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Calculus Made Easy

Silvanus P. Thompson, Martin Gardner · 10 HN comments
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Amazon Summary
Calculus Made Easy has long been the most popular calculus primer, and this major revision of the classic math text makes the subject at hand still more comprehensible to readers of all levels. With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.
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All the comments and stories posted to Hacker News that reference this book.
Was it Calculus Made Easy?

It seems easy to find a pdf on the web, but I didn't want to post that.

yes, I was looking for this book. Thank you. I wish I had read this when I was in school. I liked the book for explaining complex topic in a very simple, easily understandable way. This would be a great book to introduce calculus to your kids. I read chapter 2 (on different degrees of smallness) and found it enlightening.
You're welcome. Happy reading!
There's also a website if you don't like PDFs:
The original (not the Martin Gardner version) is public domain at this point. Project Gutenberg has a PDF of it.

Ok, thank you. I did not realize this version was PD.
I bailed on high school math, thinking I'm math dumb.

In my late 20s I decided to try again, but jumped straight into calculus. And at first regretted that decision. However, I got lucky by stumbling upon this book:

It "reads" like a book, with the ideas given context. I had an "ok" connection with Algebra, and the book explained the rest well enough for me.

In school, the textbooks were loaded with symbols, but not enough description -- I guess they relied on bored teachers making minimum wage to do that part. I went to a school with poor academic showings (but connections to state superintendent of ed got them a grant for football facilities).

Coincidentally, this book goes well with the technique described here:

Nov 19, 2015 · Jtsummers on Einstein’s First Proof
Unfortunately, not much. I was pondering that after my post. It's been a long time since I was a math student, and professionally it's had zero to do with my career. A lot of books ended up boxed up at my parents' home as I moved around a number of times right after college. I'll check my own home tonight to see what I still have, but my shelves these days are mostly filled with fiction, programming, RPG, and history books.


Off the top of my head, for CS:

Introduction to Algorithms:

Introduction to the Theory of Computation:


Calculus Made Easy: - I'm really not sure how good this one is for a beginner, I picked it up while assisting my sister in refreshing her calculus skills for grad school (Aerospace Engineering)

I can't remember the algebra and geometry textbooks (my dad's or my grandfather's) that I used, in addition to the assigned text, in high school.

Anything by Knuth. Seriously, one summer a professor and I just picked up copies of Concrete Mathematics and worked through large portions of it for fun. Technically I got some math credits for it, but it was really just because we wanted to. Actually, this one helped me a lot with understanding calculus. Somehow, up to that point while I knew calculus, may brain had never made the connection that integration was summation until I saw the discrete counterpart to continuous integration. I had a mechanical understanding, but no deep understanding until that moment.

There's also Calculus Made Easy[1], by Silvanus Thompson, relatively recently reprinted in an edition with additions from Martin Gardner.[2] The original edition is available in the US from Project Gutenberg, though.[3]

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."




> Calculus Made Easy

Thompson wrote the original edition a century ago. It is now Public Domain.

Gardner's revised edition adds introductory material, a problem set, and updates the language to keep it roughly in line with what is taught now. I can't speak to the differences between modern editions, but I have this one:

> linear algebra

To be honest, all abstract algebra is tough on new-comers. Compared to undergraduate calculus, the "aha" moments have more pay-off, but usually take a lot more time. The significance and power of vector spaces is just not something that is easily learnt, other than by working through problems with pen-and-paper math, and while doing so, constantly asking yourself "why do mathematicians do things this way, rather than some other way?"

I bought a copy of Gilbert Strang's Linear Algebra And It's Applications when I was an undergrad, and still refer to it now. It's brilliant, but it's a traditional text book, and definitely not a "primer".

It's not the type of maths you would call "hard" (integral calculus can be infuriatingly "hard") but it's the type that takes time and work to understand. Once you understand vector spaces, QM is surprisingly straight-forward.

I haven't seen the updated version, but the one on gutenberg is gold. The old language is comical on its own: he cracks jokes and it is funny because of the jokes //and// because of the old language.

