or Calculus Made Easy: https://www.math.wisc.edu/~keisler/keislercalc-09-04-19.pdf

0: http://www.gutenberg.org/files/33283/33283-pdf.pdf

http://www.gutenberg.org/ebooks/33283

[1] http://www.amazon.co.uk/Calculus-Made-Silvanus-Phillips-Thom...

Read the first pages of Calculus Made Easy, looked nice so far.

http://www.gutenberg.org/ebooks/33283

[1]: https://www.gutenberg.org/files/33283/33283-pdf.pdf

Look at new editions of "Calculus Made Easy". It was re-written from infinitesimals to limits

Calculus Made Easy by Silvanus Phillips Thompson

http://www.gutenberg.org/ebooks/33283

P.S. Gave you an upvote. Just would have preferred to know the title / have a pointer to a non-PDF reference since one was available.

https://www.gutenberg.org/files/33283/33283-pdf.pdf

Calculus Made Easy
http://www.gutenberg.org/ebooks/33283

An oldie but a goodie.

For calculus itself, I’d recommend Thompson’s enlightening and witty 1910 textbook “Calculus Made Easy”. It’s available for free at:

https://www.gutenberg.org/files/33283/33283-pdf.pdf

https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus...

Calculus Made Easy seems too dumbed down to me.

I was surprised to find out how old this text was. It hasn't aged a day!

[0] http://calculusmadeeasy.org/1.html

[0]. https://news.ycombinator.com/item?id=14161876

https://hn.algolia.com/?q=calculus+made+easy

An excellent free alternative is Calculus Made Easy by Silvanus P. Thompson, which is very good and also funny
http://www.gutenberg.org/ebooks/33283

"... I had a calculus book once that said, 'What one fool
can do, another can'..."

I have this in Chapter 9: 'The Smartest Man in the World' in
Feynman's book 'The Pleasure of Finding Things Out'.

http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...

(And you probably know this, but "Calculus" isn't the same as the "Lambda Calculus" - your comment makes it appear that you've confused or equated the two.)

Calculus Made Easy, 2nd Ed (1914)

http://www.gutenberg.org/ebooks/33283

One of the best explained calculus texts I've read.

I don't know about recommending the practical-man book; I don't recall him mentioning it elsewhere. He quoted "What one fool can do, another can" (from Calculus Made Easy) I think more than once. I've skimmed Calculus Made Easy and it seems nice, and short.

I have refreshing my mathematics knowledge via videos made by Grant Sanderson.

Search "3blue1brown" on YouTube. I started with his Linear Algebra series (recommended here on HN)and then the Calculus series and finally the Neural Networks series. (highly recommended)

He is working on a Probability Series and I am supporting him on Patreon.

I look at it now, this book is wonderful.
https://news.ycombinator.com/item?id=14161876

The Art of Problem Solving series of books are uniformly excellent.

Most mainstream calculus books suck; they tend to hedge their bets between being advanced and proof-based on the one hand, and catering to students with a mediocre grasp of algebra on the other. Thomas' book is probably the best of this bunch.

Epp does proofs and discrete math, and a little bit of algorithms. The usual favorite for algorithms is Cormen et al.'s Introduction to algorithms, although I don't know it well.

For linear algebra, Axler (as someone else mentioned) is a very nice book. I really like Knop also (more beginner-friendly). Hefferon's Linear Algebra looks very nice, and is (legally!) free online. If you prefer a more applied/computational bent, try Strang.

The popular books by mathematician Ian Stewart

http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&...

are very interesting and mathematically accurate. Some readers also like the books by Keith Devlin,

http://www.amazon.com/Keith-Devlin/e/B000APRPC6/ref=ntt_athr...

one of which I am reading right now.

I like almost every book by John Stillwell

http://www.amazon.com/John-Stillwell/e/B001IQWNS2/ref=ntt_at...

and especially recommend the latest edition of Mathematics and Its History

http://www.amazon.com/Mathematics-Its-History-Undergraduate-...

as a book you should try to obtain from a library to see what a book with challenging, interesting, but accessible problems looks like.

