First post, and as it's probably important to get a better idea about the books, I'm going into a non-math program for my first year university, but teach myself math during my spare time.
These are the books I have, and have found useful. They are mainly published by Dover, which I find has a very rich line when it comes to math:Mathematics: It's Content, Methods, and Meaning
by A.D. Aleksandrov, A.N. Kolmogorov, and M.A. Lavrent'ev. This book is a goldmine, it's actually 3 books bound as one, and covers a ton of topics. The learning curve is quite nice, and just overall I can't recommend it more.Optimal Control and Estimation
by Robert F. Stengel. I have only taken a quick look at this book, having bought it recently. Looks very promising, though, and the review portion at the beginning is helpful. Group Theory and Chemistry
by David M. Bishop. Does what it says on the can, really. I found it a neat approach when teaching myself a little bit about groups, just because you can see it applied to molecules. If you're a visual learner, it's worth a shot. It's quite small, too.Chaos and Fractals: New Frontiers of Science
, by Peitgen, Jurgens, and Saupe. I've seen a lot of books on chaos theory and fractals, some math-heavy, others not, but this one in my opinion dwarves them all. First of all, it's massive, at 837 pages as a large hardback, but somehow it's still light (I think the paper's very thin). And in terms of contents, it's fantastic. It goes into a ton of details, and it's definitely math-heavy, but still explains the relevance with examples to real life of different effects. The illustrations are clear and large, some in colour.Numerical Methods for Scientists and Engineers
, by R.W. Hamming. To be honest I haven't read a lot of this book, because I was working on a project and just needed one specific portion. For what I needed it was worth it, and that's about all I can say.Pearls in Graph Theory: A Comprehensive Introduction
, by Nora Hartsfield and Gerhard Ringel. I'm a bit of a compulsive buyer when it comes to math books... I've read through the introduction, the rest seems very nice. I learned about it on this very thread. Overall this little book has my total respect Penguin Dictionary of Mathematics
, by David Nelson. I got this for a math research project, and it proved very, very useful. It goes in enough depth to briefly explain the topic required, but remains very small and light. I used it a lot when first starting out.