Math book recommendation for a long detached engineering major?

As someone who has done an engineering major in electronics and communication almost a decade back, have used calculus, matrix algebra, some probability for doing well in exams, but, have since then have not used them extensively, what can be good math book recommendations?

The engineering degree never taught proofs or logical deduction as such. Only the applied part was taught. But, now, I want to learn about problem solving, logical proof writing and higher math like linear algebra, probability, statistics, analysis, abstract algebra, etc. Mostly on my own and using online QnA forums. Problem solving and logical deduction is the ultimate skill I am after.

I would like some suggestions on that regard. The AoPS books seemed too easy for me and I am losing interest in them. I may require something a bit harder to keep me hooked. Solution manuals are a bonus to have, if at all possible.