As someone who did not study math in higher education but now wants to learn more it is quite difficult to find out which math text books have the best content. Would someone please suggest some books and authors of great texts I can then search for?
I would ideally like to build up a bookshelf of great maths texts to go alongside the computing books I already have.
You know, I used to have a good answer, but because of New York City Mayor Bloomberg, I can't give you an answer any more. He destroyed the library with the greatest collection of introductory math books that I've ever seen.
We used to have a library in Manhattan, on a prime piece of real estate opposite the Museum of Modern Art, called the Donnell. It had collections of books for young adults, which in library-speak means high school students and above. They had librarians who understood the subjects, and worked with high school teachers to develop excellent collections of books with good content that would grab you when you took them off the shelf and started to read.
They had a collection of science books and a collection of math books in two big bookcases. Those bookcases contained every great math book I read or wanted to read in high school. Sometimes I'd find a book in the library, and buy a copy in the bookstore.
The Donnell was a beautiful library, in the 1930s style of Rockefeller Center, a fitting match for the Museum of Modern Art, where you could sit and read by huge picture windows. It was a hangout for teenagers from around the city, who used to come there to do their homework and their research. They also had an auditorium where they held poetry readings. It was a New York institution.
After 80 years, the Donnell could have used some repairs and upgrading to its heating and air conditioning system and so forth. Instead of paying for the repairs, Bloomberg decided to tear down the library. He had connections to a real estate company that came up with a plan to build a hotel on the site. They would have a much smaller library down in the basement. But it wouldn't have the same young adult science, math and other collections (which were scattered among other libraries around the City). The real estate company would make a lot of money, the City would get some, and use the money to "improve" the library system and buy more computers. It was controversial, people fought it, but Bloomberg was a billionaire and he won. They fired all the expert librarians, and tore down the Donnell.
Then the real estate market collapsed, so Bloomberg's real estate friends couldn't deliver what they promised.
I've talked to many science librarians in the public library. There is no longer any place in the City where you can find a collection of science and math books like that. They couldn't even give me a bibliography of books like that. It's gone. In fact, they fired most of the expert librarians, and replaced them with computer specialists. They don't really know the subject. You ask them a question and they look in a database.
The best thing I could recommend now is to find a math teacher. It used to be that you could go to a college campus, walk over to the math department, and find somebody who would be happy to give you advice. Now, with all the security, you might not be able to get in the door any more without an ID card. Or you might be able to find a good librarian. If you find a good bibliography, let me know.
(The classics that I remember, BTW, were The World of Mathematics, which was a historical collection of sources, Courant's Introduction to Mathematics, and Polya's How to Find It. There were so many more. If it wasn't for the Copyright Act, you could get them all free on line today.)