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Calculus Made Easy (1914) [pdf]

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Re: Calculus Made Easy (1914) [pdf]

#171

Post by tchaffee »

ankurdhama wrote: post #147
tchaffee wrote: post #113

Earlier quoted context omitted.

The latest research on how we learn and how the brain works places great importance on analogy as a learning tool.

Any references to such research?

- Baddeley, Alan, Michael W. Eysenck, and Michael C. Anderson. Memory. NY: Psychology Press, 2009.

- Cat, Jordi. "On Understanding: Maxwell on the Methods of Illustration and Scientific Metaphor" Studies In History and Philosophy of Science Part B32, no. 3 (2001): 395-441

- Derman, Emanuel. Models of Behaving Badly. New York, NY: Free Press, 2011

- Foer, J. Moonwalking with Einstein. NY: Penguin, 2011

- Lutzen, Jesper. Mechanistic Images in Geometric Form. NY: Oxford University Press, 2005

- Maguire, E.A., D.G. Gadian, LS. Johnsrude, C.D. Good, J. Ashburner, R.SJ. Frackowiak, and CD. Frith. “Navigatioanelated Structural Change in the Hippocampi of Taxi Drivers.“ Proceedings of the National Academy of Sciences 97, no. 8 (2000): 4398-403

- Maguire, E.A., ER. Valentine, J.M. Wilding, and N. Kapur. “Routes to Remembering: The Brains Behind Superior Memory." Nature Neurosciencee, no. 1 (2003): 90-95

- Rocke, AJ. Image and Reality Chicago, IL: University of Chicago Press, 2010

- Solomon, Ines. “Analogical Transfer and 'Functional Fixedness' in the Science Classroom." Journal of Educational Researd 87, no. 6 (1994): 371-77

Re: Calculus Made Easy (1914) [pdf]

#172

Post by data_hope »

pervycreeper wrote: post #66
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

>There is a much better PDF LaTeX is not an aesthetic cure-all. The original, at least, has been subjected to the critical eye of a typesetter. There is no disputing taste, but I will anyway. If you're using an e-paper device, btw, you can vectorize the text in scanned pdfs like this by applying "Clearscan" in Acrobat, or the equivalent (after which, it becomes readable).

line spacing of the gutenberg-latex-typeset version is terribly enlarged. It's a disease... Who can read that?

Re: Calculus Made Easy (1914) [pdf]

#173

Post by metaphor »

amai wrote: post #124
c517402 wrote: post #50

IIRC this the book Richard Feynman said he checked out of the library and learned calculus from. Also, Feynman made comments similar to those in the Prologue.

I thought the book Feynman mentioned was Woods: Advanced Calculus: https://www.reddit.com/r/math/comments/17dq5l/is_there_a_mod...

IIRC, Feynman mentioned Woods in the context of differentiation under the integral sign, whereas J.E. Thompson was in the context of learning Calculus as a kid.

Re: Calculus Made Easy (1914) [pdf]

#174

Post by tptacek »

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…

I do this all the time. There's nothing at all weird or embarrassing about it. 10 years ago I was sure I'd remember and have an intuition for the trig identities, but I'm still looking them up every time now.

Also, even in pretty advanced CS (at least in my field, security and, particularly, cryptography), most of the nuts-and-bolts math is high school math.

Re: Calculus Made Easy (1914) [pdf]

#175

Post by empath75 »

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…

I dropped out of college and never went higher than pre-calculus, and I went back to learn all of this stuff with Khan Academy in my 30s, as well. It's an amazing resource.

Re: Calculus Made Easy (1914) [pdf]

#176

Post by neuronexmachina »

Fun fact: The author Silvanus Thompson was an early pioneer of what is now known as transcranial magnetic stimulation. You can see him posing with his head in a device for testing neurophysiological effects of alternating magnetic fields in figure 4 of this paper: http://rsnr.royalsocietypublishing.org/content/61/1/5.figure...

Re: Calculus Made Easy (1914) [pdf]

#177

Post by InclinedPlane »

I love calculus, it's such an amazing collection of fascinating, elegant (and useful!) concepts that give you a transformative insight on mathematics in general. It's very frustrating to see it taught so poorly so often though.

One problem that teaching calculus has is that it's very dependent on having a solid foundation in other mathematics such as advanced algebra, trig, etc. In today's school systems that encourage gaming the system as students and teaching to the test as educators it's rare for most students to actually understand or be competent with material they've allegedly studied. When they hit something that starts off where they left off and builds upwards, if they have any weaknesses in that foundation it will show immediately and slow them down immensely.

Add on to that all the other problems of typical calculus instruction such as a desire to make it hard as a matter of protecting calculus education as a status symbol for "smart" people, the ability to ratchet up the difficulty arbitrarily through requiring memorization of a potentially infinite set of "trivia" (every trig. identity, every method of differentiation/integration, and so on), while generally not concentrating on the abstract concepts or the fundamentals.

Re: Calculus Made Easy (1914) [pdf]

#178

Post by OJFord »

emodendroket wrote: post #138
OJFord wrote: post #27

Earlier quoted context omitted.

It's all relative. Obviously I mean that it sounds vastly more recent than 1914 to my ear. And anyway, I confess I don't know the industry at all, but I doubt anyone would talk about 1914 as representing 'modern publishing'.

A lot of the elements of what we'd call "modernity" were either introduced or became widespread in the course of the first World War so I'm not trying to just be a jerk here; I think it really is a useful dividing line.

I'm not sure I agree to it being anything stronger than a 'catalyst' period, but regardless; as elsewhere, by 'modern' I meant 'more recent than it is'.

Re: Calculus Made Easy (1914) [pdf]

#179

Post by smnplk »

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

Yes, what a gem of a man.He also posted his email address in the comments for a young high school student for any further help. He is 88 years old now, I hope he is in good health.

Re: Calculus Made Easy (1914) [pdf]

#180

Post by [deleted] »

userbinator wrote: post #30
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

You say 1.9MB, the Gutenberg page says 1.8MB, and the download itself is only 1.18MB thanks to gzip. The main difference is that the Gutenberg PDF is a transcribed, cleaned-up version. As much as this probably makes me sound like an audiophile, I actually prefer the raw scans over what may essentially be a reprint. They show all the blemishes, unofficial additions, and other marks that make the book look more "real"…

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