Really, my favorite gentle calculus textbook has been one I recently was Thompson's "Calculus Made Easy." The way it's written is informal by the standards of when it was written, but to a modern eye reads like your whimsical grandpa decided to bust out a pipe, an expensive brandy, and serious calc knowledge.
I saw him do this a couple of years ago and it inspired me to try it myself. My handwriting isn’t nearly as good as his so I have to transcribe the lectures into TeX. Here’s Calc1 http://inperc.com/wiki/index.php?title=Calculus_1:_course, unfinished.
It somehow manages a decent balance of being fun without slipping into being trivial.
Here is an interesting project that is far more successful at math illustration and shows some promise:
(Seriously, there's a certain great charm to these sorts of things that make them strangely appealing to certain people, like me. It might not be great for learning, but it's awesome as entertainment.)
What I'd like to see is an online calculus book which takes advantage of interactive animations and graphing to demonstrate how things like integrals and derivatives work. For example, for the limit-based definition of derivatives, you could concoct an animation showing how the math works as deltaX goes to 0, and so on.
There's also clever ways of demonstrating the product rule through geometry that make the math make so much more sense. There's a lot of potential in interactive, graphical textbooks that has yet to be explored, I think.
I thought we had gone over this: EVERYBODY LEARNS MATHEMATICS DIFFERENTLY :)
This book is useless for you and wonderful for me.
I love the idea but it's very hard to read.
That's a lesson a lot of us in mathematics have trouble learning. We have this tendency to try to maximize information density, viewing empty space as inefficient because there's "nothing" there, when in reality the space communicates separation and therefore actually does contain vital information.
On a side note, I fully agree with Conrad Wolphram that basic calculus is conceptually rather easy to grasp and use on daily basis, but the focus on calculations by hand makes the subject completely inaccessible.
It's a great idea worth spreading.
I love the idea of this book and its humour, but it is quite hard to comprehend. I can actually see maths' popularity increasing as people begin to see it as a useful hobby, especially those who are learning programming.
I would willing to pay for lessons if learning maths didn't have to involve a dense textbook, but instead could graphically demonstrate the theory (think 3D modelling, moving sine waves etc.) and explain all the underlying concepts that were glossed over in formal education.
Videos or apps like this would be a great help to me, especially if it managed to retain this author's irreverence, Sal Khan's presentation style, but placing more importance on rehearsed & polished lessons, 3d animation and beautifully set typography.
Anyone know any resources that are along these lines?
"In late 1967, Kaczynski became an assistant professor of mathematics at the University of California, Berkeley, where he taught undergraduate courses in geometry and calculus. He was also noted as the youngest professor ever hired by the university. This position proved short-lived, as Kaczynski received numerous complaints and low ratings from the undergraduates he taught. Many students noted that he seemed quite uncomfortable in a teaching environment, often stuttering and mumbling during lectures, becoming excessively nervous in front of a class, and ignoring students during designated office hours. Without explanation, he resigned from his position in 1969, at age 26. The chairman of the mathematics department, J. W. Addison, called this a "sudden and unexpected" resignation, while vice chairman Calvin Moore said that given Kaczynski's "impressive" thesis and record of publications, "He could have advanced up the ranks and been a senior member of the faculty today."
I like the graphics, but your font is very difficult to read for extended periods, it is best used as a headliner at most. I understand your desire for a distinctive look, but readability is most important for a textbook. Also the pages appear to me as too cluttered. Think about it as a PowerPoint presentation with 50 million bullet points, there's a point of diminishing returns. Spread the information, users won't mind the additional pages.
I look forward to seeing this completed.
I think other attempts from "Manga Guide" series and even the "Transnational College of LEX" series are far more effective than this one.
Execution needs work though. Way too cluttered and dense. I would move more slowly and make sure 1 concept is put totally to bed before moving onto the next one.
Seriously, though, this might be a good idea, but it desperately needs improving. I shouldn't have to catch myself thinking about typography so often while reading a Math textbook.
Any estimate on when it will be complete?