Many people like the videos that feature Edward Burger

http://www.thegreatcourses.com/tgc/professors/professor_deta...

or Arthur Benjamin lecturing about math in the Great Courses (Teaching Company) video lecture series, which you may be able to find at a library.

AFTER EDIT: Here is a link for Calculus Made Easy, a book recommended by another participant here.

http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...

I've spent many years "pretending to understand" calculus, but things I remember gnawing at me, like limits & infinitesmals, are accompanied with context and history such that you can finally put yourself into the conversation and understand that my confusion is simply due to only getting a fraction of the story.

You can read the full text for free here [1]

[0] https://openlibrary.org/books/OL351037M/Calculus_made_easy

[1] http://calculusmadeeasy.org/

Ask HN: Links to older resources like Calculus Made Easy - https://news.ycombinator.com/item?id=23272635 - May 2020 (4 comments)

Calculus Made Easy (1914) [pdf] - https://news.ycombinator.com/item?id=23257303 - May 2020 (67 comments)

Calculus Made Easy (1910) - https://news.ycombinator.com/item?id=18250034 - Oct 2018 (68 comments)

Ask HN: Books Like 'Calculus Made Easy'? - https://news.ycombinator.com/item?id=14166466 - April 2017 (8 comments)

Calculus Made Easy (1914) [pdf] - https://news.ycombinator.com/item?id=14161876 - April 2017 (189 comments)

As I continued reading I found the relevant quote to the second text, Calculus Made Easy, on page 194 of Feynman's "The Pleasure of Finding Things Out", where Feynman states:

"I had a calculus book once that said, 'What one fool can do, another can.'"

While he doesn't name it, that's almost without a doubt "Calculus Made Easy". Both calculus texts are thus referred to in Feynman's "The Pleasure of Finding Things Out". In the index of that book, under the topic "Calculus", the pages of both references can be found.

You might want to read the chapter of Calculus Made Easy entitled Epilogue and Apologue ;)

Excerpt:

>Thirdly, among the dreadful things they will say about “So Easy” is this: that there is an utter failure on the part of the author to demonstrate with rigid and satisfactory completeness the validity of sundry methods which he has presented in simple fashion, and has even dared to use in solving problems! But why should he not? You don’t forbid the use of a watch to every person who does not know how to make one? You don’t object to the musician playing on a violin that he has not himself constructed. You don’t teach the rules of syntax to children until they have already become fluent in the use of speech. It would be equally absurd to require general rigid demonstrations to be expounded to beginners in the calculus.

You're not wrong, of course, but neither is Silvanus P. Thompson.

Then pick up any calculus textbook and chug through it (Thomas is good from what I've heard). Even if the questions don't have answers in the back of the book you can check your computational steps for free using: https://www.symbolab.com.

I also recommend lots of practice, so khan academy is good for drilling + any problem set book with lots of calculus problems, such as "Schaum's 3,000 Solved Problems in Calculus" or "Essential Calculus Skills Practice Workbook". They don't have to be huge calculus text, doing problems is more important than reading through 1,000s pages of colorful examples. You can find shorter calculus books that focus primarily in drilling calculus techniques. Focus on those to nail the techniques.

It's just that the quote on fools is very prominent in the beginning of Calculus Made Easy, and the author continues to hilariously refer to both other people and himself as fools. I searched inside Calculus for the Practical Man [1] on archive.org for the word "fool" without a single hit.

I'm sure Feynman read both, but I was interested in the origin of the quote, since I learned it a few days ago and think it's very inspirational. Feynman was constantly arguing that everyone has the capacity to figure things out, it's just that they rarely practice it.

[1] https://archive.org/details/calulusforthepra000526mbp

It reminds me of the preface to Elementary Calculus [1] [2] an excellent text that I discovered years after learning the subject using the limit:

> The calculus was originally developed using the intuitive concept of an infinitesimal, or an infinitely small number. But for the past one hundred years infinitesimals have been banished from the calculus course for reasons of mathematical rigor. Students have had to learn the subject without the original intuition. This calculus book is based on the work of Abraham Robinson, who in 1960 found a way to make infinitesimals rigorous. While the traditional course begins with the difficult limit concept, this course begins with the more easily understood infinitesimals.

