I want to learn quantum mechanics myself and when I open books about them I see weird symbols and different types of mathematical formulas and physics concepts. So what should I first study in mathematics and physics as well as chemistry ,so that I can teach myself some quantum mechanics, although it's difficult I want to try it, because I am interested. I am going to begin 2nd year electromechanical engineer. So I need topics which I did not cover.
I beleive when people say "I want to learn quantum mechanics" what they actually mean is not quantum mechanics but rather quantum physics or more generally modern physics. Please do not get me wrong but learning quantum mechanics is of no use if you do not need to calculate the band structure of a semiconductor or half life of a radiactive isotope or the rate of transition for an atom from an initial state to a final one, etc.
However, learning the concepts of modern/quantum physics is good fun, very useful, mind blowing, inspiring and for some fields of engineering, essential. Accordingly, I think the best way to start is to read the final chapters of a general engineering physics text books where usually the ideas and brief history of quantum physics is introduced with relatively simple math.
There are a few extremely pedagogical documentaries on modern concepts in physics hosted by celebrity professors, broadcasted on British and American TVs. These will help you to see the big picture.
At this point it would be very useful also to read some popular science kind of books on quantum physics.
After all if you think that you are not satisfied that means that you really want to learn quantum mechanics. In this case if there is no hope for you to attent a undergraduate quantum mechanics course as a guest student then find an online course (there are many on youtube) and just ignore the parts that are mathematically to heavy.
For any engineer who did good at engineering math classes there is not much of a surprise in quantum mechanics. Just keep in mind that quantum mechanics courses are usually given in 2nd or 3rd year for physics undergraduates.
The answer depends on two things: 1. What is your current baqckground, and 2. What is your purpose in learning quantum mechanics.
The background in physics that you need is classical mechanics, of course. This is minimum. But something about heat and electricity is also very desirable.
In mathematics you should be familiar with Calculus in one and several variables, linear algebra, some ordinary differential equations, and some partial differential equations and Fourier transform. All this mathematics constitute the usual mathematical curriculum for scientists and engineers in a US university.
The weird symbols that you see in the textbooks are notations used in the theory of linear operators on Hilbert spaces, which is the foremost prerequisite to approach classes in quantum mechanics. In a nutshell, it is the infinite-dimensional version of linear algebra. Notice that infinite dimensions do bring different consequences (almost all that quantum mechanics is about). A little knowledge of simple differential equations would not disturb at all.
The physical background is essentially classical mechanics. You could in principle also not have it, but then you would not understand why quantum mechanics is what it is, due to the fact that most of the times you look at why it is not as classical physics.
I might have a biased opinion, but I believe the chemistry background is irrelevant.
You would probably like to learn the different atomic structures like that of Thompson and Rutherford initially. You really need to study black body radiation as it will give a solid concept for Planck's constant. You need to learn about different experiments like Compton scattering and Young's double slit experiment. As far as mathematics is concerned, you should have a strong understanding of statistical concepts like variance, mean etc. You should be good at calculus and probability theory as well. Linear algebra is a must especially eigenvalues and eigenvectors.