Recommend a book

[Aescott]

Hi

I teach Computing Science to secondary pupils (12-18). I find that I am becoming more and more interested in mathematics, particularly as computing has evolved from the mathematics field.

I was pretty good at maths at school, but that was about 40 years ago now. I’d like to develop my maths knowledge for my own satisfaction - can anyone recommend a decent source? I prefer books to online resources (despite my field).

 

[dwk789]

What sort of level of maths do you consider yourself to be at currently or what level do you want to start from?

 

[Aescott]

I've got Higher maths (sits between GCSE and A-level), but I'd say that, with the passage of time, I'm closer to O-level. But I'm confident that I'd be able to pick up lost knowledge fairly quickly and build from that.
I'm hoping to get towards first year university standard, but like I said, it's purely for personal satisfaction.

 

[All uphill]

I can't help, but I'd like to do the same. I never really grasped calculus; I could do enough to get my A level, but didn't ever really understand.

 

[Profpointy]

One outstanding, albeit far from easy, book, is Road to Reality, by Nobel prize winner, Sir Roger Penrose. whilst the motivation is theoretical physics it is really about maths.'Makes you think quite deeply about stuff you think you know - "what is a fraction really?" for example. I wizzed through a fair few chapters thinking how good and accessible it was then it suddenly got harder. Realised that was actually the point I'd got to at university before I lost my way! It's a heavy book, but genuinely is accessible with effort for a numerate lay person

Couple of more popular books about maths but more descriptive than textbooks

A moderately accessible book for someone with some calcuus and the only textbook I kept from university (first year maths). Complex analysis (ie calculus with complex numbers) is actually rather simpler and a lot more elegant to real number calculus like we did for a
level.

A couple more descriptive but still informative books

And another about "the Hilbert problems" - a programme of work to solve the great unsolved problems of the early 20th century as set out by David Hilbert: some have been solved like the Fermat's Last Theorem (by Andre Wiles) and the Poincare conjecture (By Perlman) but many other still open. Semi technical but about the story of the maths rather than a textbook

Another useful semi-popular / semi-technical but still worthwhile book

And on specific subject here are two on Game Theory: first on is partly a biography of Von Neumann with an introduction to the subject and the other is an accessible intro to the subject proper

And I very much struggled with Tensors at uni, and hence with General Relativity for which they are vital. I found this helpful in revisiting the subject 40 years later, though still some way to go

Whilst I did extremely well at A level I rather lost my way at university very nearly dropping out. If you've done the equalivalent of nearly an A level the Penrose should a good book for you; with the more descriptive or specific ones acording to your interests

 

[Dogtrousers]

A History of Mathematics by Boyer & Merzbach is a very big book and really worth dipping into for history. Would be a bit of a challenge to read it cover-to-cover.
There are lots of popular maths books that are really good. Two that spring to mind are
Things to Make and Do in the Fourth Dimension by Matt Parker. This is probably his best book, he's spread himself a bit thin since.
Infinite Powers: The Story of Calculus - The Language of the Universe by Steven Strogatz

It's such a big sprawling subject. It depends how much you want to put into it. Do you want to actually be able to do the mathematics or just appreciate the concepts? Appreciating the concepts is the space in which the popular maths books tend to live and is a lot less effort (and is what I do these days).

About 40 years ago I hit a mathematical wall at university. But recently I've been discovering that the things that defeated me then may actually be comprehensible. If/when I get around to retiring I'm thinking of maybe doing some OU courses. A whole degree would be beyond my ambitions, but some formal education might be doable.

Lastly, I know you said books not online resources, but I can't resist a recommendation of 3Blue1Brown on YouTube (Grant Sanderson) have some fantastic educational videos. And Numberphile is always interesting. My favourite on Numberphile is Zvezdelina Stankova.