[1]: https://www.math.wisc.edu/~keisler/calc.html

[2]: https://en.wikipedia.org/wiki/Elementary_Calculus:_An_Infini...

You might also find Unknown Quantity interesting. I think Gullberg would be my #1 req for you.

Time spent learning Calculus is worthwhile; and if nothing else, understand the fundamental theorem. Overwhelmingly impressive.

Every time I've recommended Calculus Made Easy [0] it's been a huge success. The writing is lively and full of motivating examples, and it's an enjoyable read.

[0] https://news.ycombinator.com/item?id=17185577

Quoth the 'pedia: "Calculus Made Easy is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject."

[1] http://en.wikipedia.org/wiki/Calculus_Made_Easy

[2] http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/d...

[3] http://www.gutenberg.org/ebooks/33283

I hope I am not getting downvoted to hell but I always thought Strang was overhyped. I watched his lectures and bought his book and I never felt this is the most accessible way of teaching LA. At least not in the way, people hyped it up to be.

I much prefer Jim Hefferon's LA book for example. No hate towards Strang but I always felt so dumb when I watched or read his stuff after people were raving about it.

I haven't found many other books that explain calculus as well as that one. If you get that and then a book of exercises from Schaum's outlines, you'll be able to get pretty good at it. Also, the book is a really good read for a math book.

Most of them could get a better intuitive understanding of Calculus. (We should of course conduct a rigorous study comparing the effects of using different approaches to teach Introductory Calculus.) Then those who need to use the limits approach for other courses could use the intuition to learn it faster. In addition, they would understand Calculus from two different angles and could select the more suitable approach for each problem.

http://en.m.wikipedia.org/wiki/Calculus_Made_Easy

"There was a series of math books, which started Arithmetic for the Practical Man, and then Algebra for the Practical Man, and then Trigonometry for the Practical Man, and I learned trigonometry for the practical man from that. I soon forgot it again because I didn't understand it very well but the series was coming out, and the library was going to get Calculus for the Practical Man and I knew by this time by reading the Encyclopedia that calculus was an important subject...and then the calculus book finally came out ...and I went to the library to take it out and she looks at me and she says, "Oh, you're just a child, what are you taking this book out for, this book is a [book for adults]." So this was one of the few times in my life I was uncomfortable and I lied and I said it was for my father, he selected it. So I took it home and I learnt calculus from it..."

Calculus for the Practical Man was first published in 1931 when Feynman was about 13 years old, which fits the story (he was waiting for the book's publication).

So that would point to Feynman's calculus book being "Calculus for the Practical Man" by J.E.Thompson rather than Silvanus P Thompson's "Calculus Made Easy", whose second edition came out in 1914. I would not be surprised that Feynman read and used both.

The two books are quite different in approach, Practical having, to me, a rather unique physics orientation and being a more demanding text.

* How to Prove It (Velleman)

* Algebra; Trigonometry; F&G; The Method of Coordinates (Gelfand)

* Geometry (Kiselev)

* Calculus Made Easy (Thompson)

* How to Count without Counting (Niven)

* Introduction to Probability Theory (Hoel)

* The Little Schemer (Friedman)

The proceed to more advanced texts like:

* Naive Set Theory (Halmos)

* Linear Algebra Done Right (Axler)

* Geometry Revisited (Coxeter)

* Infinitesimal Calculus (Keisler)

* Concrete Mathematics (Graham)

* Information Theory, Inference and Learning (MacKay)

* SICP (Abelson)

Quality of teaching might have something to do with it.

But, also, calculus is much harder to understand at a rigorous, formal level than at an informal level.

On one level you can try to understand what the main concepts are about, be able to compute derivatives and integrals, solve optimization and related rates problems, and so on. I'd recommend Silvanus Thompson's Calculus Made Easy over any mainstream calculus book for this. In my opinion, the book succeeds amazingly at fulfilling the promise of its title.

