What Are the Best Books for Self-Studying Mathematics?

[hackedagainanda]

Hey, PF! I'm currently self-studying math and sometimes when I find the material too dry or technical it helps to have some outside literature to give me the motivation to continue on.

I have Joy of X, Men of Mathematics, Mathematical Thought from Ancient to Modern Times, Zero, e: The Story of a Number, Trigonometric Delights ,The Mathematical Experience, Princeton Companion to Mathematics, and World of Mathematics.

Do any of you happen to have any other book recommendations? I'm willing to look at Applied Mathematics too, but would prefer context and equations, instead of concepts and words.

 

[epenguin]

Except that you might already be a bit beyond it, I'd recommend as a starting point for self study "Mathematician's Delight" by WW Sawyer. Having hardly seen it again for a good half century I looked it up and it appears from the Amazon reviews that several people had the same experience as me, namely that they had read it half a century ago and it was an enlightenment. I vaguely remember having read on a train the chapter on imaginary and complex numbers which demystified and made them as clear as day, I must have learned more about them since but everything has seemed to flow very easily with that start.

One of your recommendations is on the other hand in my opinion just the opposite, Men of Mathematics is pretty intimidating, unless you read it with a bit of detachment and scepticism, also about the author's academic values. It tells you what a lot of advanced math is about, no way gives your help in getting on top of it, and you go away feeling that you will never be able to. Which is probably true unless you do at least a degree in maths. (Though one of the things I thought when I read it there gosh I will never be able to do that was Sylvester and Caley's theorem that every 5th Degree polynomial can be expressed as the sum of three fifth powers with generalisation to all odd powers.Turns out to be not such a big deal, just an exercise in consistency of linear equations as widely taught. But much of the rest I am never going to get to.)

 

[gmax137]

I liked "Gamma" by Julian Havil so much I read it a few times. Three, so far.

 

[Klystron]

Before learning calculus in a classroom setting I enjoyed the graphic (illustrated) text "Calculus for ..." series featuring f(), the Amazing Function Machine. M. Function guides the reader through the highs and lows (pun intended) of "black box" applications; a how-to of using functions, checking range, codomain and domain, etc., even with the internal workings of f() opaque.

I also enjoyed "Zero" and several books on "e" and "phi", the so-called 'golden ratio'. You may enjoy "The Physics of Superheroes" for a quick fun math-oriented read.

I read Bell's "Men of Mathematics" while completing a Math degree so not only understood his references but was often able to dig deeper into each field Bell describes. Loved it. While several years ago, I remember studying descriptive algebras in depth including books by Boole and even one by Charles Dodgson (AKA Lewis Carroll) "Symbolic Logic". I should read "Men of Mathematics" again for the third time and see what I can remember from uni.

Lucky for math fans, recent solutions to difficult math problems such as the proof of "Fermat's Last Theorem" engendered a wealth of excellent popular books on the subject including modular theory, elliptic curves and Galois theory. What great times we inhabit.

 

[pinball1970]

Hey, PF! I'm currently self-studying math and sometimes when I find the material too dry or technical it helps to have some outside literature to give me the motivation to continue on.

I have Joy of X, Men of Mathematics, Mathematical Thought from Ancient to Modern Times, Zero, e: The Story of a Number, Trigonometric Delights ,The Mathematical Experience, Princeton Companion to Mathematics, and World of Mathematics.

Do any of you happen to have any other book recommendations? I'm willing to look at Applied Mathematics too, but would prefer context and equations, instead of concepts and words.

One two three Infinity is good fun. George Gamow.
I think you can get the free PDF on line

 

[pinball1970]

Before learning calculus in a classroom setting I enjoyed the graphic (illustrated) text "Calculus for ..." series featuring f(), the Amazing Function Machine. Mister Function guides the reader through the highs and lows (pun intended) of "black box" applications; a how-to of using functions, checking range, codomain and domain, etc., even with the internal workings of f() opaque.

I also enjoyed "Zero" and several books on "e" and "phi", the so-called 'golden ratio'. You may enjoy "The Physics of Superheroes" for a quick fun math-oriented read.

I read Bell's "Men of Mathematics" while completing a Math degree so not only understood his references but was often able to dig deeper into each field Bell describes. Loved it. While several years ago, I remember studying descriptive algebras in depth including books by Boole and even one by Charles Dodgson (AKA Lewis Carroll) "Symbolic Logic". I should read "Men of Mathematics" again for the third time and see what I can remember from uni.

Lucky for math fans, recent solutions to difficult math problems such as the proof of "Fermat's Last Theorem" engendered a wealth of excellent popular books on the subject including modular theory, elliptic curves and Galois theory. What great times we inhabit.

The Simon Singh Book on Fermat's last theorem is great too

 

[pinball1970]

Also the Poincare conjecture - Donal O'Shea

The great thing about both books (and Simon Singh's book) is that they do nice little histories on how mathematics developed.

The Simon Singh book flits between the journey of Andrew Wiles and the history of some of the mathematics.

You read a book like and you want to delve into the maths and see where it started and how it developed.

The other "semi" pop maths/physics book is Road to Reality, mentioned many times on this forum.

This formidable tome penned by Roger Penrose completely floored me the first time I read it and only got maybe a third of the way through.

I have to finish it sometime!