There are many influences that helped me with my writing skills. Today, I will only talk about one.
Elementary Logic was a Philosophy class that I took in my second year, because it looked like an interesting elective. I never dreamed that I would leave the class with a life-long memory of an Eureka moment. At the time, I was struggling a little with the concept of an academic essay, especially because our Czech high school education supported a less structured, more creative writing style. I really tried to follow the prescribed essay format and to keep my writing tight, but I could not dig myself out of the B range. It was a Philosophy class, rather than an English class, that changed this. I will describe elementary logic as basic math that uses words, rather than numbers.
Writing is about communicating ideas efficiently, using language as a tool. If the ideas are not complete, it will show in the writing no matter how polished the language is (unless we try to conceal it with language, as Judith pointed out in one of our classes). Not being comfortable with using language can successfully murder the most brilliant idea. The Eureka of my Philosophy class was moving beyond the obvious and seeing language and ideas, premises and conclusion, mathematical concepts and diagrams……as one entity. This is when I learned to acknowledge my ideas and organize them better.