Reddit reviews Advanced Engineering Mathematics

This is an applied field. The books above wont help you. In fact they will do the exact opposite. I assume your math education probably stopped at the differential equations. I would recommend as refresher to start building from calculus (avoid the ones in the picture, try something from your past, it would go faster) then go directly to an engineering focused math book like this book If this transition is too sharp you can try other more basic engineering math books. These books are more focused on what works for practicing engineers but you need a strong foundation in Calculus.

For signal processing, I highly recommend a tiny book on Fourier Transformation. Antenna theory is difficult since it varies depends on what level your school covers it at, like device or EM theory or even operational. Anyway start with Calculus and avoid all the books in the picture. Read them for fun but not for study.

You're question is kind of vague, i.e. there are a lot of way's to interpret 'the basics'. Do you mean addition/substraction, etc. or possibly the content of a calculus or linear algebra course? If it's the latter (i.e. the basics of integration, ODE's, PDE's, vectorspaces, ...) I would suggest picking up a mathematics for engineers kind of book ( http://www.amazon.com/Advanced-Engineering-Mathematics-Erwin-Kreyszig/dp/0470458364/ref=sr_1_4?ie=UTF8&qid=1406991103&sr=8-4&keywords=engineering+mathematics or something). Those will have loads of excercises, and mainly go on about intuition instead of proofs (again it could be that by basics you also mean the proofs of basic theorems etc. ...).

Wathever courses that requires this book.

When I took a course on PDE's I watched a bunch of this guys videos.
My class used Strauss's book.
My brother learnt from Kreszig's book, no idea if it's any good though.

Are there any significant differences b/w Advanced Engineering Mathematics 9th and 10th editions?

Well, I appreciate your interest in engineering. You will love your college i am sure. Engineering College are like Hogwarts, there is lots of magic happening on daily basis. You need not to worry about maths. I followed this book in my college years. It is very good book.
Trigonometry is not that important as Calculus. So i would say first complete the Calculus. If you are going to Electrical Engineering, Complex Analysis is must. I hope that helps. Any doubts please ask me.

Ha that's why I hate non-Euclidian geometry. I'm not good at figuring out the curvatures. ;) But maybe you'll find it interesting?

You said you were interested in math. What got you interested? What is it about math that you like? Or what would you like to do if you had a degree in math? You can start there to figure out something you might be interested in. I would suggest a basic calculus book to learn. Really any one would do. If you find that interesting, and want to continue on advanced mathematics, then Advanced Engineering Mathematics by Kreyszig is a fantastic book.

I like algebra and statistics. That's the part of math that I work in; dealing with using statistics to better understand biology. The reason I like algebra is because, honestly, there's only one answer. There's one right answer and it's a puzzle for me to figure out. I like working with numbers. Numbers are always the same and they always follow the same rules. However, I know some people who hate algebra and love geometry. Want to figure out what curvature you should make your satellite in to receive the best signal? Or at what angle you need to point your telescope at? That's geometry. It's more pictorial whereas algebra is more numeric. That's at least a very basic start.

Advanced Engineering Mathematics by Kreyzsig. Fuck, the size of that book fills me with awe.