[madars]

Toeplitz wrote "Calculus: The Genetic Approach" and his approach of explaining math via its historical development is apparently more widely used: https://en.wikipedia.org/wiki/Genetic_method . Felix Klein remarked: "on a small scale, a learner naturally and always has to repeat the same developments that the sciences went through on a large scale"

[twbarr]

We could really take a page from this style for teaching advanced computing. We try to imagine that architectures just kind of come out of nowhere. Starting with mechanical computing and unit record equipment makes so much make more sense.

Plus, unit record equipment was cool.

[blame-troi]

Very cool. But so many of us paid not enough attention to the details. Only two of the people in my first shop attempted channel programming.

[b0afc375b5]

I always longed for a book/course on mathematics where topics are in chronological order:

1. ... (mathematical topics at the beginning of history of which I am ignorant of)

2. pythagoras theorem

3. ...

4. euclid geometry

5. ...

6. algebra

7. ...

8. calculus

9. ...

10. set theory

11. ...

12. number theory

13. etc. etc. (you get the point)

Maybe there's already something that lays out topics like this. I haven't searched too hard.

[spc476]

There is Mathematics for the Million by Lancelot Hogben, which not only covers math, but the history of math and why it was developed over the centuries. It starts with numbers, then geometry, arithmetic, trig, algebra, logarithms and calculus, in that order. It's a very cool book.

[SoleilAbsolu]

I was going to say the same! I got it years ago, it's hard to top a math book with a quote from a certain Al Einstein on the back cover singing its praises! Morris Kline's "Mathematics for the Nonmathematician" takes a similar approach, as I believe other books by the author do. Can also recommend "Code" by Charles Petzold and "The Information" by James Gleick, while not comprehensive they do cover the development of key mathematical insights over time.

[twelvechairs]

I'm sympathetic but there's no clear historic chronology. For instance the ancient egyptians dealt with both algebra and calculus (at least in part) long before Pythagoras. And thats not starting on China and India which had very different chronologies.

[PaulRobinson]

Choose a chronology that makes sense. We can see how Western ideas build, we have less clarity on how the ancient Egyptians or Chinese ideas developed, and therefore it's harder to explain to a learner.

If you're sensitive to that singular world view warping the learner's prospect, you could at each point explain similar ideas from other cultures that pre-date that chronology.

For example, once you've introduced calculus and helped a student understand it, you can then jump back and point out that ancient Egyptians seemed to have a take on it, explain it, ask the student to reason did they get there in the same way as the Western school of ideas did, is there an interesting insight to that way of thinking about the World?

Another ideas is how ideas evolved. We know Newton and Leibniz couldn't have had access to direct Egyptian sources (hieroglyphs were a lost language in their life times), but Greek ideas would have been rolling around in their heads.

[vonneumannstan]

This one was just discussed on HN yesterday with pretty good reviews: https://www.amazon.com/Math-Through-Ages-Teachers-Mathematic...

[markstock]

Here's one that starts with the concept of a straight line and builds all the way to string theory. It's a monumental book, and it still challenges me. Roger Penrose's The Road To Reality.

[biofox]

There are two books which do a fantastic job of this:

Mathematics: From the Birth of Numbers, by Jan Gullberg

and

Mathematics: A Cultural Approach, by Morris Klein

[zwnow]

A book without expecting any knowledge of mathematical notation would be a good start. I've bought 3 math books to get into it and quit all of them within the first chapter.

[-__---____-ZXyw]

In a roundabout way, I wonder does this one fit what you're after:

https://bogart.openmathbooks.org/ctgd/ctgd.html

And more directly, a quick browse showed up a book called:

"Mathematical Notation: A Guide for Engineers and Scientists" which looks like it addresses your issue directly.

[zwnow]

The issue is that I dont want to explicily learn all of the notation but step by step, topic related with usecases in the real world...

[a2800276]

Could you give a concrete example concerning what sort of notation caused you difficulty in the past? Asking because it seems odd to me that you feel you need to learn „all“ the notation to get started.

Starting in elementary school you slowly build up topics, mathematical intuition and notation more or less in unity. E.g. starting with whole numbers, plus and minus signs before multiplication, then fractions and decimal notation. By the end of high school you may have reached integrals and matrices to work with concepts from calculus and linear algebra…

It makes little sense to confront people with notation before the corresponding concepts are being taught. So it feels like you may have a different perspective on notation as a layperson that are no longer obvious to more advanced learners.

[zwnow]

Set theory comes to my mind as an example. Somewhat understood the notation but books increase the pace so much

[BobaFloutist]

Wait let me make sure I understand, you want to skip the notation all together, or you want more support in understanding it?

[zwnow]

I want to learn the notation. Just not everything at once. I need to be able to see real world usecases, otherwise I wont be able to remember and apply the notation. What I meant is learning the notation step by step, topic related.

[codesuki]

I recently read mathematics for the nonmathematician. https://www.goodreads.com/book/show/281821.Mathematics_for_t...

Although the math in the book is relatively basic I enjoyed it tremendously because it gives the historical development for everything and even describes the characters of different mathematicians, etc. The historical context helps so much with understanding.

[djmips]

Devlins book - "Mathematics: The Science of Patterns" was similar for me and you might enjoy it in addition to what you previously read.

Much better than how I was taught in my schooling.

[codesuki]

Thanks for the recommendation, looks promising!

[nkoren]

It's ontogeny recapitulating phylogeny, all the way down.