what you want: David Santos's "Precalculus: An Honours Course"
Another in that direction...
For each major of interest, ask the university:
"What percentage of ____ majors from ____ university are employed within 3-6 months after graduation?
"Of those successfully hired within that 3-6 month period, what is the starting median salary from ____ university with the ____ major?
What...
Any passers by of a similar intent might find this useful.
Maybe not on its own, but check out:
Bamberg and Sternberg: "A Course in Mathematics for Students of Physics," Volumes I & II
The information Jamesix provided is not sufficient to support that speculation.
Jamesix may have taken AB, but it appears that he intends to not do an AB course and instead, to study a full single variable text on his own in preparation for the BC exam (which covers AB material and provides an...
Sure. . I think it would be very reasonable to quickly go through Moise or Courant after AoPS Calculus. See my below endorsement of a multi-book approach.
AoPS is designed around the premise that careening through names of maths courses (and stacks of additional concepts) is less important for...
Hi MidgetDwarf,
As you seem to agree with my assessment of your interpretation, I will simply point out that you have an small inconsistency in your interpretation of Jamesix's request (see quoted abbreviation of your post).
AoPS is indeed designed to develop deeper mathematical thinking...
This is a fair statement.
I read Jamesix as asking for a problem solving oriented book and specifically not an analysis oriented book. AoPS Calculus includes Putnam problems and similar.
I think you interpret it as seeking applied rather than formal? If he has already done AoPS Calculus, I...
Hi Jamesix,
The AoPS Calculus book seems to be what you want? Velleman is a solid text that is proof-oriented but you'd want to make sure you have a way of verifying your solutions.
MIT has its Calculus of a Single Variable course (18 01) on edX split into Calculus 1A, 1B, and 1C. No book...