Does it make sense to learn mathematical concepts as you encounter them rather than in a fixed progression? I understand the fundamentals of algrebra, but have very limited knowledge of geometry and trigonometry. I wish to learn calculus at this point.
Is it reasonable to begin learning calculus, and learn these other concepts as I encounter them rather than learning the prerequisites in the standard fixed progression (i.e. Algebra I -> Algebra 2 -> Geometry -> Trigonometry, etc)? How difficult will it be to learn these concepts without the prescribed linear progression?

Here's a description of how Peter Scholze (a Fields medalist) learns math:

At 16, Scholze learned that a decade earlier Andrew Wiles had proved
  the famous 17th-century problem known as Fermat’s Last Theorem, which
  says that the equation $x^n + y^n = z^n$ has no nonzero whole-number
  solutions if $n$ is greater than two. Scholze was eager to study the
  proof, but quickly discovered that despite the problem’s simplicity,
  its solution uses some of the most cutting-edge mathematics around. “I
  understood nothing, but it was really fascinating,” he said.
So Scholze worked backward, figuring out what he needed to learn to
  make sense of the proof. “To this day, that’s to a large extent how I
  learn,” he said. “I never really learned the basic things like linear
  algebra, actually — I only assimilated it through learning some other
  stuff.”

So, I'd say that this backtracking approach to learning math is fine if you enjoy it and it comes naturally to you. But be sure to aim for true, deep understanding of the topics you're interested in rather than rote memorization.
