# What does it take to find a good math book for self study?

I'm 20 and I never learned math properly in my highschool. I found my interest in math last year and I've been searching for books since then.

I tried Khan academy but I have difficulty paying attention to videos. I prefer reading over video courses.

So how do I search for proper math books for self-study? I've tried GoodReads but unable to get any recommendations over there for school math.

• I see lots of different opinions in the answers below. The books you want will depend a lot on your level, and how you like to approach things. I've got a page full of books I've loved on my blog (pass on by the picture books): mathmamawrites.blogspot.com/p/math-books.html May 4 '20 at 15:40
• Math is a very broad subject. Are there specific levels or topics of math that you are interested in studying? May 4 '20 at 16:53
• @Abdul, are there any particular areas of mathematics you're interested in? Do you prefer any particular style of book? Are you looking for comprehensive books with exercises and solutions or are you looking for exciting story-like books? If the latter, I can recommend authors like Simon Singh, Ian Stewart, Martin Gardner, Steven Strogatz, Paul Nahin, du Sautoy, Mazur... books like Fermat's Last Theorem, The Man Loved Only Numbers, The Man Who Knew Infinity, The Music of the Primes... May 5 '20 at 9:21

Permit me to recommend the answers to this MO question: Are there other nice math books close to the style of Tristan Needham?. The emphasis here is on readable, interesting expositions, a rather different focus from Schaum's Outlines.

Here is one figure from the book, p.135:

You can almost guess the theorem from the figure: The two spheres $$S_1$$ and $$S_2$$ are orthogonal iff the two circles $$C_1$$ and $$C_2$$ are orthogonal.

If you're looking to fill in a deficient high-school education then I might recommend the OpenStax series, which has free, open-resource books for everything from arithmetic through calculus and statistics.

https://openstax.org/subjects/math

Try Schaum's Outlines. They are designed to be review material and drill manuals. Also, the text tends to be simpler writing. This is much more efficient for the adult learner and self studier (than the loquacious doorstops that are designed to appeal to professors and textbook selection committees, rather than to the learner). Check on Amazon and see the reviews. I prefer the older ones, but the newer ones still decent.

Frank Ayers First Year College Math is an excellent review of all high school math, in one text:

https://www.amazon.com/First-College-Mathematics-Frank-Ayres/dp/B009NNXQF6

Of course, you must not "read". You must work problems. But just look at the section and work the drill problems. Remember studying math is a lot like music or sports. You need to drill.

Good luck: You may surprise yourself in what comes back and in what knowledge you firm up.

• paper back is near \$1000 dollars. It must be really really good. May 3 '20 at 20:27
• No, Schaum's Outlines are garbage. OP be aware that "guest" here is a proponent of all-rote-drill and not understanding or explaining anything. I'm guessing that as someone seeking to read math from a book yourself that's the opposite of what you want. May 4 '20 at 5:13
• @DanielR.Collins Schaum's Outlines were designed to be supplements to actual textbooks for courses. With that in mind, couldn't it be at least useful to use it in that sense? As a supplement with additional worked examples instead of a textbook. May 4 '20 at 10:28
• It's not all or nothing. "All rote drill". May 4 '20 at 12:11
• @MarkFantini: The proponents of Schaum generally neglect to say that they're meant as add-on workbook supplements. E.g.: Note the answer here does not include that information. I had a colleague at my college use one as the primary textbook for a course and it was a disaster. May 4 '20 at 12:53

Here is a list of four easy-to-read, enjoyable Math books that can get you started on a journey toward a true quantitative understanding and connection with the world, which it sounds like you might be seeking right now.

1. Math With Bad Drawings, by Ben Orlin

2. The Secrets of Mental Math, by Arthur Benjamin

3. Flatland, by Edwin Abbott

4. Factfulness, by Hans Rosling

These four books, or even just one of them if it is read carefully, can help you develop that basic number sense that a person needs in order to really understand math. When it comes right down to it, basic number sense will get a person really far in math and it's impossible to get very far without that basic number sense. Too many of my students lack it.

After reading a selection of these, you can choose specific topics like geometry, statistics, probability, algebra, or calculus, and delve into each topic you choose more deeply by reading and working through "For Dummies" and "Schaums Outlines" books, which present the material in different, sometimes refreshing ways. They usually offer you practice problems to help you firm up what you've learned, too.

Although you can find some good hints through recommendations, there's nothing like scanning a book shelf (in real life or virtually), taking a peek into a book all by yourself, reading the preface (where the author details whom is the book to), maybe reading the 1st chapter and trying the exercises.

This way you'll find something that's accessible and interesting for you, something that fits into your time constrains and matches your other interests.

Schaum's books were mentioned above. But also take a look at other serious publishers like: McGraw-Hill, Dover (for example, Concepts of Modern Mathematics by Ian Stewart), Cambridge University Press (i.e. How to Think Like a Mathematician by Kevin Houston), or Oxford University Press (How to Study as a Mathematics Major by Lara Alcock).