But suppose you really try to read any mainstream calculus book, and understand everything. For example:

- Why are limits defined the way they are (with epsilons and deltas)?

- The book will probably touch lightly upon the Mean Value Theorem -- why is this important? What's the point?

- Why is the chain rule true? It reads dy/dx = (dy/du) (du/dx). Yay! This is just cancelling fractions, right? Any "respectable" calculus book will insist that it's not, but most students will cheerfully ignore this, still get correct answers to the homework problems, and sleep fine at night.

- Consider the function e^x. How is it defined? The informal way is to say e = 2.71828... and we define exponents "as usual". Most students are perfectly happy with this. But does this really make sense if x is irrational? Your calculus book might bend over backwards to define everything properly (e^x is the inverse to ln(x), which is defined as a definite integral), and it takes a lot of work to appreciate why.

In my experience, these sorts of issues mostly don't pop up in linear algebra, where the proofs tend to parallel the handwavy heuristics. I wonder if this had anything to do with your experience?

* Basic Mathematics by Serge Lang

* Calculus Made Easy by Silvanus Thompson

Then try a DIY bootcamp in the spirit of Harvard Math 55. If you are interested in continuous math:

* Vector Calculus by Hubbard & Hubbard

If you are interested in discrete mathematics and computation:

* Logic in Computer Science by Huth & Ryan

You'll need to understand calculus, i.e. understand the principles behind derivatives and integrals. You certainly won't need to be proficient in manipulating them. A brief book, like Martin Gardner's updated edition of Calculus Made Easy, is the type of background that you need. A bit more specifically, having an intuition for vector calculus and partial differential equations is important.

For QM, you will need to understand what linear algebra is for, and how it uses abstraction to simplify certain types of operations. Here's a good introduction: http://betterexplained.com/articles/linear-algebra-guide/

Honestly, I can't think of anything else that you would necessarily need to know before starting, but to get the most out of it you WILL need to follow along with his working in pen-and-paper, and get used to rewatching, or looking up topics that you struggle with.

Just one thing:

> introductory texts [...] University Physics by Young, Freedman, and Ford [...] to learn calculus, Calculus by Larson and Edwards [...] should take you a year or two to consume [...]

I disagree. Two years? I think six months should be enough time for the modern youth to learn all of first year physics, calc one and two included.

The only limiting factor is the time it takes to do the exercises, because, like you said, the main part of learning physics happens when you are figuring things out on your own. I bet that one or two semesters with a good book with exercises with answers in the back can be enough to learn how to use all of first year math and physics. If only there were such a book that teaches calculus, mechanics, E&M and linear algebra, all in one sitting. ;)

I will close on a personal recommendation from 1914. Calculus Made Easy by Silvanus P. Thompson
http://www.gutenberg.org/files/33283/33283-pdf.pdf

To anyone struggling through calculus for the first time: Use what works! For all we know, Strang himself might of learned from Calculus Made Easy. He'd be in good company if so, though it seems like RPF was rather free with the calc books, if ya know what I mean. (see the other thread)

I remember being taught about derivatives with the formal limit formula, then all the tricks for finding them (power rule etc), and finally finding function extrema using derivatives; all before developing much intuition about the concept.

> "Right. I don't believe in the idea that there are a few peculiar people capable of understanding math, and the rest of the world is normal. Math is a human discovery, and it's no more complicated than humans can understand. I had a calculus book once that said, 'What one fool can do, another can.' What we've been able to work out about nature may look abstract and threatening to someone who hasn't studied it, but it was fools who did it, and in the next generation, all the fools will understand it. There's a tendency to pomposity in all this, to make it deep and profound." -- Feynman, Omni 1979

The "what one fool can do" quote from a calculus book is probably from Calculus Made Easy that was posted on HN a couple of days ago:

https://news.ycombinator.com/item?id=14161876

In Calculus Made Easy, the exact quote is "What one fool can do, another can. -- (Ancient Simian Proverb)".

For slightly less mature students, there's Algebra by Gelfand.

