Please let me know if you know the solution to the following problem:
What is the probability of me waking up at 10am?
What additional information should be supplied so as to determine the probability? What do you exactly mean by the probability of this event? Which kind of conditional probability will make sense?
Consider the following comment by Timothy Gowers regarding the model for calculating the probability of an event involving a pair of dice:
Rolling a pair of dice (pp. 6), Mathematics: A very short introduction © Timothy Gowers, 2002 [Source]
I find probability very confusing, for example, this old post.
Recently I completed all of my undergraduate level maths courses, so wanted to sum up my understanding of mathematics in the following dependency diagram:
I imagine this like a wall, where each topic is a brick. You can bake different bricks at different times (i.e. follow your curriculum to learn these topics), but finally, this is how they should be arranged (in my opinion) to get the best possible understanding of mathematics.
As of now, I have an “elementary” knowledge of Set Theory, Algebra, Analysis, Topology, Geometry, Probability Theory, Combinatorics and Arithmetic. Unfortunately, in India, there are no undergraduate level courses in Mathematical Logic and Category Theory.
This post can be seen as a sequel of my “Mathematical Relations” post.