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by cdavidcash
5736 days ago
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During my first semester in college I took a course that used these notes. It was perhaps the most valuable course I took in college, as I subsequently became a researcher in theoretical computer science (and honestly taught myself a lot of the rest). The value in this type of course is that it introduces very green high school graduates to the type of thinking necessary to reason about proofs. The time required to build up the theory of groups/rings/modules/fields or measure-theoretic probability (is that what you want CS freshman doing?) would be wasted, as those topics are largely beside the point of the course. A sprinkling of conditional probability will at least give them something to remember in their randomized algorithms class. |
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Students, be warned: I know all the material there much deeper than there and have done applications to military and commercial problems and have published peer-reviewed work in applied math, mathematical statistics, and artificial intelligence, and I don't think that book is worth your time or effort -- you need better material.
The quality level is just too low:
A quality problem in the book is a lack of emphasis on proofs which are the main means we have to get new results we know are correct and know that long before some rack of computers has served one million unique users a day.
The math background in Knuth 'The Art of Computer Programming' is done with much higher quality.
Of course, measure theory, say, from Papa Rudin, is the way to do probability, but it is not done that way often enough in the US: Nearly the only people who take Papa Rudin are pure math grad students, and pure math in the US doesn't much like the applications to probability.
Still, it is quite possible to give a MUCH better treatment of probability with just calculus plus, say, a few theorems about calculus, e.g., about improper integrals and interchange of order of integration, usually not covered in undergrad calculus.
Yes, conditioning is a big deal, should be covered, and is touched on in the book. But more is needed in conditioning. Then the classic limit theorems should be covered -- at least the weak law of large numbers and the central limit theorem.
For computer science, it would be super nice to cover Poisson processes and the renewal theorem since operational networks and server farms are awash in these processes.
There are plenty of good books on probability without measure theory although I am not a fan of Feller I because it is too difficult to see the forest for the trees and too easy for an unguided tour to get lost.