In contrast, the article in this post is terrible. Tons of footnotes referring to exceptions. I feel like the author is trying to summarize a subject he doesn't understand himself.

Linear algebra is quite a beautiful, approachable subject; and a certain amount of it is necessary to make the leap from single variable to multi-variable calculus. Without a good grip on calculus, you can’t really what’s going on under the covers with linear algebra. What you need to do is precalculus (Simmons) -> single variable calculus -> very introductory / elementary linear algebra -> multi variable calculus (Apostol) -> less introductory linear algebra but still fairly basic (Gilbert Strang Intro to Linear Algebra) -> mathematical analysis (Apostol) -> linear algebra done right (Axler). You have to apply a spiral method where you return to subjects as you gain the tools you need to understand them better. You’ll never be done understanding geometry, algebra, or analysis.

Also, math is a problem solving art, and you can’t solve problems by reading, you solve them by thinking. Seek out problems that challenge and consolidate your understanding. You should be able to prove everything in Simmons and it should seem totally natural and intuitive. Then you’re ready to struggle with calculus, which is a subject humanity struggled with for centuries before getting a rigorous handle on. You probably want to get a handle on the mechanics and intuition, first, and for that I’ve heard that “Calculus Made Easy” by Silvanus Thompson is good.

Don’t try to eat too much all at once, you’ll make yourself sick. Don’t try to cheat yourself of the patient struggle to understand, confusion is completely natural when striving to really know something.

An informal, brief book on vector calculus is Schey's Div, Grad, Curl and all That. I have not read it personally, but I have heard good things about it. It is probably the quickest way of achieving your immediate goal of understanding Maxwell's equations.

Free online copy: ftp://collectivecomputers.org:21212/books/morebooks/Mathematics/Div,%20Grad,%20Curl%20and%20All%20That%20-%20Shey.pdf

For single variable calculus, if you want an entertaining and enlightening quick read, I recommend Thompson's Calculus Made Easy:

https://www.gutenberg.org/files/33283/33283-pdf.pdf

No proofs, but lots of helpful informal explanations.

Textbooks after first-year university are normally much better and bullshitfree. Graduate textbooks are usually solid.

Also, there are many free textbooks out there that are essentially bullshit free, e.g. Calculus Made Easy by Silvanus P. Thompson available at http://www.gutenberg.org/ebooks/33283

A book with an easy approach really needs to make the chapters super easy to restart and spiral through concepts. Stories and characters didn’t hurt to have too though.

I came across Silvanus Thompson's 1910 reprinted textbook Calculus Made Easy [1], and it was hands down the best primer on any topic I've delved into.

1. http://www.amazon.co.uk/Calculus-Made-Easy-Very-Simplest-Int...

Without further details, it's hard to know what your current level is. Most math bootcamps cover algebra and calculus. A great high school level one is:

* Basic Mathematics by Lang

* Calculus Made Easy by Thompson

If that is too simplistic, try a Math 55 like approach:

* Linear Algebra Done Right by Axler

* Principles of Mathematical Analysis by Rudin

You can replace Axler by Finite-Dimensional Vector Spaces by Halmos. But it's harder. Sadly the latest edition of Axler has distracting pictures and boxes that have done away with some of it's TeX elegance.

You can also replace both books by Vector Calculus, Linear Algebra, and Differential
Forms: A Unified Approach, by Hubbard & Hubbard.

An alternative route is to do a bootcamp where logic and abstract algebra is the area of focus. I've never seen such a course offered to beginners, but I think it'd be great if you are later focusing on things like formal methods.

Calculus Made Easy by Silvanius P. Thompson (Feynman taught himself calc with this book)

Concrete Mathematics by Knuth, Graham, Patashnik

Fundamentals of Applied Probability Theory by Alvin Drake

You probably want to learn Linear Algebra - get Gilbert Strang's book.

The Schuam's outlines in each topic are good for review. I like the ancient ones, usually there are dozens of them for next to nothing at any good used bookstore.

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.

For young students, a great introductory textbook is Calculus Made Easy. It is around 100 years old, and develops all the material using infinitesimals. Which is essentially modern non-standard analysis, minus rigor. It is also the way Newton and Leibniz thought about calculus, and the way most physicists intuitively think about problems.