 

[Profpointy]

A History of Mathematics by Boyer & Merzbach is a very big book and really worth dipping into for history. Would be a bit of a challenge to read it cover-to-cover.
There are lots of popular maths books that are really good. Two that spring to mind are
Things to Make and Do in the Fourth Dimension by Matt Parker. This is probably his best book, he's spread himself a bit thin since.
Infinite Powers: The Story of Calculus - The Language of the Universe by Steven Strogatz

It's such a big sprawling subject. It depends how much you want to put into it. Do you want to actually be able to do the mathematics or just appreciate the concepts? Appreciating the concepts is the space in which the popular maths books tend to live and is a lot less effort (and is what I do these days).

About 40 years ago I hit a mathematical wall at university. But recently I've been discovering that the things that defeated me then may actually be comprehensible. If/when I get around to retiring I'm thinking of maybe doing some OU courses. A whole degree would be beyond my ambitions, but some formal education might be doable.

Lastly, I know you said books not online resources, but I can't resist a recommendation of 3Blue1Brown on YouTube (Grant Sanderson) have some fantastic educational videos. And Numberphile is always interesting. My favourite on Numberphile is Zvezdelina Stankova.

Well I've just gone and bought the history of maths one on your recommedation. Yet another addition to my "to be read" pile. Hey it was only a fiver

 

[Dogtrousers]

Well I've just gone and bought the history of maths one on your recommedation. Yet another addition to my "to be read" pile. Hey it was only a fiver

I was really tempted by your description of the Penrose book, but I'm not sure I'd be prepared to put in the effort right now.

 

[Profpointy]

I was really tempted by your description of the Penrose book, but I'm not sure I'd be prepared to put in the effort right now.

As a former mathematician it will be a lot more accessible to you than an A level person. I reckon I'd have done a lot better back then had the book then been available.

I don't know if you remember the Riemann surface thing, where in the proof/explanation you envisage an arbitrary cut so you can "change levels" so to speak. I never quite got this, but Penrose explains it so much better and more elegantly, and even refers to the inelegant "cut" thing in the way was taught it back in the day. Given he's an insanely clever man, he is exceptionally good at explaining to us lesser folk

 

[dicko]

I have recently read Queens Gambit and found it an enjoyable can’t put it down read. Queens Gambit is readily available second hand for around £3. This book is very well written and is a joy to read the story is fascinating.

 

[Dogtrousers]

As a former mathematician it will be a lot more accessible to you than an A level person. I reckon I'd have done a lot better back then had the book then been available.

I don't know if you remember the Riemann surface thing, where in the proof/explanation you envisage an arbitrary cut so you can "change levels" so to speak. I never quite got this, but Penrose explains it so much better and more elegantly, and even refers to the inelegant "cut" thing in the way was taught it back in the day. Given he's an insanely clever man, he is exceptionally good at explaining to us lesser folk

I wasn't doing maths at uni, I was doing physics. So not quite as full on. It was a combination of partial differential equations and eigen-thingies (eigenvalues and eigenvectors) that did for me. Fortunately I had a very good memory in those days so I could churn out stuff that I didn't understand in exams.

 

[Profpointy]

I wasn't doing maths at uni, I was doing physics. So not quite as full on. It was a combination of partial differential equations and eigen-thingies (eigenvalues and eigenvectors) that did for me. Fortunately I had a very good memory in those days so I could churn out stuff that I didn't understand in exams.

Sadly I lacked the maturity to simply learn by rote and regurgitate. Physics is near enough applied maths in any case

 

[Dogtrousers]

Sadly I lacked the maturity to simply learn by rote and regurgitate. Physics is near enough applied maths in any case

Actually I think rote learning is more a sign of immaturity. As a student "maturity" was never something I had.

 

[dwk789]

I've got Higher maths (sits between GCSE and A-level), but I'd say that, with the passage of time, I'm closer to O-level
I'm hoping to get towards first year university standard....

The books I had in mind may be at a lower level than what you had in mind. I studied them just before I started some foundation courses before university started. There's 2 volumes which take you from knowing very little up to sort of A level 'ish'. They called 'Countdown to Mathematics', volume 1 & 2. I lent my original copies and never got them back so bought my present ones second hand. They're handy to remind yourself of the basics sometimes. Now to try and get some pictures into the message...

 

[Aescott]

Thanks all. I’ll go over the suggestions and get some for holiday reading.