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Calculus Made Easy (1914) [pdf]

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Re: Calculus Made Easy (1914) [pdf]

#181

Post by flor1s »

lunchladydoris wrote: post #115
theCricketer wrote: post #51

MIT recorded a set of Calculus video courses back in 1970s that they have since made publicly available. It is taught by a lecturer named Herbert Gross. His style of lecturing is clear, he states why things are defined the way they are and derives everything from first principles. There is an unusual mix of rigor and focus on building understanding - where everything comes from. It also taught me that math is about r…

I just had a look at the first video in the first course on YouTube [0] and was delighted to see Herb Gross responding in the comments. Clearly this is a man who loves his subject and loves introducing it to others. [0] https://www.youtube.com/watch?v=MFRWDuduuSw

That's so beautiful that I have to admit my eyes started to tear a little bit. It's lovely to live in a world in which wonderful people are empowered to touch people all over the world in such a powerful and profound way.

Re: Calculus Made Easy (1914) [pdf]

#182

Post by mindcrime »

djhworld wrote: post #119

I'm embarassed somewhat to say this, but over the past few weeks I've been taking the courses on Khan Academy on mathematics. I'm nearly 30. and I'm not talking about brushing up on my linear algebra, that comes later, I'm talking high school level mathematics, stuff that I've largely forgotten or didn't "get" first time round. I've seen these "machine learning for hackers!" articles who try to dish out a bit of math…

Nothing to be embarrassed about. This stuff is very "use it or lose it" so unless you're really using it regularly, it fades from mind very easily. Heck, I've taken College Algebra like 3 times over the years, and I still keep going back to Khan Academy or watching various Youtube videos and the like, for a refresher here and there. And that's just to keep the basic algebra stuff in mind.

Re: Calculus Made Easy (1914) [pdf]

#183

Post by theoh »

dmix wrote: post #164
theCricketer wrote: post #51

MIT recorded a set of Calculus video courses back in 1970s that they have since made publicly available. It is taught by a lecturer named Herbert Gross. His style of lecturing is clear, he states why things are defined the way they are and derives everything from first principles. There is an unusual mix of rigor and focus on building understanding - where everything comes from. It also taught me that math is about r…

Reminds me of the MIT SICP lecture videos from the 80s. The concepts of black box abstraction and the simplicity of using LISP like lego building blocks blew my mind and made me switch from being a UX designer dabbling in Rails to a full blown programmer. It was still entirely relevant to today even though it was a few decades old as the fundamentals of computer science are still fundamental. https://www.youtube.com/…

The Book of Proof is freely available online: http://www.people.vcu.edu/~rhammack/BookOfProof/

Re: Calculus Made Easy (1914) [pdf]

#184

Post by Baeocystin »

lunchladydoris wrote: post #115
theCricketer wrote: post #51

MIT recorded a set of Calculus video courses back in 1970s that they have since made publicly available. It is taught by a lecturer named Herbert Gross. His style of lecturing is clear, he states why things are defined the way they are and derives everything from first principles. There is an unusual mix of rigor and focus on building understanding - where everything comes from. It also taught me that math is about r…

I just had a look at the first video in the first course on YouTube [0] and was delighted to see Herb Gross responding in the comments. Clearly this is a man who loves his subject and loves introducing it to others. [0] https://www.youtube.com/watch?v=MFRWDuduuSw

That was a delight to watch. Genuine enthusiasm always is. Thanks for making me aware of Mr. Gross.

Re: Calculus Made Easy (1914) [pdf]

#185

Post by pervycreeper »

psibi wrote: post #85
tzs wrote: post #6

That PDF is just a bunch of scanned images of the book. It's large and cumbersome in many readers. There is a much better PDF at Project Gutenberg [1]. The Gutenberg PDF is only 1.9 MB, compared to 12 MB for the scanned image PDF. The Gutenberg page for this book [2] also has a link to the LaTeX source for the PDF. [1] http://www.gutenberg.org/files/33283/33283-pdf.pdf [2] http://www.gutenberg.org/ebooks/33283

Is there a easy way of converting it into Kindle friendly pdf (or mobi) ?

see my other comment in this thread.

Re: Calculus Made Easy (1914) [pdf]

#186

Post by sebastianconcpt »

appleiigs wrote: post #39
noam87 wrote: post #35

Earlier quoted context omitted.

This is why I love used books. My copy of Schopenhauer's collected essays has gone through 4 owners since 1914, all 4 of whom have signed and dated the front cover, all of 4 of whom have marked and underlined at different spots (including, now, myself). My copy of Riverside Chaucer went through two students before me. And they all pick up their own unique scents along the way (my girlfriend jokes that I only buy book…

I'm with you guys! This book has some serious character. The cover, handwriting, imperfections, and on top of it all, the writing style. The problem with used books tho is that sometimes I find hair. Ugh.

Might be proof of DNA of a previous owner. Depending on the historical value that could be golden

Re: Calculus Made Easy (1914) [pdf]

#188

Post by thanatropism »

taejo wrote: post #116
jacquesm wrote: post #41

Earlier quoted context omitted.

> Why didn't my professors do that? Because to them it's obvious. Most maths teachers are so far ahead of the students they forgot they once were students themselves. I've had 3 different ones in high school and the difference was incredible. All the way from 'only the best students learn anything' to 'everybody earns at least a passing grade'. Maths and physics were the classes where the quality difference between t…

> Because to them it's obvious. And to them it's wrong! Much is said in this book which is difficult (but not impossible) to rigourously justify. It took centuries for calculus to be placed on a rigourous mathematical foundation; this foundation (called "real analysis", largely developed in the 19th century) is quite different from the intuitive ideas presented in this book. The presentation here (in particular the i…

"dx^2 is negligible" can be alternatively (rigorously) obtained in standard analysis/calculus in the following sequence:

0) Intermediate value theorem (continuous function with image between b and c must be such that there is x such that f(x)=d for d between b and c. This can be first proved where d=0 -- it's the method of bisection by nested intervals, really -- and then generalized) 0.5) The actual definition of derivatives known to everyone. 1) Rolle's theorem, i.e. the Intermediate Value Theorem on first derivatives (if something goes up and down then it must have a critical pont). 2) Mean Value Theorem (Rolle's theorem but rotated) 3) Taylor's theorem.

Re: Calculus Made Easy (1914) [pdf]

#189

Post by thanatropism »

sundarurfriend wrote: post #165
taejo wrote: post #116

Earlier quoted context omitted.

> Because to them it's obvious. And to them it's wrong! Much is said in this book which is difficult (but not impossible) to rigourously justify. It took centuries for calculus to be placed on a rigourous mathematical foundation; this foundation (called "real analysis", largely developed in the 19th century) is quite different from the intuitive ideas presented in this book. The presentation here (in particular the i…

> this foundation (called "real analysis", largely developed in the 19th century) is quite different from the intuitive ideas presented in this book. ... (in particular the idea that dx² is negligible) Thank you for posting this! Such things always bothered me in high school, seemed like approximations that ought to bite you in the behind at least in some corner cases. Another example from TLA: > dy = 2cos(θ + 1/2 dθ…

But this is true of every level of mathematics. See humorous proofs that 2=3 amounting to manipulations like 0a = 0b, cut the zeros, a=b. This is no fault of "nonrigorous elementary algebra", it's a matter of remembering all notations are abbreviations and you have to know how to manipulate them.

You can get away with dy and dx if you just think "I'm not writing integral signs because they're annoying" and remember the rules of working with integrals. This is how stochastic differential equations work -- they're not even differential equations because Brownian motion is not differentiable, they're just notation.

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