I just read a really funny post at Ars Mathematica and had to share it with all of you with commentary. Apparently, the question's come up with what McMaster's University's self-made gazillionare James Stewart did with all his royalites from the famous/infamous-depending on how much you care about mathematics-calculus book every other university's department uses.
Apparently, he built a gigantic house with his own personal concert hall in the middle of it. You don't believe me? See for yourself :
This was so he-a trained violinist-could perform with his friends in the privacy and comfort of his own mansion. Talk about hubris worthy of being struck down by the Gods with the Ceres asteroid.
Apparently the only way Stewart's fragile self esteem could make it as a violinist in a concert hall was to have one built for himself where he'd be the star of the show every single night.
Only in America would that seem like a logical action and not a gigantic excess of self-centered indulgence. I recently passed-on my way to the bus-a recently homeless family of 4 living in their car with their 4 year old daughter crying to the mother, "Mommy,what happened to my bed?"
Meanwhile, this grotesquely overpaid hack without an ounce of mathematical talent is spending 3 times what these poor people's former house was worth because he doesn't want to embarrass himself in public with his violin playing.................
But be that as it may-I was honestly asked:How bad is Stewart's book and what are some of your favorite texts?What would you use to teach calculus given the chance?
Well,sadly,since I was a complete imbecile in high school and didn't know grades mattered in life-and my parents being laborers,well,they didn't know either-I ended up at The City University Of New York instead of a real college.(I made many friends there and learned a lot-but let no one be deceived my lack of pedigree and relatively advanced age will give me a huge battle ahead for any degree of success.)
So my first exposure to calculus was Stewart.
In all fairness,I was being a bit disingenuous up to this point. It's not as bad as many people make it out to be. The real positive about the book is the immense number of exercises with complete solutions.
Unfortunately,that's a double edged sword and it's the main reason it's completely unpalatable for mathematicians:It reduces calculus to a step-by-step, plug-and-chug bag of techniques without any real mathematical insight or thinking. Anything that requires more thought then a baboon is either completely omitted,put in rushed optional sections or shunted to a mythical "advanced calculus" course.
The students don't have to do any real thinking at all. Which is why most students-particularly the non-science majors-love it,of course.
Let's face it-that's why the bottom feeding universities buy it every year-so the premeds,accounting students,actuaries,pre-law and all the rest of the master cheaters that form the vast majority of bodies filling the enormous lecture halls of the average 200 student calculus course can program the solutions of all their exams into their programmable calculators.
"This is Anerica. Let the Japanese waste their time thinking and just give me my f***ing A so I can go out and screw people over for 6 figures a year working for Goldman-Sachs,geek."
It's also why Stewart would never have become so absurdly wealthy writing a book that is the very pinnacle of mediocrity in any other academic system but America's.
It's why a piece of crap like Charmed was on for 7 years while great shows like Farscape vanish, why Transformers:The Revenge Of The Fallen-with a mindless plot and racist "black" Autobots-is the #1 film in America at this writing.
It's why we sold our blood won freedoms to a stupid evil Texan from a rich family we elected king for the illusion of safety while Americans lost the entire Bill of Rights for 8 years.
"Americans aren't stupid!"
Really? You must be living in a different USA then I am.
So it goes.
My favorites? Well,when anyone tells you Micheal Spivak's Calculus
is the best calculus book ever-ever-it's really hard to argue. It's incredibly beautiful and a model of clarity. But much more then that,with every word,picture and exercise, Spivak asks the reader to think about the concepts before him or her before setting the task of doing it. Really THINK about it.
Is it too hard for the average student?
Well,depends on what you mean by the average student.
The average student cheating their way through every homework and test and sleeping with TAs to get a 4.0 to get into Harvard medical school,sure.
But if you're talking about a typical smart and curious undergraduate student-not necessarily a mathematics or natural science student-who reads everything with a real effort,wonders and asks real questions even if they don't understand or particularly like it because they're there to learn something?
I think they can.
Yes,it would be a struggle-particularly in learning how to calculate with epsilonic limit arguments for the first time. But with a good,patient teacher by their side, they could definitely get through it.In the process,they'd learn an enormous amount-not only about calculus, but logical thinking and problem solving. Which is useful in all walks of life, not just the sciences-and they'd be all the better for it.
For the mathematically talented, the book will become a treasured keepsake for a lifetime.The chapter on infinite series alone is worth photocopying and keeping.
I refuse to recommend soft,"applied" books.To me,the pure/applied mathematics distinction is a symptom of the problem above. There is no pure math or applied math-there is only mathematics. If you don't realize that,you're not part of the solution,you're part of the problem. That being said-the main problem with using Spivak is that he has virtually no applications-just one lame application of vector algebra to celestial mechanics late in the book. The main point of calculus is to calcul-ATE. Theory is important and all well and good, but teaching calculus as real analysis completely devoid of application is a little like teaching music students the complete mechanics of writing scores and symphonies,but never teaching them how to play!!!!
A book that fascinates me and I'd love to try using for a basic calculus course one day is Donald Estep's Practical Analysis In One Variable
. Estep,a numerical analyst, teaches a basic real analysis course combined with a basic calculus course, using numerical methods to motivate the rigorous development of the real numbers via Cauchy sequences of rationals and epsilon-delta arguments-with dozens of actual real-world examples from chemistry and physics!!! It's precisely the kind of book I wish there were more of-a book that combines application and fully careful mathematical development. I'd be a little scared to use the book,though-Estep makes a couple of really strange choices. The biggest one is deciding not to discuss infinite series. To Estep, infinite series is best done with complex variables,so he decides to omit them altogether. Huh?!? I hope there's a second edition where he adds a chapter on infinite series. Still, it's a relatively minor flaw in an altogether marvelous book that should be in everyone's library who loves calculus.
My favorite all around calculus book is a nearly forgotten one by a legendary teacher-Calculus by Edwin E.Moise.
It's based on both the regular and honors versions of the course in calculus that Moise taught for many years at Harvard and won several awards for. It's completely rigorous, yet beautifully intuitive with many,many pictures and geometric insight motivated using Euclidean geometry such as lines,planes and conic sections, as well as many physical applications. It's not quite as rigorous as Estep or Spivak,but it is considerably more careful then the average calculus book.
It breaks my heart this book is out of print and I'd love to republish it myself one day. This is the book I would use to teach my children calculus.Go to the library and check it out for yourself if you're disappointed with the ton of fluff the departments are trying to push on you to teach calculus with.
You'll thank me later,I promise.
Stewart and his private concert hall.Yet another example we are living in the era of the barbarians at the gate. It's so frustrating-with no address,you can't even drive by and throw a firebomb through his window to burn it down...........LOL