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Calculus Made Easy (1914) [pdf]

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Re: Calculus Made Easy (1914) [pdf]

#111

Post by theCricketer »

joericky233223 wrote: post #109
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…

>MIT recorded a set of Calculus video courses back in 1970s that they have since made publicly available. Could you please post the links to this videos.

Sorry I should have made it more clear - the links are at the end of my comment.

Re: Calculus Made Easy (1914) [pdf]

#112

Post by baldfat »

The prologue is 100% dead on and what I have always thought in terms of the easy part of calculus needs to be taught early. I would have never been able to vocalize what he said in the short half page of text.

We teach math backwards. We have a population that can barely do 4th grade arithmetic and it is socially okay.

Children and people believe that decimal points are accurate and that fractions are abstract when the exact opposite is true. 1/3 of a pizza is real and 0.333333 is a fake number.

We also teach movement and change as a word problem i.e. a train leaves Chicago at 25 MPH and another train leaves Flint, MI at 35 MPH when will the trains meet? That answer is an estimation of an unattainable constancy but people believe it is logical conclusion.

Pre-Calculus (needs to be repackaged with the idea of the one consistent in our world is change) should be taught before Algebra and Geometry. Make math into something where people can truly understand abstract and concrete. People actually think calculus is a hyper abstract algebra when in fact it is putting math into real world solutions.

The number one problem is calculus is 100% dependent on the teacher. A great teacher will make this work and a lower skilled teacher can absolutely kill almost all learning.

Re: Calculus Made Easy (1914) [pdf]

#114

Post by ziikutv »

TsukiZombina wrote: post #92
ziikutv wrote: post #67

Earlier quoted context omitted.

So a while back, I said I am going to start writing "Colloquial books" about all of the courses I took as I relearn all of the stuff in my and other Engineering Branches (minus the grade-gun pointed at my head). One of the first courses are of course Calculus. I skimmed through some of these video lectures, I wonder if I even should write books for this. Or simply href. Thank you for the share. Will be of great help…

I thought the same as you!

Its going to be open source so, you can put your thoughts into action if you want. =D

Edit: add smiley face.

Re: Calculus Made Easy (1914) [pdf]

#115

Post by lunchladydoris »

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

Re: Calculus Made Easy (1914) [pdf]

#116

Post by taejo »

jacquesm wrote: post #41
partisan wrote: post #26

Earlier quoted context omitted.

As someone who struggled through calculus, this book would have made a huge difference for me. Just reading through the first few pages brought a smile to my face that someone could so plainly explain these critical concepts in such a familiar way. Why didn't my professors do that?

> 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 idea that dx² is negligible) can be made rigourous through "non-standard analysis", but this 20th century development is less-known (in fact, unknown to many mathematicians) and perhaps even more difficult than real analysis.

Rigour is not necessary to understanding, and can even be fatal to understanding, but it's how mathematicians work, and generally mathematics is taught by mathematicians.

Re: Calculus Made Easy (1914) [pdf]

#117

Post by taejo »

ankurdhama wrote: post #55

In my experience, everything is easy if you DON'T try to learn it using analogies and metaphors.

I think that is a very "mathematician" thing to say; my own experience of doing mathematics is largely in accord. A little experience of teaching mathematics shows that this doesn't work for most people.

Re: Calculus Made Easy (1914) [pdf]

#118

Post by laughingman2 »

baldfat wrote: post #112

The prologue is 100% dead on and what I have always thought in terms of the easy part of calculus needs to be taught early. I would have never been able to vocalize what he said in the short half page of text. We teach math backwards. We have a population that can barely do 4th grade arithmetic and it is socially okay. Children and people believe that decimal points are accurate and that fractions are abstract when t…

I think you this will interest you. Its a mathematician's lament on how the current system of teaching math is wrong.

https://www.maa.org/external_archive/devlin/LockhartsLament....

Re: Calculus Made Easy (1914) [pdf]

#119

Post by djhworld »

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 maths saying that's all you need, but I don't think you can escape the fact that sometimes you just need to start from the beginning and work your way up

Re: Calculus Made Easy (1914) [pdf]

#120

Post by jacquesm »

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…

> in fact, unknown to many mathematicians

> and generally mathematics is taught by mathematicians

So that leaves the door wide-open to a whole army of mathematicians to who it is unknown that are teachers.

And those are the ones for who all of the above does not apply and who still treat their 'entry level problems' as obvious to all their students even when the evidence strongly suggests that to the students it is not at all obvious.

And I'm writing this as a high school kid who was pretty good in math but totally lost interest due to such teachers (that, and computers were far more interesting).

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