For a more mature audience, I like Infinitesimal Calculus by Henle & Kleinberg.

Here is a famous quote where he references a passage from the book's prologue:

"Right. I don't believe in the idea that there are a few peculiar people capable of understanding math, and the rest of the world is normal. Math is a human discovery, and it's no more complicated than humans can understand. I had a calculus book once that said, 'What one fool can do, another can.' What we've been able to work out about nature may look abstract and threatening to someone who hasn't studied it, but it was fools who did it, and in the next generation, all the fools will understand it. There's a tendency to pomposity in all this, to make it deep and profound." -- Feynman, Omni 1979 (http://c2.com/cgi/wiki?FeynmanAlgorithm)

I've seen several (quite a few actually) books with this title on Amazon. Some of them written by Martin Gardner and Silvanus P. Thompson, others written by Thompson alone. Do you recommend a particular edition? (and what's the deal with the plethora of different editions?)

> For QM, you will need to understand what linear algebra is for, and how it uses abstraction to simplify certain types of operations. Here's a good introduction: http://betterexplained.com/articles/linear-algebra-guide/

Could you recommend a wood-pulp version of this kind of material?

As a side note, I'm finding both Calculus Made Easy and Concrete Mathematics incredibly useful. Thanks for the suggestions.

The book itself
http://djm.cc/library/Calculus_Made_Easy_Thompson.pdf

Wikipedia:
http://en.wikipedia.org/wiki/Calculus_Made_Easy

It gives you a working knowledge to get going with almost any practical problem you may encounter that needs to be approached with mahtematical analysis.

I would say that Spivak books are more about learning the culture of working mathematicians, and while with its merits one must be careful with commitment of investing her personal time to it.

Also, here is a great page to learn about good (and usually public) books for different branches of mathematics and physics by a Nobel-winning theoretical physicist G. t'Hooft
http://www.staff.science.uu.nl/~hooft101/theorist.html

- George Polya - How to Solve It

Interesting book on proofs and a logical approach to problem solving. Original title was "School of Thinking"…

- Lancelot Hogben - Mathematics for the Millions
- Silvanus P Thompson - Calculus Made Easy

Two older books that came well recommended (have been mentioned in this thread already). Not sure if that's due to the readers or their teachers nostalgia or well founded yet.

- The Manga Guide to Calculus

Erm, yeah. (I did like the Manga Guide to Databases, though)

- Benjamin & Shermer - Secrets of Mental Math

How to do mental arithmetics quickly. Good for igniting the spark and impress your friends…

Also, some book on mathematics by Russian, who employ some different methods in teaching, but I can't find the book nor its title right now, must be in some moving box. (Generally, talk to Russians. They're creepy when it comes to maths and chess)

[1] https://www.youtube.com/watch?v=04MWqyhD61g

I gave up on mathematics after my first college course but found that for everything I wanted to get into, Machine Learning & Bayesian stats, it was essential . A year later I know math better than ever before even though I haven't stepped inside a classroom in years.

You're probably getting bored because most math books are hundreds of pages long and in addition to the material they include mathematicians bio's, several solution methods, and the explanations of edge cases.

"Now any fool can see that if x is considered as made up of a lot of little bits, each of which is called dx, if you add them all up together you get the sum of all the dx's (which is the same as the whole of x). The word 'integral' simply means 'the whole'"

After reading this and more I asked a few people who I know knew calculus how they would explain an integral (figuring that they would give a similar definition and would delight in finding a book which explained it so clearly) and was shocked to discover how many could calculate it without really understanding what it was or at least being able to describe what it was in clear terms

The calculusmadeeasy.org website does include at least one useful footnote that the other versions don’t: “The term billion here means 10^12 in old British English, ie, trillion in modern use.” [3]

[1] https://archive.org/details/CalculusMadeEasy/page/n3/mode/2u...

[2] https://www.gutenberg.org/ebooks/33283

[3] https://calculusmadeeasy.org/2.html#fn1