This book is so good, that gutenbeg volunteers took the time to typeset all the math in latex so the PDFs are very good for reading or printing out.


   Considering how many fools can calculate, 
   it is surprising that it should be thought 
   either a difficult or a tedious task for any 
   other fool to learn how to master the same tricks.
   Some calculus-tricks are quite easy. Some are 
   enormously difficult. The fools who write the 
   textbooks of advanced mathematics—and they are 
   mostly clever fools—seldom take the trouble to 
   show you how easy the easy calculations are. 
   On the contrary, they seem to desire to impress 
   you with their tremendous cleverness by going about 
   it in the most difficult way.

   Being myself a remarkably stupid fellow, I have had 
   to unteach myself the difficulties, and now beg to 
   present to my fellow fools the parts that are not hard. 
   Master these thoroughly, and the rest will follow. 
   What one fool can do, another can.
Aug 29, 2012 · lutusp on Teaching Kids to Love Math
That might sometimes be true, but the textbook the OP referred to is less than $16.00:

Which is why no one will ever use it, because you can't justify a $200 price tag for a 100 page text books.

e.g. no college will ever endorse this book as a text, because they need to sell 60k in calc 101 text books each semester so they can get their cut.

> ... no college will ever endorse this book as a text ...

Yes, fair enough, however I think the discussion is not so much about schooling as education. Not all education takes place in college -- and with costs rising as they are, I predict a future with many more autodidacts -- self-educators.

"I have never let my schooling interfere with my education." -- Mark Twain

Can you now teach me how I (~20 year old) can be interested in math?

The popular books by mathematician Ian Stewart

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

one of which I am reading right now.

I like almost every book by John Stillwell

and especially recommend the latest edition of Mathematics and Its History

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

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.

After Vector Calc, I wanted to go back to the fundamentals, to understand instead of remembering.

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.


Available on Project Gutenberg here:
I don't have a link handy, but there is a very clear scanned pdf of the second edition of Calculus Made Easy from 1914 available on
Have to agree on Calculus Made Easy. Found it in high school and quickly learned intro calculus better than anyone in the AP Calculus class.
I've Silvanus sitting in my shelf, but am yet to look into it yet.

A couple of recommendations (not specific to just Calculus):

- What is Mathematics? (Courant

- Calculus (Apostle

- Mathematics from the Birth of Numbers ( This book was written by a Swedish surgeon without any background in Mathematics. He started working on this when his son started attending university. A recommended read.

- The Calculus Lifesaver (Adrian Banner). This book is supposed to be a guide for students to crack their exams. But I found the book surprisingly informative.

- Godel Escher Bach. I've read only the first couple of chapters. My interest in mathematics was rekindled to a great degree by Godel and the Incompleteness Theorem. (

- The concept alone makes me happy! Metamath is a collection of machine verifiable proofs. It uses ZFG to use prove complicated proofs by breaking it down to the most basic axioms. The fundamental idea is substitution - take a complicated proof, substitute it with valid expressions from a lower level and keep at it. It introduced me to ZFG and after wondering why 'Sets' were being taught repeatedly over the course of years when the only useful thing I found was Venn diagrams and calculating intersection and union counts, I finally understood that Set theory underpins Mathematical logic and vaguely how.

- The Philosophy of Mathematics. From the wiki: studies the philosophical assumptions, foundations, and implications of mathematics. It helped me understand how Mathematics is a science of abstractions. It finally validated the science as something that could be interesting and creative.

I think the Philosophy of Mathematics should be taught during undergraduate courses that has Maths. It helps the students understand the nature of mathematics (at least the debates about it), which is usually pretty fuzzy for everyone.

If you've only read the first few chapters of Godel Escher Bach, you should really set a goal to continue reading. The book is filled with so much good information presented in a digestible format. Topics are slowly revealed throughout the book until you just get it. It's a great experience.
If you've never read it before this book is a very intuitive introduction (and refresher):
This book is currently out of copyright (published 1910):

Also available at the Gutenberg project, here:

It seems to be a rather nifty book.

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