Book Publication Dilemma
I am looking to publish a book on mathematics next year. It is around 450 pages and the material in it somewhat advanced, but very applicable to hobbyists (eg. a physics student or engineering student may find the material intriguing). Choosing a publisher has been somewhat of a headache for me. I have done a fair amount of research on some of the larger publishers like Springer but am unsure if it is even worth publishing academically. In my research I have often seen that the self publication route, on Amazon, has been worthwhile under the stipulation that the publisher knows how to advertise the book; advertisement should not be an issue; the problem I have seen with Springer and the other academic publishers is that they tend to charge more per book than Amazon where you are allowed to edit the price of your work. I am not so worried about how much I make from it, but rather-so how many people read it; with a larger price point, I feel less people would read the book.
Also -- the time frame. I need the entire publication process to be less than or equal to 8 months. Is academic publishing (on Springer) even possible for the size of my book and time frame? Would it be more worthwhile [have a larger audience] for me to publish academically or through Amazon?
Here is a question similar to this one; it addresses the same topic but does not speak on specific publishers like Springer.